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Full text of "Claudii Ptolemaei Opera quae exstant omnia"

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CLAUDId PTOLEMAE(B 

OPERA aUAB EX8TANT OMNIA 

VOLUMEN I. 



8YNTAXI8 MATHEMATICA 



EDIDIT 

J. L. HEIBERG, 

PROPESSOR HAUNIENSIS. 



PARS I 

LIBROS I— VI CONTINENS. 





LIPSIAE 

IN AEDIBUS B. O. TEUBNERL 

MDCCCLXXXXVIII. 



PA 



lilPSIAE: TYPIS B. G. TEUBNEEX 



PRAEFATIO. 



Ad Ptolemaemn edendiim adcessi aBibliopola hone- 

stissimo rogatus, nec inuitus obsecutus sum, cum id 

maxime opus esse uiderem, quod praestare me posse puta- 

bam, ut codicibus denuo collatis aestimatisque fundamen- 

tum quoddam recensionis iaceretur. nam editio princeps 

Sjntaxis (Basileae 1538), ut mos erat illorum temporum, 

uno nec eo bono codice nititur, et Halma, abbas Pari- 

sinus, qui deinde solus Graecam editionem curauit (Parisiis 

1813 sqq.) hodie rarissimam, ut optimum codicem Parisi- 

num adhibuit, ita neque negotii critici neque sermonis 

Graeci satis peritus fuit. mihi igitur incipiendum erat a 

codicibus conquirendis, inspiciendis, conferendis, ubi opus 

esse uisum erat. quem laborem ut per annos 1893 et 

1894 profligare possem, effectum est ope et liberalitate 

summi Ministerii, quod cultui scholisque Daniae 

praeest, maximeque Instituti Carlsbergici, bonarum 

avtium in rebus angustis adminiculi locupletissimi , cuius 

praesidibus hoc loco ex animi sententia maximas ago gratias. 

Inspectis examinatisque codicibus, qui quidem innotuis- 

sent, omnibus, de quibus in Prolegomenis partis\ poste- 

rioris agam, hos elegi ut recensioni et utiles et sufficientes: 

A — codex Parisinus Graecus 2389, membranaceus in 

folio, litteris uncialibus binis columnis scriptus s. IX 

(u. Omont, Inventaire II p. 251), charactere, ut Henrico 

Omont uidetur, Aegyptio. constat foliis 376, quorum 

primum ad extremum librum XIII pertinet et paene 

detritum est, foll. 207—210, 255 — 270, 374 — 375 



IV PRAEFATIO. 

suppleta sunt s. XV (a); post fol. 68 quattuor folia 
desunt (u. p. 200, 7 et p. 209, 21), ut ex quaternionum 
ratione coUigitur. scriptus est codex omnium praestan- 
tissimus duabus manibus eiusdem temporis, quarum una 
(A siue A^) atramento rauo, altera (A^) badio utitur; 
A.\ quae a fol. 175 (p. 487, 17) incipit, sed iam in 
priore parte nonnulla correxit, litteras inclinatiores habet, 
L adscriptum interdum ab A^ semper fere omittit, ad- 
centus uero spiritusque plures adponit quam A^. spe- 
cimen exstat apud Omont Facsimiles des plus anciens 
Manuscrits Grecs en onciale et en minuscule de la Biblio- 
theque Nationale tab. IX. correctiones paucae manibus 
recentiori (A^) et recentissimae (A*, s. XVI) debentur. — 
contuli ipse Parisiis 1893. spiritus adcentusque hic ut 
semper in adparatu neglexi. 

B — codex Uaticanus Graecus 1594, membranaceus in 
folio s. IX, quo nullum pulchriorem elegantioremque 
unquam uidi. constat foliis 284, sed olim plura habuit^ 
nam fol. 284^ legitur: i^ §^§^og avx7\ XT^g (leyaXrig 6vv- 
xd^E(og eiu cpvXlcc xie %ctl Svo eig xriv ccQiriv xov §l§Xlov 
anoXvxcc. post fol. 65 unum folium excidit, cui manus 
recens s XV duo substituit (u. p. 224, 14 et p. 228, 20). 
contin codex: fol. 1 — 8 Prolegomena anonyma adPtole- 
maeum, fol. 9 — 263 Ptolemaei Syntaxin cum scholiis, 
fol. 264— 272^^ Ptolemaeum de apparentiis, fol. 272^— 
276 Pt^lemaeum Tteql kqlxyiqiov^ fol. 27 7^^ tabulam cate- 
goriarum (fol. 277^ uacat), fol. 278—283^ Ptolemaei 
hypotheses, fol. 283^ — 284 notasuarias. inde afolio 271"^ 
extremo duabus columnis uti desinit. — inuestigaui 
ipse et, quoad potui^ contuli Romae 1894. P. 232, 4 
— p. 546, 20 mea causa contulit loannes Tschiedel. 

C — codex Marcianus Graecus 313, membranaceus infolio 
s. X, ab imperito librario pulcherrime scriptus non sine 
compendiis maxime uersus finem. correctus est duabus 
manibus recentioribus (C^ s. XIV — XV) et una recen- 
tissima (C^, fortasse ipsius Halmae; nam fuit Parisiis 
initio huius saeculi). continet: fol. 1 — 30^ Pro^egomena 



PRAEFATIO. V 

ad Ptolemaeum ab initio mutila, fol. 30'' — 370 Ptole- 
maei Syntaxin cum scholiis. ex archetypo codicis B 
descriptus est. — contuli ipse Uenetiis 1893. 

D — codex Uaticanus G-raecus 180, membranaceus in 
quarto s. XII, compluribus manibus eiusdem temporis 
scriptus, saltim alio alibi calamo atramentoque, et dua- 
bus minimum manibus antiquis (D^D^), una recentiore 
(D^) correctus. continet: fol. 1 — 2 notas quasdam astro- 
nomicas a manu recenti, fol. 3 — 280"^ Ptolemaei Syn- 
taxin cum scholiis, fol. 280^^ notas uarias manuum 
recentium, in imo mg. 6(jlov cpvXla o s§do(irjOiovrcc eitxa 
(debuit computari 278). deriuatus est ab exemplari 
optimo et uetustissimo, quod saepe cum codice A con- 
sentiebat contra BC, saepe etiam solum ueram scriptu- 
ram seruabat, sed ab homine rerum perito audacter 
interpolatum erat siue ipsum siue aliquod eius apo- 
graphum; nam imperitis librariis codicis D interpola- 
tiones illae adtribui minime possunt. quorum errores 
incredibiles , ex itacismo et ex compendiis male intel- 
lectis plerumque ortos, saepe omisi, sed numquam nisi 
monito lectore (u. ad p. 4, 3; 12, 20; 27, 2; 29, 23; 
cfr. p. 40, 20). compendiorum usum significaui, quia 
ad aetatem genusque archetypi definienda utflia sunt. — 
contuli ipse Romae 1893 — 94. 

E — codex Marcianus Graecus 310, chartdceus s. XV. 
continet: fol. 1 — 13"^ Prolegomena ad Ptolemaeum, 
fol. 13^ — 151 Ptolemaei Syntaxin cum scholiis (fol. 152 
uacat), fol. 153 — 261 Theonis commentaria in Sjntaxin 
(fol. 262 — 264 uacant), fol. 265 — 286 alia manu Ca- 
basilae commentaria aliaque eius opera, fol. 287 — 288 
Barlaami quaedam. adcedit ad BC. inspexi paucis 
locis Uenetiis 1893. 

F — codex Parisinus Graecus 2390, bombjcinus s. XIII, 
de quo u. Omont Inventaire II p. 251. arte cohaeret 
cum BC. hic illic inspexi Parisiis 1893. 
Horum codicum ope uerba Ptolemaei talia restitui 

posse 'confido, qualia a uiris doctis Alexandriae anno cir- 



VI PRAEFATIO. 

citer 500 legerentur. interpretationibus commentariisque 
Arabum uti non potui, Latinis nolui. interpretationem 
meam siue Latinam siue linguae recentioris in tanta rerum 
difficultate addere ausus non sum; de ea re uideant astro- 
nomi, si intei*pretationem desiderauerint. 

In adparatu ad p. 227, 10 et p. 481, 15 pro Halma 
reponendum ed. Basil. ad p. 522, 49 delendum g'] /.' A^?; 
nam etiam in A est g', ut ab Henrico Omont postea 
certior factus sum. ad p. 539, 7 baec adnotatio addatur: 
7. hvog] scripsi, ivrog A-^BCD. 

In plagulis corrigendis opem peritam diligentemque 
beneuolenter mihi praestitit Henricus Menge amicus. 

Scr. Hauniae mense Maio MDCCCLXXXXVm. 

J. L. Heiberg. 



KAATAIOT nTOAEMAIOT 
MA©HMATIKHS STNTAHEiiS 



Ptolemaeus, ed. Heiberg. 



A'. 

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d'. OTL xal 71 yrj 6(paLQ0£i8rig £6tlv nQog ai'6d"r]6LV cag 

Tcad'' oAa (i£Qr]. 
f'. OTL fi£6rj Tov ovQavov £6tlv rj yrj. 

<5'. OTL 6rjfl£L0V X6y0V £X£L TCQOg TCC OVQ(XVLa 'fj yfj. 10 

^'. OTL ovdh XLvrj6LV TLva fi£TaPaTLxriv %OL£LTaL rj yij. 

r}\ OTL dvO dLa(pOQal TcbV 7tQG)TC0V XLV7]6£(x)V £l6LV £V 

T& ovQava. 
'&''. %£qI t&v xaTa fi£Qog KaTakriil)£cov. 
L . %£q\ Tr\g TtrjhxdTfjTog Tcbv iv rco xvxXg) ^vd^^Lcbv. 15 
La\ KavovLOV t&v iv t& thSkXco ^vd^^Lcov. 



1. A''] v.lav8tov TtToXsfiULOv (iccd"r]ficctLyifig cvvtcc^scog a ngo- 
OLfiLOV A, yiXuvdLOv TttoX8(icciov ficcd^rjficctLyiTig Gvvtd^soog ^l^XLov 
TtQ&tov B, om. CD. 2 — p. 4, 5. om. A. 2. mdf] corr. ex 
tccd' D^. TCQcotcp — 3. Gvvtd^EOig'] a D. 4. a'] om. D, et 
sic deinceps. 5. td^scog'] D, Gvvtd^eoag BC. 6. ctpaLQOELSmg 6 
ovQccvog^ 6cpccLQ0SL8r]g 6 ovQavbg xat ccpaLQOELSoag cpsQStccL D. 

7. v.ccL — 8. (iSQT]] 6cpaLQ0SLSr}g yial rj yr) D. 10. sxsl'] post 
ras. 2 litt. B, sxsl r] yfi T). tcc — y?)] tbv ovQavov D. 11. 
TtoLSLtaL (ista^atLv.riv D, noLsitaL corr. ex TtOLfjtaL m. 1. 12. 
st6Lv] om. D. 15. tfig 7tr]XLy.6tr]tog] om. D. rc5] om. D. 

16. ta'] ca B, et similiter deinceps. yiavovLOv — svd^sL&v] 
xal syid^seLg v.avovLV.r] D. -AavovLOv — P- 4, 1. nsQL] in ras. 
m. 1 B. 



4 KAATAIOT nTOAEMAIOT 

ip\ JtSQl tfjg ft£Ta|v t&v tQOTtiKGiv JceQLqjSQeiag. 
ly'. TtQoXa^pavofisva elg tag 6(paLQi7tag d£L%6Lg. 

ld\ TCBqI tCbV ^Sta^i) tOV L^TI^SQLVOV XVxXoV 7tSQL(pSQSLCbV. 

Ls\ xavovLOV Xo^G)0£(og. 
5 fcs'. jtSQl t&v S7t hQ^fig rij^ 6(paLQag ava^pOQcbv. 

a. Uqoolillov. 
ndvv xaXcbg ot yvrjffLCjg cpLXo6ocp7J6avtsg^ d) 2Jvqs^ 
doKov0L fiOL xsxcoQLKSvaL To d-scoQrjtLxbv trjg (pLXo6o(pLag 
aito tov jtQaxtLXOv. xal yccQ sl 6v^p£^i^X£ xa\ rw 

10 TtQaxtLxa 7tQ6t£QOv avtov tovtov d^£C3QrjtLXip tvyxdv£LV^ 
ovd£v ^ttov dv tLg £vqol ^^ydXrjv oi)6av iv avtolg 
dLa(pOQdv^ ov ^idvov dLa tb t&v ii£v rjd^Lxcbv dQ£tcbv 
ivCag vndQ^aL dvva^d^aL jtoXXotg xal ^optg ^ad^rj^^cog^ 
tfjg d£ tG)V oXcov d^^cjQLag ddvvatov slvai tvxstv dv£v 

15 dLdaaxaXCag^ dXXd xal ta f^v TtX^Cetrjv d^piX^Lav £X£l 
[i£v ix trjg iv avtolg totg 7tQdy^a6L 6vv£xovg iv£Q- 
y^Cag^ iv^dd£ d' ix trjg iv totg d^^coQrj^a^L TtQoxoTtfjg 
TCaQayCyv^^d-aL. £v^£v riyrj^d^^d^a 7tQo6r]X£LV iavtotg 



1. TtSQKpsQeCag] corr. ex TtSQLcpSQLug D^. 2. Ssil,SLg] corr. 
ex dsL^ig D^. 3. tov] post ras. 3 litt. D. y.v-nXov] corr. ex 
xov D'. TtsQLcpSQSLoav] corr, ex nsQicpSQL&v D^; similes errores, 
quibus scatet D, posthac non notabo. 4. "navovLov Xo^oiGscog] 
om. D. 5. ccvccq)OQ&v] rov Slcc (isgcov ■nal tov lorifiSQLvov 

GvvvatpoQcbv D {a supra scr. D^). Seq. oW oxl d-vrjrbg scpvv 
y-al icpdfiSQog' aXl' otav aGZQoav \ Ixvsvco xara vovv a[icpLdQ6[iovg 
sXLtiag, I ovv,st' snLipavco yaLTjg 7to6LV, ScXXcc naQ' avr&L | ^rjvl 
dLotQocpsog 7iL(i7tXa[iaL aii§Q06L7}g CD (idem in mg. inf. B, sed 
dLotQScpsog). 6. a'] om. A, mg. B, y,XavdLOv ntoXsfiaiov (lad^rj- 
liatLTifig 6vvtd^scog C, ntoXs^iaiov Gvvtai^ig D. nQOOL(iLov] om. A. 
8. v.sxcoQ't]v,svaL D, sed corr. 9. xat (alt.)] del. D. 10. 
TCQa-AtLv.m] corr. ex nQayLtLVOV C^. avtov tovtov] mut. in 

avto tovto C*. 14. aSvvatov] corr. ex dvvatov A^ 16. 

nQocy(ia6Lv D. 18. naQayLVS^d^ai, yL- in ras., D^. 



MA0HMATIKHS STNTASESiS A'. 5 

tccq ^ev TCQd^eig iv tatg ax)TG>v tcbv (pavta6icbv ini- 
^olatg Qvd^^t^eLV^ oTtcjg ^rjd' iv totg tv%ov6iv im- 
Xavd^av^^ed-a tfjg TtQog tijv xaXijv xal evtaxtov xatd- 
6ta6Lv i7tc6xerpe(og^ tfj de 6%oXfi xaQit^e^^-ai to %ket6tov 
elg tijv tcbv d^ecjQrj^dtcov TCokXcbv xal xaXcbv ovtov 5 
didaaxaUav^ i^aiQetcog 8e elg tijv t&v IdCcag ;caAov- 
^evcov ^ad^rj^atix&v. xal yaQ av xal tb d^ecoQr^tLxbv 
6 ^AQL6totekrig jtdvv iin^ekcbg eig tQia td TtQcbta yevrj 
dLULQet rd te (pv6Lxbv xal tb ^ad^rj^atLxbv xal ro d^eo- 
koyLKdv. Ttdvtcov ydQ t&v '6vtcov tijv vnaQ^LV ix^vtcov 10 
ex te vXrjg xal eCdovg xal xLV7]6ecog xcoQlg ^ev exd6tov 
tovtcov xata tb {jTtoxei^evov d^ecoQet^d^ac ^ij dvvaiievov^ 
voet^d^aL de fiovov^ xal dvev tcbv koLJt&v^ tb ^ev tfjg 
tcbv oXcov TtQcotrjg XLV7]6eG)g itQcbtov attLOv^ et tLg xatd 
t6 dnXofJv ixXa^pdvoL^ d-ebv ddQatov xal dxCvrjtov dv 15 
riy7]6aLto xal tb tovtov ^rjtrjtLxbv eldog d^eoXoyLxbv 
dvcj jtov jtSQl td ^etecoQotata tov x66^ov tfjg tOLavtrjg 
iveQyeiag vorjd^eC^rjg dv ^6vov xa\ xad-djta^ xex(0QL6^e- 
vrjg tcbv ai^d^rjtav ov6Lcbv' ro de tfjg vXLxfjg xal aiel 
XLVOVfievrjg %OL6tritog dLeQevvrjtLxbv eldog iteQi te tb 20 
Xevxbv xal ro d^eQ^bv xal ro yXvxi) xal ro ditaXbv 
xal td toiavta xatayLyv6^evov cpv6Lxbv dv xaXe6eLe 
tfig tOLavtrjg ov6iag iv totg cpd^aQtotg cag inl tb TtoXv 
xal vTtoxdtco tfjg ^eXrjVLaxfjg 6(paiQag dva^tQecpo^evrjg' 
ro de tfjg xatd td eldrj xal tdg ^ieta^atLxdg XLVij^eLg 25 

2. inLXavd^avmfjiEd^a] inLXcclQ^avm^sd^cc A, v add. A*. 3. 
T^c] corr. ex zr} D^ 4, An ttJs Se axoXfis? cfr. BoU, Studien 
iiber Cl. Ptolemaus p. 68 not. 3. 8. 'AQL6toriXT]g] Metaph. E 1 ; 
cfr. Boll p. 71. 9. Tf] om. D. fia&rirL-Kov D, corr. D*. 

15. iv.Xafi^dvsL D, corr. D*. ccnLvqTOV xal aoQatov D. 17. 
fisrtcaQmtata C, sed corr. 19. alsL'] 6csl CD. 20. ts] om, D, 

22. v,atayLv6^svov C et corr. ex natayLvo^iivaiv D. 23. Ante 
tfig del. s' D. 24. xai] om. D. 



6 KAATAIOT nTOAEMAIOT 

jtoiotrjtog i^q)ccvL6tLxbv sidog 6')(ri^cct6g te xal 7Co66- 
trjtog xal TtrjXtx^trjtog ett ts toTtov xal xq6vov xal 
t&v ofiOLCOV t^rjtrjtLxbv v7tdQ%ov hg fiad-rj^atcxbv av 
dq)0Qi6Ei8 trjg toiavtrjg ov6vag ^sta^v cSdTtSQ SKsCvav 
5 tcav dvo TtLTttovdrjg ov ^6vov ta xal Sl at6^ri6sGig 
xal x^Qf-S aL6%"Yi6sG)g dvva^d^aL vost^d^aL^ dXXd xal tm 
7ta6iv djtX&g tolg ov6l ^v^^sfirjxsvaL Tcal d^vrjtotg xal 
dd^avdtOLg totg ^sv alsl ^sta^dlXov6L xatd tb stdog 
tb dx(OQL6tov 6v^^sta^aXlo^svrjv ^ totg ds dLdCoLg xal 

10 trlg ald^SQchdovg q)v6scag 6vvtrjQ0v6av dnCvrjtov tb tov 
sldovg d^stdpXrjtov. s^ cjv dLavorjd^svtsg^ otL td ^sv 
dkXa dvo ysvrj tov d^scoQrjtLKOv ^aXlov dv tLg SLxa6Cav 
ri xatdXrjil^Lv s7tL6trj^ovLxr}v stitOL^ tb ^sv d^soXoyLxbv 
dLa tb TtavtsXcbg dq)avsg ai)tov xal dvsjtCXrjTttov ^ tb 

15 ds (pv6Lxbv dLa tb f^g vXrjg d6tatov xal dSrjXov^ cjg 
dLa tovto firjdsTtots dv sX7tC6aL TtSQL avtcbv ofiovofj^aL 
tovg (pLko6o(povvtag^ fi6vov ds tb fiad^rjfiatLX^v^ sl' tLg 
s^sta6tLXG)g avtip 7tQo6sQXOLto^ ^s^aCav xal dfistditL^tov 
totg fistaxsLQL^OfisvoLg trjv sl'drj6LV TtaQd^xoL cjg dv 

20 trjg djtodsC^scog Sl' dvafKpL^^rjtrjtav od&v yLyvofisvrjg^ 
dQLd^firjtLxrjg ts xal yscofistQCag^ TtQorjx^rjfisv STtLfisXrj- 
d^rjvaL fidXL6ta Ttd^rjg fisv xatd dvvafiLV trjg tOLavtrjg 
^•scoQCag^ s^aLQStcog ds tfjg TtSQL td d^sta xal ovQdvLa 
xatavoovfiEvrjg^ cog fi6vrjg tavtrjg jtSQl tijv tcbv aCsl 

25 xal co6avtcog sx6vtcov S7tC6xsil)Lv dva6tQS(pofisvrjg dLa 

3. iiuQ-TiiLaxi-Aov B. 5. 8i] Sid BC. 8. totg] supra 

scr. D^. ccCaL'] A, a£L BCD. fi8ta^dXXov6l\ A. t6 et^og] 
mg. add. D^ 9. ds] S' D. 13. stnoL] corr. ex stnsv D. 

14. 7tavT£l&g] -(b- in ras. B. v.c£l] xal Sl' C. av£7tLlr]7tTov] 
cc- in ras. 2 litt. C, post -75- ras. 2 litt. D. 16. fir]ds7t0T' D. 

18. ccpLStdTtLatov] mut. in diistdTtsLatov D^. 19. Mg. yg. 

avvsidsLGiv D*. 20. yLvofisvrig CD. 22. (idlLata] supra 

scr, D^. 24. atsC] A, dsL BCD. aisl yial wa-] in ras. D^ 



MA0HMATIKHS STNTASESiS A'. 7 

rovt6 t£ dvvatfjg ov6rjg xal avtfig TteQt ^sv triv 
oiKeCav ocatdXrjipLV ovts adrjXov ovts ataKtov ov6av 
alsl xal G)6avt(x>g sxsiv^ ojzsq s6tlv tdiov S7CL6tri^r}g^ 
^Qog ds tag aXXag ov% -^ttov «vtwv sxslvcov 6vvsQystv. 
To ts yaQ d-soXoycxbv sidog avtrj ybdkLGt av jtQooSo- 5 
7C0i,i]6sLS ^ovrj ys dvvafisvi^ xakcog 7iata6to%dis6^aL trjg 
dxLvrjtov xal x(0QL6tYig svsQysCag aTcb trjg syyvtrjtog 
tcjv tcsqI tdg aC^d^rjtdg ^sv xal XLV0v6ag ts xal xlvov- 
lisvag^ aLdCovg ds xal djcad^stg ov6Cag ^v^^s^rjxotcov 
tcsqC ts tdg (pOQag xal tdg td^SLg tcav XLvrJ6sc3V' TCQog 10 
ts tb (pv6Lxbv ov tb tv%bv dv 6v^pdlXoLto' 6xsdbv 
yaQ tb xad^oXov rijg vkLxfjg ov^Cag IdLOV dnb tfjg xatd 
tfiv ^sta^atLxrjv xCvr]6LV CdLOtQOTcCag xatatpaCvstaLj 
cjg ro ^sv ipd-aQtbv avtb xal tb d<pd-aQtov dicb tf\g 
svd^sCag xal tfjg syxvxXCov^ ro ds ^aQv xal ro xovcpov 15 
ri ro TCad^rjtLxbv xal ro TCOLrjtLxbv dicb tfjg stcI ro fis6ov 
xal tfig dnb tov ^s6ov. TCQog ys ^ijv tfjv xatd tdg 
TCQd^SLg xal ro fjd^og xaXoxaya^Cav jcdvtcjv dv avtrj 
^dXL6ta dLOQatLXOvg xata6xsvd6SLSv dicb tfjg tcsqI td 
d^sta d^scoQOVfisvrjg ofiOLOtrjtog xal svta^Cag xal 6vfi- 20 
listQCag xal dtvcpCag SQa6tdg [isv jC0L0v6a to^bg %aQa- 
xoXovd-ovvtag rov d^sCov tovtov xdXXovg^ svs^Ct<ov6a 
8s xal &67CSQ <pv6Lov6a TCQbg tfjv b^oCav tfjg ipvxfjg 
xatd6ta6LV. 

tovtov dfj xal avtol tbv SQCsta tfjg tcbv alsl xal 25 
c}6avtcog sxovtcav d^scnQCag xatd ro 6vvsxsg av^scv 

1. Tf] corr. ex de D. t»jv] mut. in toLv C. 3. aUi] AB, 

dtC CD. Post y.uL del. a)(y| D. 7. ^tco^KJT^g] corr. ex ^oo^l? 

ti)g C^ 8. Tf] supra ras. 3 litt. D^. 11. t6 cpvGLyiov] corr. 

ex tmv (pvGL-amv C. 14. avto] -6 e corr. D^ 15. sv&sLccg] 

in sv&sCag D. 16. ocTto] corrigere uoluit C*. 18. rjd^og] r]- 

in ras. D^ 19. nsQL td] bis C. 25. dsC D. 26. ixovtmv] 
pr. V ins. A*. 



8 KAATAIOT nTOAEMAIOT 

TtSLQafied^a fiavd^dvovtsg ^ev ra Tjdrj xateLXrj^i^dva r&v 
roiovtcov ^ad^Tj^ccrcov vjtb r&v yvtj^Lcog Tcal ^rirrjrLxag 
avrolg TtQo^eXd^ovrcov ^ TCQoaLQOv^evoL de xal avrol 
ro6avrrjv TtQo^d^Tjxrjv 6vveL6eveyxeLV ^ o6rjv 6xedov 6 
5 7CQo6yeyovG)g a% exeivcav XQOVog {lexQL rov xad'' rjfiag 
dvvaLr av 7teQL7tOLf}6aL. aal o6a ye d^ vofiL^o^ev eTtl 
rov jtaQOvrog elg (pcbg rj^tv eXrjXvd^evac^ 7teLQa66^ed-a 
dia ^Qa%eG)v (bg evL iidXL6ra^ xal Sg av ol fjdrj xal 
ejtl 7to6bv 7tQOxeKoq)6reg dvvaLvro naQaxokovd^elv^ vTto- 

10 fivi]iiarL6a6d-aL rov fiev rekeiov rf^g TtQayfiareiag evexev 
ccTtavra rd xQ7j6Lfia TtQbg rrjv r&v ovQavLcov d^ecsQLav 
xard ri^v olxeCav rd^Lv exrtd^efievoL^ dLa de rb fifj fia- 
XQOV TtoLetv rbv X6yov rd fihv vjtb rwv TtaXaLCOv rjXQt- 
^cofieva dieQxbfievoL fi6vov^ rd de rj firjd' oXcog xara- 

16 Xrjipd^evra ij iirj wg evfjv evxQ^i^^rcog^ ravra de xard 
dvvafiLv e7te^eQya^6fievoL. 

/3'. neQL rfjg rd^ecjg r&v d^eoQrjfidrcjv. 

Tfjg d'^ TtQOxeLfJLSvrjg rjfitv 6vvrd^ecog TtQorjyettaL fiev 
t6 rfiv xaO-dAov 6xs6lv idetv bXrjg rfjg yfjg TtQbg oXov 
20 rbv ovQav6v^ r&v de xard fiSQog rjdrj xal iips^fjg JtQco- 
rov (JLSV dv strj rb dLS^sXd^stv rbv k6yov rbv TtSQL rfjg 
d^s^scog Toi) Xo^ov xvxlov xal r&v r^itcov rfjg xad" 
rjfiag oixovfisvi^g sn rs rfjg %Qbg dXXrilovg avrrai/ 
xa%^ sxa6rov bQi^ovra TtaQd rdg iyxki6SLg yLvofisvrjg 



1. yiaT£LXr}ii\(i(i£vcc C. 2. (iad'r}(idtcov'] -(id- supra scr. D^. 

3. TtQosX&ovToav C. 5. TtQoaysyovmg'] BD, TCQoyeyovmg AC. 

8. ^QaxBcav'] corr. ex Ta%E(ov D^ 9. Mg. nQoayiBv,v(p6TBg C^. 

11. ra] ins. D^ 14, ri\ supra scr. D^ oXog C. 15. di] 
del. C^ 17. fi'] om. CD, xftp. ^ Dl 18. 8r[\ de C. 19. 
t6] seq. ras. 1 litt. D. 23. hi ts] sItcc D. 24. iyaXictig] 
-yiXi- in ras. D. 



MA0HMATIKHS STNTASESiS A'. 9 

iv tatg td^£6iv diacpoQag' TCQoXaiiPavofisvrj yaQ rj 
tovtcov dscoQia tiiv t&v Xoltccov iTtC^xeilfLv svodcjti- 
Qav TtaQSxsL' dsvtSQOv ds jcsqI trjg 'f^lLaxTlg xcv7]6£cog 
xal tfjg 0£XrjVLaKfjg xal tcjv tavtaig iTtL^v^^acvovtcov 
du^sXd^^tv xcsQlg yccQ trjg tovtov TtQOKatalrjxl^^ajg 5 
ovdh ra 7t£Ql tovg a6tiQag ol6v t£ av yivoito di,€^o- 
dix&g d^scoQfj^ai,. tsk^vtaCov d' ovtog cjg TtQog avtriv 

t^V £(podoV tOV 7t£Ql tCOV a6tiQG)V loyOV 7tQ0td660Vt0 

^hv av £LK6tcog xal ivtavd-a td jt£Ql tfjg tcbv djtlav&v 
xaXov^ivov 6(paCQag^ moLto de td 7t£Ql tcbv 7civt£ 10 
Ttkavritcov 7tQo6ayoQ£vo^ivcov, £xa6ta d£ tovtcov 
Tt^LQa^^^i^^^a d£LXVv£LV dQxatg ^lv xal a67t£Q d^^^i^XCoLg 
£Cg tiiv dv£VQ£6Lv %QGiiL£V0L totg ivaQyi6L (paLvo^ivoLg 
xal tatg ddL6tdxtOLg tcov t£ 7takaLG)v xal tcbv xa^^ 
rjfiag trjQr]6£C0Vy tdg d' iq)£^fjg tcbv xataXi]if£(Ov i(paQfi6- 15 
t,ovt£g dLa t&v iv tatg yQa^i^Lxatg i(p6doLg d7tod£C^£C3v, 
tb ^£v ovv xad-6Xov toLOvtov dv £tr} 7tQola^£tv^ 
otL t€ 6(paLQ0£Ldrig i6tLV 6 ovQavbg xal (piQ£taL 6(paL- 
QO^Ldag^ xal otL rj yfj t(p fi£v 6%ri^atL xal avtf] 6(paL- 
Q0£Ld7]g i6tLV 7tQbg al^d^ri^LV ag xad"' oXa ^iQr] la^^a- 20 
vo^ivr]^ tfi dl ^i6£L ^i6r] tov jcavtbg ovQavoi) x£ttaL 
xivtQCp 7taQa7tXr]6Ccog^ ta d£ ^^yid-^L xal r» d7to6tr]- 
fiatL 6r]^£Cov k6yov £X£l TCQog tf]v tcov d^cXav&v 
d6tiQCov 6(patQav avxf] iir]d£^Cav iiL£ta^atLxf]v xCvr]6LV 



1. xd^sGi BD. 2. BvoScoTiqav'] svo- e corr. D. 3. TtiQi] 
rb TCFQL A. TiiVT^Gscog yiul Tfjg CBXrjVLayiTis] 'nccl caljiVLccnfig v,Lvri- 
6S(og D. 6. T£] t' D. 7. d'] 8i D. 8. nQotdGOLto D. 

12. TCELQCCGOilsd-Cc] COTT. Gx nsLQCiGcoiLsQ^a A}. 13. svaQysGLV D, 
y e corr. Deinde add. -AaC comp. D^. 14. Ante ts del. 

nsv C^. 15. tJiQLGscov C, corr. Cf d'] 8s D. 19. tw] 

corr. ex t6 C*. 20. sGtL B. XaiL§avoiisvr]L C. 24. avrrj] 
avtr] BC. 



10 KAATAIOT nTOAEMAIOT 

jcoiov^evtj. TtSQl rovtcjv d' ixd6tov trig vTto^vrjesc^s 
€V€X£v ^Qaxsa dLsXsv^ofisd^a. 

y' . "Oti ^(paLQOSLd&g 6 ovQavbg q)SQStai. 

Tag iisv ovv TtQmtag svvoCag TtsQl tovtcav aTio 
6 toiavtYjg tivog TtaQatrjQTj^scog totg Ttalaioig svXoyov 
TtaQaysyovsvaL' scjqcjv yaQ rdv ts 7]Xlov Ttal ti^ 
6sXrivriv xal toi>g dlXovg a0tSQag (psQo^svovg aito 
avatoXcbv STtl dv6^ag alsl oiata 7taQaXX7]Xc3v xvxXcjv 
aXlTJXoig xal ccQXO^svovg fisv avacpsQS^d^at xdtcod^sv 

10 ccTtb tov taTtSLVov xal g)6%sq ii, ai)trjg tfig yijg^ ^stsca- 
QL^o^svovg ds xatd ^LXQbv slg vi^og^ sitSLta TtdkLv 
xatd tb dvdkoyov JtSQLSQ^o^svovg ts xal sv tajtSLvco- 
6SL yLyvo^svovg^ scjg dv tsXsov G)67tsQ ifi7ts66vtsg slg 
trjv yrjv dtpavL^d^cb^LV^ sit av TtdXiv xqovov tLvd 

15 ^SLvavtag sv t(p d<pavL6fim cD67tSQ ajr' dXXrjg dQxrlg 
dvatsXXovtdg ts xal dvvovtag, tovg 8s ;ij()dvovg tov- 
tovg xal stL tovg tcov dvatoXcov xa\ dv6scov tOTtovg 
tstay^svcog ts xal bfiOLcog cog S7tL7tav dvtaTtodtdo- 
fisvovg. 

20 fidXL6ta ds avtovg rjysv slg tijv ^cpaLQLxijv svvoLav 
r] tcbv atSL (pavsQcbv d6tSQCov 7tSQL6rQ0(pri xvxXotSQrjg 
d^scoQovfisvrj xal 7tSQl xsvtQov sv xal tb avtb 7tSQL- 
TtoXovfisvrj' 7t6Xog yaQ dvayxaCcog sxstvo tb 6rjfiSL0v 

1. d'] 8s D. 2. TtQoSLsXsvGOfisd^a D. 3. y'] B, om. 

ACD, xfqp. y D^ 6(paLQ08t,dmg 6 ovQuvog] GcpcciQOSLdrjg 6 

ovQavbg v,aL ccpaLQOSLS&g D. 7. cpsQOfisvovg] q)aLVO[isvovg BC, 
corr. C^. 8. asL D. 13. yLvofisvovg D. scog] tog BC, 

corr. C^ atansQ] manSQ tcccXlv D. 14. iidXLv] n- e corr. A, 
om. D. 15. iisLvavtsg D, corr. D^. maTtSQ] ndXLv waitsQ D. 

16. di] 8- in ras. A. 17. dvascov] dvafi&v D, supra (i ras. 

18. cbg] om. D, xat ag supra scr. D^. 20. 8s] d' D. 21. 
&SL CD. dazQcav D. 



MA0HMATIKH2 STNTASESiS A'. 11 

iyCvEXO tfjg ovQavcov 6(paLQag xcbv ^hv ^akkov avxfp 
TtXrj^La^ovxov xaxa ^cxQOxeQCov xvxXcov iXL66o^6V(ov^ 
x&v S' dTtcoxsQG} TtQog xriv xrjg dLa0xd6£G)g dvakoyCav 
fisC^ovag xvxXovg sv xfj TtSQLyQacpT] Ttoiovvxov^ scjg dv 
rj d7t66xa6cg xal iisxql xav dq^avi^o^svcav (pd-d6ri^ xal 5 
xovxov ds xd fisv syyvg xmv alsl (pavsQ&v d^XQcov 
scjQcov STt oXCyov xqovov sv X(p d(pavi6[io ^svovxa^ 
xd d' djtcod^sv dvakoycog TtdXiv sitl itXsCova' cag xrjv 
lisv dQxrjv dtd ^ova xd xotavxa trjv TtQosiQrnisvriv 
svvoiav avxovg ka^slv^ i]drj ds xaxd trjv icps^fjg ^scj- 10 
Qiav xal xd lotTtd xovxoig dxolov^^a xaxavo7}6at 
Ttdvxcov djtXcbg xcbv (patvo^svcov xatg sxsQodo^otg sv- 
voCaig dvxi^aQxvQOvvxcov. 

(psQS ydQ^ SL xig vTtod^oixo xijv xcov d^xsQcov (poQav 
iit svd^sCag yivo^svrjv S7t' ccTtSLQOv cpSQS^d-ai^ xad^djtSQ 15 
XL6lv sdo^sv^ xCg dv STtLVorjd^sCrj xQOTtog^ xad^' ov ditb 
tr]g avxrjg dQxfjg sxa6xa xad'' ri^SQav (psQo^sva d-sco- 
QTj&ij^sxaL; Ttcbg yaQ dvaxd^TtxsLV sdvvaxo xd d6xQa 
iit ditSLQOv bQ^cj^sva; 7] jtcbg dvaxdfiJtxovxa ovx icpaC- 
vsxo'^ rj Ttog ovxl xax' olCyov ^SLOV^svav xcbv fisys- 20 
d-cbv ri(pavCt,sxo^ xovvavxCov ds ^sC^ova ^sv bQco^sva 
TtQog avxotg xotg d(pavL6^otg^ xaxd ^lxqov ds i7tL7tQ06- 
^ov^sva xal cj6jtSQ dTtoxs^vo^sva xfj xfjg yfjg iitL- 
cpavsCcc', dkkd ^fiv xal xb dvditxs^d^aC xs avxd ix xfjg 
yfjg xal Ttdltv sig xavxrjv dTto^^svvv^d-aL x&v dXoycj- 25 
xdxcov dv (pavsCrj Ttavxskcbg. Xva yaQ XLg 6vyxcoQiJ6rj 



3. d'] Se D. ccncor^QO}] ccTicotiqoii AC, anorSQaL B, 

cc7ta)X8Qco B^ 6. ocsi CD. 8. S'] mut. in 8b D^ anoi^sv D\ 

14. cc6T£QCi}v] corr. ex aaTQoov D*. 16. sdo^s D. 18. sdvvaro] 

i- in ras. A, Tjdvvccto D. 22. xara] corr. ex %a A*. 24. ocXlcc 

lir]v xat] in ras. D. 25. xavtr]v'] avf^v D. aloyordvoDV B. 



12 KAATAIOr nXOAEMAIOT 

ri)v ro0avtYiv td^iv sv ts totg iisyi^E6iv xal tatg 
no66tr]0LV avt&v^ etu de dLa6t7J^a6LV xal tonoig xal 
XQOvoig ovtcog sixfj xal cog itv%Bv anotskste^ai^ koI 
tods ^sv Jtav t6 ^SQog tf}g yijg avaittixriv s%slv cpveiv^ 
5 t6ds ds 6ps6tLX7]v^ iiaXkov 8s tb avtb totg ^sv avdit^ 
T£M/, totg 8s 6psvvvvaL^ xal t&v a^tQcov td avr«; 
totg fisv ildi] dvrnnisva tJ s6^s6^sva tvy^dvsLV^ totg 
ds firjdsTtci)^ sl' tLg^ ^Wh ^«vi^o^ ndvta 6vyxcaQ7]6SLEV 
ovtog ovta yslota^ tC dv TtSQL t&v aisl (pavsQ&v 

10 sxoLusv SLTtstv tcbv fi^^ts dvatsXk6vtG)v iirits dvv6vtCDv; 
ij dia TtoCav altCav ovjji td ^sv dva7tt6^sva xal 6^ev- 
vv^sva TtavtaxT] xal dvatikXsL Tcal dvvsL^ td ds ^ij 
Ttd^xovta tovto Ttavtaxri s6tLV aisl vnsQ yijg; ov yaQ 
StI ys td avta totg \Csv aisl dvafpd^ri^staL kol 6^s6d"ifi- 

15 6staL^ totg 8s ovdsv ovddnotE tovtcsv 7tsC6staL^ jtavtd- 
7ta6LV svaQyovg ovtog tov tovg avtovg d^tsQag Tta^d 
liEv tL6Lv dvatElksLV ts xat dvvsLv^ TtaQ dXkoLg ds 

fLrjdstEQOV. 

6vvEk6vtL d' SLTtstv^ xdv 6jtot6v tLg dkko 6xrj^a 
20 tijg t&v ovQavCcav (poQccg vTt^d^tjtaL Ttk^^v roi) 6(paL- 
QOSLdovg^ dvC6ovg dvdyxrj yCyvs^d^aL tdg d%b trjg yfjg 
ijtl td ^iiQrj tav ^stSG^Qcov d7to6td6SLg^ OTtov dv avtri 
xal cog dv vTtoxirjtaL^ co6ts ofpsCksLv xal td ts ^syid^rj 
xal td TtQbg dkkrjkovg dta^trj^ata tav d^tiQCJv dvL6a 



2. dLUGx-^iiaCL C. 3. f tx^] slyi- in ras. D. 4. sxslv] corr. 
ex 8x^L B^. 8. GvyxcoQsCasLsv C, sed corr.; -q-^gsl- in ras. A. 
9. ScsL CD. 10. dvvovtcov] alt. v ins. D^ 13. ScsC D. 14. 
ScsC D. 16. ovzog] corr. ex ovrcog D. 19. S'] ds D. 20. Post 
oi}QavC(ov ras. 1 litt. D. cpoQ&g] corr. ex cpaiQ&g D; similia 

posthac non notabo. vTroTi-O-tTat D, -Tt- eras. 21. ylvsGd-aLl). 

22. onov — 23. vno%Cr}TaL] in mg. sup. add. D, mg. D^. 

23. xat (pr.)] ly ■nai CD^ vnoyiSTjtaL] corr. ex vnoy.aCritaL C*, 
vn6%SLxaL D. ts] om. D. 24. alXriXa D. 



MA0HMATIKHS STNTAlEjESiS A'. 13 

fpaiVE6^aL totg avtotg xad'^ ixdi0tr}v %SQi(poQCiv cjg av 
7tot€ ^£v £7tl ^ectovogy Ttoth d' iTtl YJttovog ytyvo^sva 
dvaetriiiatog^ o%£q ov% bQatac 6v^^atvov. aXla yaQ 
xal tb TtQog tolg 6QL^ov6tv ^st^ova tk fisyed^rj (paCve- 
Cd-ac ov% 7] a7t66ta6ig iXdttcjv ov6a TtOLSt^ aAA' rj 5 
tov vyQOv tov TtEQiixovtog tiiv yr^v dvad-v^taacg 
[ista^v trjg te oi^ecjg rj^atv xa\ avrav yiyvoiiivrj^ 
xad^aTteQ xal td eig vdcoQ i^^Xrjd^ivta ^ec^ova (paL- 
vetac^ xal o0a) dv xatcatiQco x^QV^ to6ovt(p ^eCt^ova, 

TtQoddyet d' eCg trjv 6(paLQLxriv evvotav xal td lo 
totavta to te iirj dvva^J-O-at xar' dXXrjv vjtod^e^tv tdg 
t&v c3qo6xo7iCg)v xata6xevdg 6v^(pc3vetv rj ^ovrjv tavtrjv^ 
xal ott trjg t&v ovQavCcjv (poQctg dxcoXvtov te xal 
evxtvrjtotdtrjg d7ta6cbv ov6rjg xal tcbv ^xrj^dtcov evxtvrj- 
totatov v7tdQxet t&v ^ev i7tt7ti8c3v tb xvxXtxdv^ tcbv 15 
de 6teQecbv tb 6(paLQLx6v^ G)6avtcog d' ort, tS)v l'6rjv 
7teQC^etQov ixovtcDv 6xrjfidtcov dLa(p6Qcov i^teLdrj ^eC^ovd 
i6tLV td 7toXvycovLcbteQa^ tav ^ev i7tL7tidc3v 6 xvxXog 
yCvetaL fieC^ov^ t&v de 6teQea)v r] 6(patQa^ ^eC^cov de 
xal 6 ovQavbg tG)v dXXcov 6c3^dtcov. 20 

ov ^rjv dXkd xal dTtb €pv6LX&v tLVCov e6tLV OQfirj- 
d^fjvaL 7tQbg tijv tOLavtrjv i^tL^oXriv olov oxl tcbv 



1. cpuCvBaO^ai] corr. ex cpsQea&ai D^. cbg] inter o) et g 
ras. parua D. 2. 8'] di D. yLvofisvcc CD. 3. dLaazi^- 

(larog] corr, ex dLaatrjfidrcov D^. ovx] corr. ex ovx D'. Ante 
allci ras. 1 litt. D. 4. oQL^ovaL D. 7. ra] om. D. yivo- 
(isvT] CD. 9. TiatcoTSQcoL BC. XOQji'] corr. ex ^^co^at D^ 

lisi^ovaL BC, corr. B^ 10. d'] S^ CD. slg] ins. D«. 

11. ■Katd D. 12 oiQoayiOTtLOJv] C^D^, aQoayionL&v ABCD^, 

OQoaiiOTCL&v D. 14. sv-nLvrjyiotcitrjg C, svv,Lvi]tLY,cotcx.t7]g C^. 

xat] corr. ex Y,atcx, D^. 15. vnaQxsL] mut. in vtcccqxsl D^ 

t&v] corr. ex rd C*. STtLnsScov] corr. ex inLnsXcov C^. 18. 
satL B. noXvycovotsQa D, corr. D^. 



14 KAATAIOT nTOAEMAIOT 

6(0flCCt(DV JtCCVtCaV kS7ltOll€Q£6teQOg Xal 6^0CO^SQ86t6Q6s 

i6tiv 6 ai%"ifiQj tav ds oholo^sq&v ofiOLO^EQstg at stcl- 
(pdvsiai^ o^OLO^SQStg ds STCicpdvsiai fiovai ^ ts xvxko- 
tSQYjg sv totg STtiTCsdoig xal iv totg 6tSQS0tg rj 0(pai,QLXi^' 
5 tov ds aid^SQog ^ij ovtog iTCijisdov^ dlXd 6tSQS0v, 
xataXsinstaL avtbv sivai 6(pai,Q0SLdrj. xal b^ioCtog^ ort 
7] (pv6ig td 66fiata jcdvta td fisv ijccysia xal cpd^aQtd 
oXcjg ix TCSQKpsQcbv^ dvo^oioy.SQG)v fiivtoi 6xrj^dtcov 
6vvs6t7]6ato^ td d' iv t» atd^sQc xal d^sta Tcdvta ndXcv 

10 ii b^oio^SQcbv xal 6(paLQixcbv, inscTCSQ iiCiTCsda ovta -i} 
di^xosidfj ovx dv 7Ca6i totg ix dia^poQcov tfjg yfjg 
toTCcov vTcb tbv avtbv xqovov bQcb6i xvxkixbv ivscpaCvsto 
6%7iy.a' did tovto (f svkoyov slvai xal tbv 7CSQis%ovta 
avtd aCd^sQa trjg b^oCag '6vta (pv^scog 6(paiQ0Sidfj ts 

15 sivai xal did tfjv biioiOfisQSiav iyxvxkCcog ts (pSQS^d^ai 
xal b^aXcbg. 

d\ "Oti xa\ t} yfj 6(paiQ0Sidrig i6tiv TCQbg 
al^d^rj^iv d)g xa%^ oAa ^SQr^. 

'''Oti ds xal rj yfj 6(paiQ0Sid7]g i6tiv TCQbg al^d-rj^iv 

20 cog xad"^ ola ^SQr] Xa^fiavo^ivi^ ^ fidXi6t dv ovtcog 

xatavo7]6ainsv' tbv r]liov yuQ jcdXiv xa\ tf]v 6slr]vriv 

xa\ tovg dkXovg u6tiQag s6tiv Cdstv ov xatd tb avtb 

jcd6iv totg i7c\ tfjg yfjg dvatskkovtdg ts xa\ dvvovtag^ 

1. xal dfiOLo^EQsatSQog sezLv'] A, supra scr. D^, om. D, 
S6TLV BC. 2. ds] d' D. 3. -vsLcci — sTtLcpd-] mg. Dl 4. 
Iv(alt.)] om. D. roLg arsQSOLg] tmv arsQS&v D. 7. xat] xal zd D. 

8. avofiOLOfislfisQ&v D. (ievtol] Sh t&v D. 9. d'] di D. 

11. a7t&6L D. 12. toTtcov'] corr. ex tonov C^ 13. d'] ts D. 

15. syKvnXLcog] svv,vv.XLaig D. (piQS6Q-aL] -sq- in ras. D. 17. 
8'] B, om. ACD. ort — 18. iisqt]] otl 6cpaLQ0SL8r]g -nal i} yfj 
mg. sup. D. 19. \(paLQ0SL8rig D. 20. ovrco D. 22. ^6rLv] 
ins. D^ 23. na6L D. 



MA0HMATIKHS 2TNTASE5i2 A'. 15 

aXXk ^QOtsQOcg ^ev aUl totg TtQog dvatoXag oi7iov6iv^ 
v6t8Q0cg de totg TCQog dv6^dg. tdg yaQ 'biio tbv avtbv 
XQOVov dTtotEkov^evag exXsLTCtcxdg (pavta6iag xal 
^dh6ta tdg ^sXrjVLaxdg svql6xoh6v ovx sv tatg avtatg 
wQaig^ tovts6tLV tatg tb l'6ov ditsxov^aig trjg ^s6rj^PQiag^ 5 
TtaQa 7ta6iv dvayQacpo^svag ^ dXld Jtdvtots tdg itaQd 
totg dvatoXixcjtsQOig tcbv t7]Qi]6dvt(ov dvaysyQa^i^svag 
aQag v6tSQiiov6ag tcov JtaQd totg dvtixcjtsQOig. xal 
tfig diacpOQccg ds t&v Sqcjv dvaXoyov totg dia6t7J^a6i 
tG)v xoiQGiv svQi6xo^svr]g 6(paLQixriv dv ng SLXotcog lo 
tijv trjg yrjg iiticpdvsiav VTtoXd^Oi trjg jcatd trjv xvQto- 
tr^ta Tcad'' oXa ^SQrj Xa^^avo^svrjg oiiOiO^SQSiag dva- 
koycjg atsL tdg S7tL7tQ06d^r]6SLg totg scps^rjg TtOLOv^svrjg' 
SL ds ys rjv tb 6%ri^a stSQOv^ ovz dv tovto 6vvs^aLvsv^ 
cog l'doL tLg dv xal sk tovt cov. 15 

xoLXrjg ^sv ydQ avtr]g V7taQxov6rjg TtQOtsQOLg dv 
scpaLVSto dvatsXXovta td d6tQa totg dv6^LXcotsQOLg^ 
S7tL7ts8ov 8s 7ta6Lv dfia xal jcatd tbv avtbv xQ^vov 
totg STtl trjg yrjg dvstsXXsv ts xal sdvvsVj tQLydivov 
ds t) tstQayG)vov rj tLvog dkXov 6xr]^atog tcbv Ttolv- 20 
ychvcov 7ta6Lv dv 7tdlLv bpLoCcog %al xatd ro avtb totg 
S7tl trig avtfjg svd^siag olkov6lVj OTtSQ ovda^cog cpaCvstaL 
yLvo^svov. otL ds ovds xvXLvdQOSLdrjg dv str]^ Xva r] 
^sv 7tSQicp6Qr]g 67ticpdv6ia 7tQbg tdg dvatokdg xal tdg 
dv66Lg f] t6tQa^^svr], tcbv ds s7tL7ts8cov ^d6scov aC 25 



1. ccEL D. 3. xQovovov C. &7toxBXovn,Bvccg\ corr. ex ano- 
rsXoviiBva A^. 6. rdg] ins. D^. Ttaga] om. D, 7. ava- 

ToXiyiOTEQOLg BC, corr. B^ 8. vGTSQv^ovoas] v- ins. D^ 13. 
asL D. 17. "to. aoTQa avarsXXovTa B (notas adpos. B^). 

19. avsTslsv C. 20. ds] corr. in t6 Dl 21. av] om. D. 

22. ovda(ifi D. 23. otl] inter 6 et tl ras. 1 litt. C. 25. 
TSTQa(i(iivTi] TS- in ras. D. snLTCsdmv] corr. ex sTtLTtslcov D^ 



16 KAATAIOT nTOAEMAIOT 

TclsvQal TCQog roi)g xov k66^ov jrdAovg, otcsq av xivsg 
•bTCold^oLSv G)g md-avcoxsQov ^ sxstd^sv dTjXov ovdsvl 
yaQ av ovdsv aisl tpavsQOv syiyvsxo xcbv d6xQG)v 
xCbv STcl xrjg KVQxrjg S7CL(pavsiag oixovvxcov^ aAA' t) 
6 Tcdvxa 7Ca6iv xal dvsxsXXsv xat sdvvsv, rj xd avxd xal 
xb l'6ov dcps6xcbxa xcbv jcoXcov sxaxsQov 7Ca0cv dsl 
d(pavYi xad^i^xaxo' vvv d' o0g) dv iiaXkov TCQog xdg 
ccQxxovg TCaQodsvcj^sv^ X060VX(p xcov ^sv voxlcoxsqcjv 
dexQcov dTCOKQVTCxovxaL xd Tcksiova^ xcov ds ^oqsloxsqcov 

10 dvacpaivsxac^ cog drikov slvaL^ dLoxc xal svxavd^a rj 
xvQXoxrjg xfjg yrjg xal xdg inl xd TcldyLa ^SQrj stcl- 
7CQo6d^Yi6sLg dvaldycog jcoLOVfisvrj %avxa%6%-sv xh 6xr}^a 
xb 6(paLQOSLdsgdicodsixvv0LV^ [isxd xov^ xdv 7CQo67cXscofisv 
bQS6LV ^ XL6LV 'btl^rjXotg %coQioLg d(p 'fj^drJTCOxs ycoviag 

15 xal TCQbg r]vdri7Coxs^ xaxd ^lxqov avxav av^6^sva xd 
fisysd^rj d-scoQst^d^aL xad^d^csQ s^ ai^xrjg xrjg d^akdxxrjg 
dvaxv7Cx6vxcov ^ 7Cq6xsqov ds xaxads8vx6xcov d^d xijv 
xvQx6xrjxa xrjg xov vdaxog S7Ci(pavsiag, 

s. "OxL ^.s6r] xov ovQavov s6xlv rj yf}. 

20 Tovxov ds d^scoQrjd^svxog^ st XLg S(ps^fjg xal 7CSqI 
xfjg d-i^scog xfjg yfjg dLakd^oL^ xaxavoiJ6SLSV dv ovxoog 



1. Snsg'] corr. ex onsv C^. 2. nsLd-ccvooTSQOV C. 3. 

icsi CD. iyivsTO D. 5. ScvstsXXs D. Post ij add. nara D^. 

6. t6] tcc D. noXcov'] corr. ex noXXav D. 7. d'] Si D. 

occo] 0- supra scr. D^. ar] om. D. 8. naQoSsvtoiisvl corr. 
ex nuQoSsvo^sv A^, mut. in nccQodsvofisv D, nuQodsvo^sv C. 

voTSLOTSQcav D. 9. Scno-KQvnTSTUL D. Tcc\ om. D. ds~\ 
supra scr. D^. 10. dfiXov] df]- e corr. D^ 11. (isqti] -rj 

in ras. D. 13. ccnodsLV,vv6i D. nQOGnXscoiLSv] corr. ex nQoa- 
nXsofisv D^. 14. jjoj^totg] corr. ex xoQOLg C^. 15. rjvS^^noTs] 
-V- supra scr. D^ 16. Q-ccXdaaris D. 19. s'] B, om. ACD. 

ort — yi]] mg. sup. D. 



MA0HMATIKH2 STNTASESiS A'. 17 

(lovcog 6vvr£X£6d"rj66fi6va ta (paLvdfieva jtSQi avtrjv^ 
£1 ^£6rjv rov ovgavov xad^djc^Q xevrQOv 0cpaLQag vTto- 
arrj^ac^^d^a. rovrov yaQ drj firj ovrcog £%ovrog £8£l 
rjrov rov ^lv a^ovog ixrbg ^lvai rijv yrjv^ £xar£Qov dh 
rmv TtoXcjv l'6ov d7C£%£iv^ rj iitl rov a^ovog ov6av TtQog 5 
rbv ereQov rcov noXcov JtaQaK£%coQrjK£vai rj ^rjr£ iitl 
tov cc^ovog £lvai ^rjr£ ixariQOv r&v ^roAojv l'6ov 
ditix^LV. 

TtQog [ihv ovv rijv TtQcorrjv rcbv rQL&v ^ieiv ix^tva 
fidx^raL^ orL^ £l ^£v £Lg tb dvco rj tb xdtco tLV&v 10 
TtaQax^xcoQrjxvta vorjd^^Lrj^ tovtoLg dv 6v^7tL7ttoi iitl 
fji£v dQd^rjg trjg OcpaCQag tb ^rjdi7tot£ L6rjy,£QLav yLV£- 
^d^ai £Lg dvi6a 7tdvtot£ dLaLQOv^ivcov V7tb tov bQL^ovtog 
rov re v7t£Q yfjv ocal rov V7tb yfjv^ i^tl d£ rrjg 
iy7C£xli^ivrjg rb rj firj yCv^^xtai TtdUv oXcog C6rjfi£QCav 15 
tI (lij iv rrj ft£ra|v ^taQodco rfjg r£ d^^Qivfjg rQOTtfjg 
xal rfjg x£i^£Qivfjg dvC^cov rcbv dia6rrj^drcov rovrcov ih, 
dvdyxrjg yivo^ivcov dicc ro ^rjxin rbv L6rj^£QLvbv xal 
liiyL6rov rcov 7taQakXrjXcov rcbv rotg 7t6koLg rfjg 7t£Qi- 
(poQccg yQacpofiivcov tcvkXcov dixoro^^tad^ai VTtb rov 6qC- 20 
^ovrog^ dkX £va rmv 7taQaXX,rjXcov «vtkI Kal ^roi 
PoQ£ioriQcov rj voncoriQcov. coiioXbyrjrai Si y£ V7tb 
Ttdvrcov aTtkcbg^ 6n rd dia6rfj^ara ravra l'6a rvyxdv£i 



3. 8ri\ om. D. b%6vxois\ corr. ex i%ovxtos C^ 4 sq. a, 

(j, y, ^ mg. D^ 9. ■jiQwxr^v] -m- e corr. D. 11. ituQav.s^co- 
QjyAviav C, -V del. C^ roTj^d-ftrj] -el- e corr. C*. 14. xat 

— yr]v'\ supra scr. D^. 15. syv.8v,XnjL£VT]g\ -i- inter duas ras. D. 

ri\ supra scr. D^. 16. xb\ om. D. 18. iari^EQiv6v\ -t- 

ins. C. 19. x&v nccQcclXril(ov\ om. D. Supra x6v xoig ras. D. 

7t6Xoig\ corr. ex noXXoig D. Supra nsQtcpoQccg add. ecpuCQag D^. 

21. a-uTw] corr. ex avxtov D. 22. voxia}xSQ(ov\ corr. ex 

vcoxicoxsQcov C, ex voxsLoxsQcov D^. oiiioX6y7]xaL\ corr. ex 6(io- 
XoysLxaL D^ ys\ om. D. 23. xvyxdvsLV D, -v eras. 
Ptolemaeus, ed. Heiberg. 2 



18 KAATAIOT nTOAEMAIOT 

Ttavraxi]^ r« xal tag jiaQa rrjv t6r}^sQLav av^7]6eLg tfjg 
^syL0Trjg tjy^eQag iv taig ^SQLvaig tQOJtatg l'6ag slvai 
taig nsiG)0s6c t&v ska%C0t(ov tj^SQcov iv tatg xsi^SQivatg 
TQOTtatg. st 8s sig ta JtQog avatoXag ij 8v6^ag iisqtj 
6 tiv&v TtdXiv rj 7taQaxG)Qr]6ig 'bjtotsd'Sii^^ Tcal tovtotg 
av eviifiaivoi tb ^7]ts t«: ^sysd^rj xal ta dia6t7]^ata 
tG)v a6tQG)v i'6a xal ta avta xatd ts tbv saov xal 
tbv s67tSQiov oQi^ovta (paCvsG^^ai ^7]ts tbv d%^ dvato- 
Xrig yi'SXQf' ^s6ovQav7]6sG)g ;u()dvov t6ov dTtorsXstdd^ai 

10 rm djtb fis6ovQav7J6sG)g ijti dvdv^ ditSQ ivaQycbg itavtd- 
7ta6iv dvtCxsitai totg q^aivo^svoig. 

TtQbg ds tr]v dsvtSQav r&v %'s6sg)v^ xa%-' r\v inl 
tov d%ovog ov6a %Qbg tbv stSQOv tG)v 7t6lG)v %aQa- 
xsxG)Qr]Kvta vori%"ifi6stai^ %dXiv av ttg v%avtr]6sisv^ ort, 

15 £^ rov'9'' ovtG)g SiX£v^ ^cc^^ sxa6tov dv t&v oiXi^dtG)v 
tb tov bQC^ovtog i%C%sdov dvi6a diacpoQG^g i%oCsi 
%dvtote to ts v%SQ yfjv xal tb v%b yrjv tov ovQavov 
xat^ alXrjv xal dklr]v %aQaxG)Qr]6iV xal %Qbg savtd 
xal %Qbg dXXr]2.a^ i%l ^sv iiovrjg trjg OQ&rjg 6(paCQag 

20 dixoto^stv avtr]v dvva^svov tov oQC^ovtog^ i%l ds tf]g 
syxXC6scog tfjg %Oiov6r]g tbv iyyvrsQov tcov %6Xg)v dsl 
(pavsQOv ro [isv v%sq yfjv %dvtots ^siovvtog^ tb ds 
7)%^ yf]v av^ovtog^ m6ts 6v[i^aCvsiv tb xal tbv did 
lie6G)v tG)v t,G}dCG)v xtjkXov ^eyi6tov eCg dvi6a SiaiQet- 

25 ^d^ai v%b tov tov oQCt,ovtog i%i%edov^ o%eQ ovSafimg 



1. tccg nccQcc ttjv] rci in' avtriv seq. lac. 8 — 9 litt. D, 
corr. D^. 2. iv Tatg] in ras. D. 3. Tatg (alt.)] t corr. ex t D^. 

13. noXoav] -6- e corr. C. 15. sixsvl corr. ex elxs D^ 16. 
tov] bis D, sed corr. SLcccp&OQCQg A, yQ. dLacpoQcog mg. A^, 

17. Tf] om. D. yijv (alt.)] y corr. ex t D. 18. yicctcc D. 

TtQog] -g e corr. C. 21. aisC D. 22. Si] S' D. 23. tov] 
corr. ex to C^. 



MA0HMATIKH2: STNTASEiiS A'. 19 

ovtcog exov d^ecoQstTcct , e^ ^lv dsl xal jtd0L (paivo- 
fisvov {)7c}q yfjs dcodsxatrj^oQLCov ^ ?| ds t&v XoinCbv 
a(pavG)v ovtcov, slt ai) tcccXlv sxstvcov ^sv oXcov xata 
t6 avtb (paivo^svcov vtcsq yfjg^ t&v ds koiTCGiv «fta iiij 
(paivoiisvcov' cog dfjXov tvyi^kvsiv^ oti xal ta tfiTJ^ata 5 
tov ^codiaxov dixoto^sttac 'bno tov bQitpvtog sx tov 
ta avta rniixvxXia oXa nots fisv vtcsq yfjv^ icots ds 
VTch yfjv dnoXa^Pccvs^d^at. 

xal xad^oXov d' av evvs^acvsv^ stjcsQ ^fj vtc^ 
avtov tbv i6riiLSQLvbv si%s tijv %^s6lv rj yfj^ ^Qbg 10 
ccQxtovg ds rj TCQbg ns^rj^^QLav cctcsxIlvsv iCQbg tbv 
stSQOv tcbv TcdXcov^ To ^rjxstL ^rjds JCQbg af^d^rj^Lv sv 
tatg i^rj^SQLaLg tdg dvatokLxdg t&v yvco^ovcov 6xLdg 
tatg dvtLxatg i% svd^siag yiyvs^d^aL xatd tcbv TCaQ- 
akXrjXcov tw oQL^ovtL stcltcsScov^ otcsq dvtLXQvg TCavtaxf} 15 
d^scoQsttac TCaQaxoXovd^ovv. cpavsQOv d' avt^^^sv^ otL 
^rjds tfjv tQLtrjv tcbv d^s^scov olov ts 7CQo%coQstv sxa- 
tSQCOv tcbv sv tatg TCQCotaLg svavtLCOfidtcov stc' avtfjg 
6v^Prj6o^svcov. 

evvsXovtL d' SLTCstv jcdea dv avyxvd^SLrj tslsov 20 
r] td^Lg rj tcsqI tdg av^o^SLCo^SLg tcbv wxd^rj^sQcov 
^scoQOv^isvrj fiij ^S0rjg vjcoxsL^svrjg tfjg yfjg ^std tov 
^rjds tdg tfjg 6sXrjvrjg sxXsLipSLg xatd icdvta td ^SQrj 
tov ovQavov TCQbg tfjv xatd dcd^stQOv ta rjXCco 6td6Lv 
d7CotsXst6d-aL dvva^d^ac tfjg yfjg TCokkdxLg firj sv tatg 25 

1. aUt D. 4. v-JtsQ — 5. (pciivo^iivaivl supra scr. D^. 6. 
^oj^taxov] -ci- supra scr. D^ 7. oXa'] seq. ras. 1 litt. D. 

11. ccTtETiXLVs D. 12. Post [ir]di eras. xl D. 14. fv-S-ftag] 
corr. ex sv^^siaig D. yCvs6%^ai D seq. ras. 4 litt. 15. Post to5 
eras. Si D. STnnsdoiv^ corr. ex STtLTtsdoot D^. 19. 6vfi^r}60- 
^svcov] ante -o- ras. C. 20. S'] 8s D. 6vvxvQ-SLr] C. 21. 
Tcc^Lg] I corr. ex 8 B^C^. av^ofiLm^SLg AD, corr. A^ 23. sti- 
XsiilfSLg] -SL- in ras. D. td] om. D. 24. ■natci] om. D. 

2* 



20 KAATAIOT nTOAEMAIOT 

dia^£rQ0v6aig TCaQodoLg i7tL7tQ06d'ov6r}g avtotg^ akXa 
iv totg iXdxxo6i tov yj^ixvxIlov dLa6t7J^a6LV. 

g\ "Oti 6rj^£L0v koyov £%£l itQog ra ovQavLa 

ri yij. 

5 ^AXka iiriv otL xal 6rj^£L0v koyov £%£l TCQhg 

at6%^ri6LV ri yfj TCQog tb ^iixQL trjg t&v djtXav&v xakov- 

^ivcov 6(paLQag d:t66trj^a^ ^iya ^£V t£x^7JQL0v tb 

djtb Jtdvtcjv avtfjg tCbv ^£QG)V td t£ ^£yi%ri xal td 

8La6tri[iata t&v d6tQC3v xatd tovg avtovg xQovovg 

10 l'6a xal oiiOLa q)aLV£6%'aL Ttavtaxfj^ xad^dTt^Q at dnb 
dLag)6Qa)v xlL^dtcov inl tcav avtcbv triQrJ6£Lg ovd£ 
tb iXdxL6tov £VQL6xovtaL dLa(pcovov6aL. ov firjv 
dlXd xdx£tvo TtaQaXrjjttiov tb tovg yvcofiovag toijg iv 
<p8ri7tot£ iiiQ£L trig yfig tLd-^^ivovg^ £tL dl td t&v xql- 

15 xcjtcbv 6(paLQcbv xivtQa tb avtb dvva^d^aL ta xatd 
dXri%£Lav tfjg y^g xivtQca xal dLa6(xit,£LV tdg dL07tt£v6£Lg 
xal tdg tcbv 6xlcjv 7t£QLaycoydg ovtcog 6^oX6yovg tatg 
VTtod^i^^^L tcov (paLVO^ivcov^ cog dv £l 8l avtov tov 
XYig yfjg ^i6ov 6rj^£L0v yLv6^£vaL itvyxavov. 

20 ivaQyhg d£ 6rj^£tov tov Tav-O"' ovtcog £X£lv xa\ tb 
Ttavtaxfj td dLa tcbv oil)£cov ix^aXX6^£va iitLTt^da^ d 
xaXo\)iL£v bQL^ovtag^ dLXOto^£tv 7tdvtot£ trjv oXrjv 
6(patQav tov ovQavofjj 07t£Q ovx dv 6vvipaLV£v^ £l tb 



2. sXdtToaiv D. 3. g'] om, ACD. ort — 4. y?)] ott, 

6r](iEiov Xoyov sxv] t} y^ TCQog tk ovqccvlcc mg. sup. D. 7. vsin/j- 
Qiov D. 11. yiXrifidtayv A. 14. yiQtyicot&vl corr. ex ■hqlko- 

a. 

tmv A^D^ 15. 8vva6ca A. >tar' D. 17. ratg] t corr. 

ex t D^ 18. vno^i6b6iv A. cpuivoiisvoav^ cp- in ras. D, 

Sil 7] 8i D, xat 8i D^. tov\ om. BC. 20. hvccQyatq C. 

21. a] supra scr. D^. 23, bI\ corr. ex elg D. 



MA0HMATIKHS STNTASEiJS A'. 21 

fieysd^og trjg yrig aL6d"rjtbv fjv TtQog rriv tav ovQavLCJv 
a7i66ta6iv^ aXXa \i6vov \ji\v av ro 8ia tov ^cara ro 
TttvtQOv tfig yfig ^rnieCov dLSK^a2.l6\isvov STtCnsdov 
dLxoto^istv '^dvvato tijv 6(paLQav^ ta 8s Sl rj^drj- 
Tcotovv S7iL(pavsLag trjg yfjg jiSL^ova av jtdvtots ta 5 
vjcb yrjv sitoCsL t\iri\iata tav i}7tsQ yfjv. 

J'. "OtL ovds KCvrj6LV tLva fistapatLxrjv TtoLsttaL 

Kata ta avta 6s totg SfiTtQoad^sv dsLi%^ri6staL^ di6tL 
firjd^ r]vtLVOvv xCvrj6LV sig ta JtQOSLQrj^isva TtkdyLa 10 
[iSQri f^v yf]V ol6v ts 7toLSL6^aL ij oAcog fnsd^Ceta&^aC 
Ttots tov %atk tb xsvtQov t^Jtov td avtd ydQ 6vv- 
dpuLVSv «V, ditSQ SL xal tfjv d^s^LV dklriv itaQd tb 
\is6ov s%ov6a stvy%avsv. &6t s^iOLys doxst 7tSQL60cbg 
dv tLg Tcal tfjg STtl tb \is6ov cpoQdg tdg attCag sm- 15 
t,ritfi6SLV djtah, ys tov, oTf. rj ts yfj tbv \is6ov STtsxst 
tbjtov tov x66\iov xal td pdQrj Ttdvta sit' avtfjv 
(psQStat^ ovtcjg ovtog svaQyovg s^ avtcbv tmv (paLvo- 
\isv(ov. xdoistvo ds \i6vov 7tQO%SLQ6tatov dv sCg tfjv 
tOLavtrjv xatdlrjil^iv yCvoLto tb 6(paLQOSLdovg xal 20 
\is6rjg tov 7tavt6g^ d)g scpa^isv^ d^todsdsLy^isvrjg tf^g yfjg 



2. x6 (alt,)] om. BC. 3. rfig yfjg'] om. C. G7]^slov] corr. ex 
6ri(i8L0V D. 4. r}adr}7totovv] corr. ex rjGTtotovv D^. 7. ^'J 
om. ACD. otL — 8. y^] mg. sup. D. 7. noLELXccL fisxa- 

^uxLv.fiv D. 10. ra] seq. ras. 1 iitt, A, 12. -asvxqov^ corr. 
ex Y.s\xQOv A^. av 6vvs^aLvsv D. 14. siioC C. 7CSQL6cog D. 

15. rpOQag] mut. in cpoqaig C^ siiL^rixfi^SLv] mut. in stil- 
^ritr]6SLSv D^; fort. s7CL^rjtfi6ai. 16, xs yf]] e corr, D^ xov] 
corr. ex xmv A^. 18. svaQyovg] supra scr. D^. (paLvofis- 

vcov] seq. ov D, corr. in mv D^. 19. yiayisLvo] seq. ras. 1 litt. A. 

ds] suprascr. D^ 20. yLvoLto] corr. ex ysvoLto D^ 6(paL- 
QOVSLdovg C, V del. C*. 



22 KAATAIOT nXOAEMAIOT 

iv ana6LV cc%l&g totg fi£Q£6LV avtrlg tdg ts 7iQo6v£v6SLg 
xal tag t&v pdQog sxovtov ^o^dtcov cpOQag^ Xsycj ds 
tag idCag avt&v^ TtQog OQd^dg ycovCag Tcdvtots xal 
jcavtaxrj yCvs^d^at ta did tTjg xatd triv s^7ttc36Lv 
5 £7tag)7}g dLSXpallo^svG) dxhvst sitmsdG)' dfjXov ydQ did 
tb roi)'9'' ovtcog ^X^lv^ ott xaC^ £l ^rj dvt£x67ttovto 
VTtb tfjg £7tL(pav£Cag r^g ;^ijg, 7tdvt(og dv £7t avtb ro 
xivtQov xattjvtcov^ £7t£l xal 7] £7tl t6 xivtQov dyov6a 
svd^^ta TtQbg OQd^dg ycovCag d^l yCv£tai ta di,d tfjg 
10 xatd triv i^tacpijv to^flg icpa^tto^ivm tfjg 6(paCQag iTti- 
TtiSip. 

0601, dl 7taQddoiov olovtat tb fir]t£ p^^rjxivat Ttov 
^rjts cpiQs^d^ai tb trjhxovto paQog tfjg yfjg^ doxov6C 
pLOL 7tQbg td xad'' savtovg ^tdd^rj xal ov TtQbg tb tov 

15 OAOV IdLOV d7tO^Xi7tOVtEg tfjV 6vyXQL6LV TtOLOVpbSVOL 

dLa^aQtdvsLV. ov ydQ dv oi^aL %^av^a6tbv avtotg stL 
(pavsCrj t6 TotovTor, sl i7tL6tr]6aLSv ^ otL tovto t6 tfjg 
yfjg ^iysd-og 6vyxQLv6^svov oX(p ta ^tsQtixovtL 6G)^atL 
6rj^sCov 7tQbg avtb Xoyov sxsi' dvvatbv ydQ ovto 
20 d6i,SL t6 xatd kbyov iXdxL6tov V7tb tov ^tavtsl&g 
pbsyC6tov xal oy^OLO^SQOvg dLaxQatsl^d^aC ts xal dvtSQsC- 
ds6%^aL ^tavtax^d-sv t^cog xal b^oLOxXLV&g tov ^sv xdtca 



1. n&GLV D. iLiQtaiv^ corr. ex (isQsaL D. nQOGvBvh D, 



, ?? 



nQOGvsva^ D^. 2. ds] dri D. 4. yLyv86&aL BC. sfinToaaLv] 
corr. ex nt&aLv D^. • 5. ^tex^aUo/xfVoo] S corr. ex a D^ 

ayiXivfj BC. 6. ro] om. D. 7. Post yf^g add. at cpoQuC 

mg. BC (pro scholio). avxb to] utrumque -d in ras. B, 8. 
v.ivtQOv] -ov in ras. B, v.ivtQov ai cpoQaC D. 10. roft^g] -g 

add. D^. iniTteScov A, sed v eras. 12. naQado^ov] do^ov C, 
mg. yQ. naQddo{^ov) C^, Xo^ov B. ^s^ri^TjHSvaL D, sed corr. 

13. tiqXLyiovto] mut. in tT^XLKOvtov D^ 14. avtovg D. 16. 
av] supra scr. D. hi] supra scr. D^ 17. sl] corr. ex ij C^ 

19. ovtto] e corr. D^ 



MAeHMATIKHS 2TNTASESi2 A'. 23 

rj avcD ^rjdsvbg ovrog iv rw x66^q) TCQog avri^i/, 
xad^ccTCSQ ovds iv 6(faCq(x, rig av rb roiovrov eTCivoiq- 
6SL6Vy r&v ds sv avra 6vyxQi^drGiv rb o(Sov stcI rfi 
idca xal xara (pv6Lv iavr&v cpoqa r&v ^sv xovtpcjv 
xal Xsjcro^SQCJv sig rb s^ca xal cag TCQog rriv tcsql- 5 
(psQSLav dvaQLTCLt^o^svGiv ^ doxovvrcjv ds slg rb naQ^ 
sxd6roLg avo rriv OQ^r^v TCOLSted-aL dta rb xal Tcdvrcov 
rj^av rb vtcsq xscpakfig^ avco ds xaXov^svov xal avro^ 
vsvsLv cog TCQog rr^v icsQLSxov6av ixLCpdvsLav ^ rcbv ds 
fiaQscjv xal jcaxv^sQcov iicl rb ^s6ov xal mg TCQog rb lo 
xsvvQov (pSQOiisvcav^ doxovvrcDv ds stg rb xdrw TciicrsLv 
dLoc rb xal jcdvrcov icdkLV rj^cbv rb TCQbg rovg TCodag^ 
xaXov^svov ds xdrco^ xal avrb vsvslv TCQbg rb xsvrQov 
"^^S y^S 6vvL^rj6LV rs slxorog tcsqI rb [is6ov ^.a^^avovrcjv 
VTcb rrjg JCQbg dXXrjXa jcavraxod^sv L6rjg xal b^oCag 15 
dvrLXOTCrjg rs xal dvrsQsC6scog. roLydQroL xal sCxorcjg 
xaraXa^pdvsraL rb oXov 6rsQsca^a rfjg yrjg ^syL6rov 
ovrcjg bv ag TCQbg rd cpSQO^sva in avrrjv xal vicb rfjg 
rcbv Tcdvv ilaxC6rcov paQ&v OQ^fjg drs dij Tcavrax^d^sv 
drQS^ov6a xal co67Csq rd 6v^7cC7crovra ixdsxo^svrj. si 20 
8s ys xal avrrjg rjv rLg (poQa xoLvij xal [iCa xal rj 
avrri rotg dXXoLg pdQs6LV^ scpQ-avsv dv jcdvra drjXovorL 
dta rrjv ro6avrrjv rov ^sysd^ovg vjcsQ^oXriv xaracpsQo^svrj^ 
xal 'bTCsksCnsro ^sv rd rs t,ma xal rd xard ^iSQog rcbv 

1. jLtTj-O-fvog D. avtrjv] ccitov D (corrigere uoluit D^. 

3. a-urra] avTOtg BC. GvvyiQifidrcov A. t&] ins. D^ 060v] 
mut. in 06ai D^. STtl tjj tdLcc] corr. ex snitridEiai D^, stil 

tfi 8Cai C, iTtl tTj Idlai C^ 4. avtibv D. ^>0Q&] corr. ex 

(poQai D^ 5. to] corr. ex tov D. cpiQSiav C. 6. avaQQi- 
Tti^ofiEvwv A^C^D. 7. e-ndetoig] con-. ex gjtacTTTjs D^. 13. 
avto] corr. ex avt& C^, avtb vsvs A, avtb vsvsi A^ 14. ts] 
corr. ex ys D^ 18. cpaiQ6(isva D, corr. D^. 21. cpOQcc] ante 
Q ras. 1 litt. C. 22. aXoig C, 



24 KAATAIOT nTOAEMAIOT 

paQG)v oxov^svcc €7il rov dsQog^ avzrj de xd%L6ta tikeov 
dv ix,7te7tt(x)K£L xal avtov tov ovgavov. dlXd td 
toiavta ^EV xal ^ovov iTtivorjd^ivta Ttdvtaxv dv (pavaCri 
ysXoidtata. 
5 i]dr^ di tcvEg^ Sag y ofovtai^ jttd-avcatSQOv^ tovtotg 
^£v ovx £%ovt£g^ 0, ti dvtSLTtOLSv^ CvyKatatCd^svtaL^ 
doxov6L ds ovdhv avtolg dvtL^aQtvQr]6SLv^ sC tbv fisv 
ovQavbv dxCvrjtov v7to6trj6aLvto Xoyov %dQLv^ trjv dh 
yriv TtSQl tbv avtbv d^ova 6tQSCpo^ivriv dTtb dv6ii&v 

10 S7t' dvatoXdg sxd^tr^g rj^iQag ^Cav syyL6ta 7tSQL6tQ0(priv^ 
ri xal d^cpotsQa xlvolsv 66ovdt]7tots^ ^ovov 7tsQC ts 
tbv avtbv d^ova^ dyg scpa^sv^ xal 6v^fiitQ(x}g t^ TtQog 
dXXrika TtSQLxataXri^SL . 

XiXrjd^e ds avtovg^ otL tCov ^sv TtsQl td d6tQa 

15 (paLvo^ivcav svsxsv ovdsv dv c^cog xcaXvoi xatd ys tr^v 
d7tXov6tiQav S7tLpoXrjv tovd"^ ovtcjg s%slv^ «tto ds tmv 
TtSQl rj^dg avtovg xal tcbv sv diQL 6v^7ttco^dtcov xal 
Ttdvv dv ysXoLOtatov ocpd^sCrj tb tOLOvtov. Xva ydQ 
6vy%G)Qri6G)iiLSv avtolg tb 7taQd cpv6LV ovtog td ^sv 

20 Xs7tto^SQi6tata xal xov(p6tata i) ^i^d' oXcog xLVSL6^aL ri 
ddLacp^QCog totg trjg svavtCag cpv^ecog t&v ys TteQl tbv 
diQa xal ^ttov XeTtto^eQav eva^ycbg ovtojg ta%vtiQag 
tcjv yeco8e6tiQcav Ttdvtcov (pOQag TtoLov^ivcov^ td de 



3. inLvoTj&svta] corr. ex STtovori&BVTcov J). 5. y'] om. A. 

6. GvvHaraT Cd-svrccL D, 7. avTotg ov8iv D. tov /LtgV] corr. 
ex iLsv Tov D^ 9. tov] bis C. 10. |jr'] sni IX ueql- 

OTQOQpriv] -ocpriv in ras. D. 12. GvfisTQcog D, corr. D^. 13. 
TtSQiytaTaX-^ipsv] post -r?- ras. 1 litt. D. 14. lsXr]&Ev BCD. 

avTOvg] -g add. D^. 15. ovSsv] corr. ex ovSs C^, ovd^iv D. 

%(oXvoC\ H- corr. ex a in scrib. D. 17. nsQC] tieqC ts D. 

Tcbv Ev asQi] A, Tov asQa BCD. 18. av] corr. ex ccy C^ 

om. D. 20. }i7]8'] -73- e corr. D. 21. adiacpoQoog] corr. 

ex diacpoQcog C^D^. ys] corr. ex ts D^ 



MA0HMATIKHS 2TNTASES>S A . 25 

7taxv^£Q£6rata xal ^aQvtaxa XLvrj^tv idiav b^elav 
ovtcag xal oftaAi)!/ 7toLEl6%^ai tcbv yscjd&v TtdXtv 6^0- 
Xoyoviiivog ^rjds JtQog tijv vit aXXcov xlvtj^lv eTtt- 
trjdsLCog ivLOte exovtcov^ aXTJ ovv o\3ioXoyr\6aLev av 
6(podQotdtr}v trjv 6tQ0(piiv tfjg yfjg yCyve^d^aL djtaecbv 5 
aTtXag tcbv TteQL avtrjv 7CLV7]6ecov cog dv to6avtrjv ev 
^QaxeZ %^ovG) TtoLov^evrjv d7toxatd6ta6Lv ^ C36te Ttdvta 
dv td ^ri ^e^riKota ^Tt avtfjg ^tav del tr]v evavtCav 
tfj yfi xCvr]6LV e^paCveto itOLOv^eva^ xal ovt dv veq)og 
Ttote edeCxvvto TtaQodevov JtQog dvatoXdg ovte dXXo 10 
tL tav LTtta^evcov tj paXXo^evcov q^d^avov^rjg del Jtdvta 
T^rlg yfjg xal 7tQola^pavov6rjg trjv 7tQbg dvatoXag 
xCvr]6LV^ co6te td koLJcd 7tdvta elg td 7tQog dv6^dg xal 
v7toXeL7t6^eva doxelv 7taQaxooQetv. 

el yaQ xal tbv deQa cpij^aLev avtfj 6v^7teQLdye6d^aL 15 
xatd td avtd xal L6otaxG)g^ ovdev ^trov td xat 
avtbv ytvo^eva 6vyxQC}iata 7tdvtote dv idoxet tfjg 
6vva^q)OtBQcov xLV7J6ecog vTtoXeC^te^d^aL^ -Jj elneQ xal 
avtd Go67teQ rivco^eva tm deQL 6v^7teQL7]yeto^ ovxet 
dv ovdeteQov ovte ^tQorjyov^eva ovte vitoXeLTto^eva 20 
itpaCveto^ ^evovta de del xal ^rjte iv tatg 7tt7]6e6LV 
ILrite iv tatg fioXatg TtoLov^ievd tLva 7tXdvr]v rj ^etd- 

1. 7caxvfiSQ£6Tccrcc] -cit- e corr. A^ o^stav'] post 6- ras. 
1 litt. A. 2. tav'] -V supra scr. D^. yecoS&v] -d- corr. 

ex X D^ 5. yCyvEGd^ai r^g yfig B. yLVSG&ai D. 6. avtijv] 
-r\- in ras. D^. 8. ItiC D. asC] supra ras. scr. D^. ttjv] t- 
. e corr. D^. 9. ovt] o^ts seq. ras. 1 litt. D. 11. r\ ^aXXo- 
y^hvoiv'] supra scr. D^. 12. ■jiqoXa}i^avov6r\^ post -0- ras. 1 

litt. B; Tr^ocXaft^avovffT]? C, sed -6- del. C^ 13. ftg] tts ra D. 
17. yevoiisva D. 19. GvfinsQii^ytto] -r\- ins. C^. 20. ov8t- 

tSQOv] ovdstSQa A^, mut. in ovSstSQa D^ 21. ds] 8' D. 

Ttti^asaLv] TitriasaL B, cpoQatg D, ^olatg D^. Deinde ins. [irits 
sv rarg cpoQaig mg. BC (pro scholio). 22. poXatg] ntijasaL D. 
7cXdvT]v] ABCD, mg. 79. naQaXXay^v C^ 



26 KAATAIOT nTOAEMAIOr 

^a^LV^ ccTteQ aitavta ovrcjg svaQy&g oq&^sv aTCoteXov- 
^sva cjg ^rjds ^Qadvtfjtog tivog olc^g tj ta%vtYitog 
avtotg aTtb tov ^rj s6tavai tijv yfiv TCaQaxokovd^overjg. 

ifl , "Oti dvo dcacpoQal t&v TCQtotcov iCLV7]6s(hv 
6 sl6lv sv ta ovQav^. 

Tavtag ^sv di} tag vTtod^s^SLg avayxaLCog itQoXa^- 
^avo^isvag sCg tag xata ^iSQog 7taQa866SLg xal tag 
tavtaLg aHoXovd^ovdag dQxs6sL xal ^s%ql tav to0ov- 
tG)v cag sv xsfpaXaCoLg v7totstv7CG)0%aL PsPaLc^d-rj^o^svag 

10 ts xal STtL^aQtvQrjd^rjao^svag tsXsov s^ avtrjg trjg tcbv 
dxoXovd-cjg ;c«l scps^fjg dTtodsL^d^rjao^svcov TtQog td 
cpaLvd^sva 6v^(pcovLag. JtQbg ds tovtOLg stL xdxstvo 
tcbv Tcad^oXov tLg dv rjyii]6aLto dLxaLCjg itQoXa^stv^ otL 
6vo dLacpoQal tatv TtQCJtcav XLV7]6s(hv sl6lv sv tc5 

15 ovQavKty iiCa ^sv v(p ^g cpsQstaL jtdvta ditb dvatoXcbv 
iitl dve^dg dsl coaavtcjg xal L6ota%cbg jtOLOV^svrjg trjv 
TtsQLaycoyrjv xata TtaQakXTJlcov dXXTJXoLg xvxXcdv tcbv 
yQa^pofLSvcov drjXovdtL totg tavtrjg trjg Ttdvta b^aXcbg 
TtsQLayovGrjg 6(paCQag jtoXoLg^ g)v 6 ^syL6tog xvxXog 

20 i6rj^sQLvbg xaXsttaL dta tb ^ovov avtbv VTtb ^syC6tov 
bvtog tov bQctfivtog dC%a Ttdvtote diaLQst^d^aL xal trjv 
xar' avtbv yLyvo^svrjv tov 'fjXCov 7tSQL6tQ0(priv L6r]fiSQCav 
TtQbg al^d^rj^LV 7tavta%ov TCOLStv^ rj ds stSQa, xa%-^ tJv 



4. rj'] om. ACD. ort — 5. ovquvw»'] mg. sup. D. 5. f^atf] 
supra scr. D^ 6. 7CQoaXa}i^ccvoiiivccg D, sed corr. 8. ccq- 
7t£<7£t] corr. ex ccQ-aiGL C^ 9. iv] iy C. vTtoretvTtoad^aL C. 

^EBcciod^Tjao^ivag C. 10. ze] om. D. 13. rjy^GaLTo] -l- 

ins. D. TtQoXa^sLv] tb itQoXa^sLv D. 15. fiLa] seq. ras. 1 

litt. C. 16. Ante inL ras. 3 litt. D. 18. Tfjg] -g e corr. D. 

19. TtoXoLg] corr. ex noXXoLg D. 22. yLvo^ivr]v CD. 23. 
Ttavtaxfi D. t]] corr. ex ai D^ 



MA0HMATIKHS STNTASESiS A'. 27 

at t&v a6xBQG)v 6(patQac xato: ta ivavtCa tri xCQOstQrj- 
^svT] (poQa TtoiovvtaC tivag ^staxLvrJGsig TtSQl jtolovg 
EtsQovg Tcal ov tovg avtovg totg tfjg TCQattjg TtSQia- 
ycjyrjg. xal tavta de ovtcjg exaiv vTtotid^s^ed-a dia 
ro £x ^lv tfjg ;cara ^Cav sxd<Strjv ri^SQav d^scoQCag 5 
jtdvta djta^aTtX&g td sv ral ovQavm xatd t&v o^osc- 
dG)v xal 7taQaXXr]X(ov ta i6rniSQiv^ tcvxXg) toTtaav 
TtQbg aied^rj^tv 6Qd6d'ai, Ttocov^sva tdg ts dvatoXdg 
jcal tdg ^s6ovQavrJ6scg Tcal tdg dv6scg idCov ovtog tov 
tocovtov tfjg 7CQ(6tr]g (poQag^ sk ds tf]g i(psi,fig xal lo 
6vvs%s6tsQag TtaQatrjQtj^scjg td fisv dXXa Ttdvta tcbv 
a6tQ(DV dcatrjQOvvta (paCvs^d^ac koc td JtQog dllrjXa 
dca6trj^ata xal td TtQog tovg ocxsCovg t^ TtQchtri cpoQa 
tojtovg STtl 7tXsc6tov cdccD^ata^ tbv ds rjXcov xal trjv 
6slrjvriv xal tovg 7tlav(X)}isvovg d6tSQag ^stapd6scg 15 
tcvdg Ttocsc^d^ac TtocxClag ^sv xal dvC6ovg dkkrikacg^ 
7td6ag ds wg JtQbg tijv xad^dXov xCvrj6cv scg td TCQbg 
dvatoXdg xal 'bjtoXscjto^sva fiSQrj tcov 6vvtr]Qovvta)v 
td TtQbg dXXrjXa dca6tr]^ata xal m67tsQ V7tb ^cdg 
6(paCQag 7t£Qcayo^svc3v d6tQcov. 20 

sc ^sv ovv xal rj tocavtrj ^std^a^cg tcov 7tXavG)- 
fiEvcjv xatd 7taQaXXvXc3v xvxXov syCvsto t(p C6rj^SQCv(pj 
tovt£6tcv 7tSQl 7t6Xovg tovg tr]v 7tQ(btrjv 7tocovvtag 
TtSQcaycayiqv ^ avtaQXsg dv syCvsto ^iCav riysc6d-ac xal 



2. noXovg] corr. ex iioXXovq D, ut saepius. 3. avtov(s\ 

-xov- e corr. I). 4. 8e'\ 8' D. dta] -d e corr. D. 6. 6(io- 
SLddjvl -si- in ras. post ras. 2 litt. A, dfiOLOsi-dcbv D. 7. xvxZoj] 
om. D, comp. BD^, del. B^. toncov'] -v euan. D. 9. IdCov^ 
corr. ex ISCova D. ISCov oVxrog] corr. ex Idiovvtoq C^, mg. 

ovtog. 12. cpaCvsttti D. 18. avvtTjQovvtcov^ pr. t ins. D^, 

post 7] ras. 2 litt. 19. dXlr]la] e corr. A. 20. aGtSQoav D. 
21. 17] supra scr. B^C^. n7.avoybsv(ov D. 22. xara] corr. 
ex v.al td BC^. syivsto C, corr. C^. 



28 KAATAIOT nTOAEMAIOT 

triv avTYjv Ttdvrcov icsQKpoQav axoXovd^ov rg 7tQ(6tTj' 
TCLd^avbv yccQ av ovtcog scpdvrj Tcal ro triv ycvo^svTiv 
avtcbv iistd^a0LV %a%'^ vTtoXsvipeig diacpdQOvg otal ^ri 
Tiatd dvtcKSi^svrjv xivri6iv aTCotsXsi^d^ai. vvv ds d^a 
5 tatg TCQog tdg dvatoXdg ^stapd6s6iv 7taQa%c3Q0vvtsg 
dsl tpaCvovtai 7tQ6g ts ccQxtovg xal JtQog ^s^rj^PQiav 
^rjds o^aXov d^scoQOv^svov tov ^sysd^ovg tfjg toiavtrjg 
7CaQaxcoQ7]6sc3gy S6ts do^ai dt' i^cod^rj^scov tivcov tovto 
t6 6v^7ttcj^a yiyvsad^ai TtSQl avtovg^ dXX' dvco^dXov 

10 ^sv cog 7tQbg trjv totavtrjv VTtovoiav^ tstay^svrjg ds 
dog 'bTtb xvxXov Xo^ov TtQbg tbv i6rjfiSQivbv dTtotskov- 
fisvrjg' od^sv xal 6 toiovtog xvxXog slg ts xal 6 avtbg 
xal tcbv TtXavcoiisvcov Idiog xataXa^fidvstai dxQi^ov- 
fisvog fisv xal co^tcsq yQacpdfisvog VTcb trjg tov rjUov 

15 xiV^6scog^ 7CSQiodsv6(isvog ds xal V7c6 ts tfjg 6sXrjvrjg 
xal tcov TcXavcofisvcov Tcdvtots 7CSQi avtbv dva^tQS- 
q)Ofisvcov xal firjds xatd tb tv^bv sx7Ci7Ct6vtcov tfjg 
d^cotsfivofisvrjg avtov xad'^ sxaatov Sfp' sxdtSQa td 
fisQrj TCaQaxcoQTjescog. S7csl ds xal fisyi6tog ovtog 6 

20 xvxXog d^scoQSitai did tb ta 1'6g) xal ^OQSibtSQov xal 
voti6tsQov tov CarjfisQivov yiyvsad^ac tbv rjkiov^ xal 
7CSQi sva xal tbv avt6v^ cog scpafisv^ al tav Tclavco- 
fisvcov Tcdvtcov TCQbg tdg dvatoXdg fistapd^sig d%o- 
tsXovvtai^ dsvtsQav tavtrjv diacpoQav tfjg xad^6Xov 

25 xiV7]6scog dvayxatov ijv v7to6tr]6a6d^ai trjv TtSQl 7t6Xovg 



2. ovx(og\ corr, ex ovx(o D^. icpdvrjt A. 4. xar' D. 

ccnoTsXsLGd-uL] -71- 6 corr. C^ post n ras. 1 litt. A. 5. xtkq] 
om. CD. fi£xccpd686L D. 7. ofiaXov] post a ras. 1 litt. A. 

8. i^cod"i]6£(ov] i^od"t]6£G)v C, post -f- ras. 1 litt. D. 9. yLve- 
6^aL CD. 10. 8e] d' D. 15. xs] om. BC. 20.^ xm t6tp] 
corr. ex xb i'6ov C^. 21. yive^Q-ccL D. 22. nXavofiivoov CD. 

25. mvq^soos] -6- corr. ex X in scrib. D. 



MA0HMATIKHS STNTASESiS A'. 29 

tov xat 8 iXrj^^svov Xo^ov xvxXov Koi sig ta ivavtiec 
Tt}g TtQcatrjg (pOQ&g ccTCotskov^evrjv. 

iav 8ri vo7]6g)^6v tbv did^ t&v stdlcov d^cpoteQOJv 
tCbv TtQoecQrjiisvcov KVTckcov yQa(p6nsvov ^syi^tov 
xvxXov^ bg f'! dvdyxrjg sxdtSQov ixsCvov^ tovts6tiv rdv 5 
ts L6r]^sQivbv xal tbv TCQbg avtbv iyxsxXviisvov , di%a 
ts xal JtQbg dQd^dg ycavCag tsfivst,^ ts66aQa ^lv s6tai 
0rj^sta tov Xo^ov xvxlov^ 8vo ^sv td vnb roi) i6ri- 
^SQLvov xatd didiLStQov dXXrjXoig yivo^sva^ xakov^sva 
8s CerjiiSQivd^ cov tb fisv ditb iisarj^^QCag JtQbg aQXtovg 10 
s^ov trjv TtdQodov iaQivbv Isystai^ tb ds ivavtCov 
^stojtcjQivov^ dvo ds td yivo^sva vTtb tov dt' d^Kpo- 
tSQOv t&v TtoXcov yQacpo^svov xvxXov^ xal avtd drj- 
lovoti xatd did^stQOV dXXriloig^ xakov^sva ds tQOJtixd^ 
(bv tb fisv ditb ^serj^PQCag rov l6rjfisQivov %siiiiSQivby 15 
Xsystai, t6 ds dit' ccQKtcjv ^SQivov. 

vorjd^rj^stai ds rj ^sv ^Ca xal jtQCotrj (poQd xal 
7tSQiS%ov6a tdg dXXag 7td6ag 7tSQiyQa(po^svrj xal a67tSQ 
d(poQi^oiisvrj V7tb tov di' diKpotSQcov tCbv ^tokcov yQa- 
(po[LSvov ^syC6tov xvxkov TtSQiayo^svov ts xal td 20 
loi7td 7tdvta 6v^7tSQidyovtog dTtb dvatoX&v i7tl dv6^dg 
TtSQl tovg tov i6ri^sQivov TtoXovg ^sprixotag cj67tSQ 
ijti tov xakov^svov ^s6rj^^Qivov^ bg tovtco ^ovo) tov 



2. q)OQas] corr. ex y,LV . . . D. cc7totsXovfi8V7]v] corr. ex 

ccTCorslovfisvcov D^. 5. Ante xvhXov eras. xv D. eyidcxsQov] 
-o- in ras. D^ 7. tsooccqo] corr. ex tsaasQu D^. 12. ysvo- 
^svcc D. ccficpotiQcov] -cov e corr. D. 13. ■kv-aXov] (isyCGtov 

KvtiXov, -yiGtov in ras., D. yiaC — 20. y.v%Xov] mg. D^ (^tftft), 
in textu supra scr. XsCnsi. 21. awTtsQidyovtog AC. sni] 
slg D. 22. §s§r]yi6tag] BCD, mut. in ^sprjyiota A, in §s§t]- 
Kotog B^. 23. ^sarifi^Qivov, og] corr. ex fis6r](i§QLvovg C. og] 
in ras. B^; corr. ex ag D, ut saepius. tovto)] tov- e corr. B^ 



30 KAATAIOT nTOAEMAIOT 

TtQoeiQrjiievov dLcc(piQ(ov rc5 iiri xal dca rcbv xov Ao|oi) 
xvxXov 7c6X(ov Ttccvtots 'yQ()C(p£6d'aL ati xal dia tb TCQOg 
OQd^ag yovLag t& ^QL^ovtL 6vv£XG)g voaleO^aL xaXettaL 

li£6YlllL^QLv6g ^ i7t£L -§ tOLaVtYl Q^i^Lg £XCCt£QOV t6 t£ 

5 V7C£Q yriv Kal tb 'bjib yfiv rj^L^^paLQLOv dLXOto^ov6a 
xal tcbv vvx^tj^iQcov tovg ^i6ovg ;c()di^ot>g 7C£QLix£L. 
Yj df d£vtiQa xal 7Cokvfi£Qrjg 7C£QL£xo^ivri ^ihv V7cb r^g 
7CQ(btrjg, 7C£QLixov6a d£ tag t&v 7cXavcj^ivcjv 7cdvtc3v 
6(paLQag^ cp^QOfiivrj ^£v V7cb tfjg 7CQ0£LQr]iJLivrjg ^ Sg 

10 £(pa^£Vy dvtL7C£QLayoiLivri d\ eig rd ivavtCa 7C£ql tovg 
tov Xo^ov KvxXov 7c6kovg^ oX oial avtol p£prjx6t£g d^l 
xatd tov tr^v ^CQCotrjv 7C£QLyQa(priv 7COLOvvtog xvxlov, 
tovti6tL tov dt' d^KpotiQav t&v 7c6Xc3v^ 7C£QLdyovtaL 
t£ £ix6tcog 6vv avrw xal xatd f^v £ig td ivavtCa trjg 

15 d£vtiQag (poQdg xCvrj6LV tijv a-^r^v Q-i^Lv d^l 6vvtri- 
Q0V6LV tov yQa(poiiivov Sl' avtfjg ^£yC6tov xal lo^ov 
xvxkov 7CQbg tbv L6rj^£QLv6v. 

d''. II^qI tcbv xatd fii^og xataXrjil;£a}v. 
'H likv ovv 6Xo6x£Qrjg TCQodLakrjxl^Lg cog iv X£(pakaCoLg 

20 tOLaVtriV dv £X0L tijV £X^£6LV tCbV 6g)£Ll6vtCOV 7CQ0V7C0- 

x^L^d-aL' fiiXXovt£g de ocqxs^^ccl tcbv xatd ^iQog dTCo- 
d£C^£C0Vj G)v 7CQ(htr}v VTCaQXSLV rjyov^^d^a^ dt' ^g ^ 

1, diacpiQcov tov TtQosLQrjfievqv D. ro5] corr. ex x&v C, 
supra scr. D^ t&v'] corr. ex ro D^. 2. noXcov] supra scr. D^ 

4. rf] in ras. D^. 5. y?Jv (alt.)] y corr. ex r D^. 6. vvx&r]- 
usQoov'] --9'- ins. D^ xQovovg] xqov- e corr. D. 7. tceql- 

fjjojLtfVr]] ri 7tSQi£xo(isv7] D. 9. q)SQOfiivr]] seq. ras. 1 litt. D. 

Ante tog ras. 3 — 4 litt. C. 10. Ss stg] corr. ex (isv C. rovg] 
corr. ex rijg C^. 13. twv] corr. ex roi^ C*. 14. ts] seq. 

ras. 1 litt. D. 15. ccIsl D. 6vvtr}Qov6Lv'\ GvvtriQOvGLV ot 

TcoXoL A. 16. avtcav D. 18. -9^'] om. ACD. 19. itQo- 

dLdXjiipLg] corr. ex 7rQ068idXri(iipis D. iv] iy C. 22. 7}] 

corr. ex ol C^. 



MA0HMATIKHS STNTASESiL A'. 81 

^Sta^V tcbV TtQOSLQrjfieVCOV 7C6XC3V TCSQL^pSQSia tov Sl 

avt&v yQacpo^svov ^syL^tov %v%kov TtrjkLxr] tLg ov6a 
tvyxdvsL xataXa^pdvstaL^ dvayxatov OQ&fisv tcqosx- 
d^sGd^aL trjv TtQay^atsCav trjg TtrjXLXotrjtog tcbv sv ttp 
xvkIg) svd^SLcov ccTta^ ys ^sXXr]6ovtsg sxadta yQa^^LX&g 5 

djtodSLXVVSLV. 

l'. IIsqI trig TtrjXLXOtrjtog tcov sv t& xvxXg) 

SVd^SL&V. 

IlQbg ^sv ovv tr^v i^ stOLy,ov XQfi^LV xavovLxrjv 
tLva ^std tavta sxd^s^LV TtOLrjao^sd^a trjg TtrjlLXOtrjtog lO 
avt&v tijv ^sv TtSQL^stQov sig t^ t^rj^ata dLsXdvtsg^ 
TtaQatLd^svtsg ds tdg vito tdg xad'' r]^L^OLQLOv TtaQav^ri- 
6SLg tcbv jtSQLcpsQSL&v i)7totSLVOiisvag svd^SLag^ tovtsatt 
Ttdacjv SL6lv t^rj^dtcov d)g tfjg dia^stQOV did ro s^ 
avt&v tcbv S7tLXoyL6^cbv (pavi^66fisvov sv totg dQLd^fiotg 15 
svxQr]6tov sCg qx t^ij^ata dLrjQYjfisvrjg. 7tQ6tSQOv ds 
dsC^onsv^ 7t&g dv hg svu ^dXLdta dt' oXCycjv xal t&v 
avt&v d^scjQrj^dtcsv stf^sd^^dsvtov xa\ ta^stav trjv 
STtLpoXrjv trjv 7tQbg tdg 7tYilLx6tritag avtatv ^tOLoC^sd^a^ 
07tG)g [1^1 ^6vov sxtsd^SL^sva td ^sysd^rj t&v svd^SL&v 20 



1. fieralv] in ras. D^. 2. iiByi6xov\ supra scr. D^. jttj- 
Xlv,7\\ -t} e corr. C^ 3. Tvyxdvsi\ om. A. 5. ancc^'] -n- e 
corr. C. yf] corr. ex xs D^. {iflXri6ovxsg\ -6- e corr. C^, 
mut. in {LBlXri^avxEg B^D^ 7. l'\ om. ACD. r^g nrilL- 

%6x7]xoq\ om. D. Tc5] om. D. 8. hvQ^tL&v] svd^simv v.ccl sv,- 
-^-ffftg yiavovLyn] D. 12. xag vnb tdg\ scripsi, xdg ABCD. 7]^l- 
fioiQLav D. TiaQav^i^esLg^ mut. in Ttagav^rj^Lv D^. Deinde 

add. xal xdg B^. 13. v7Cox£Lvo^Evag\ corr. ex vnoxLVOfi^vag A. 
X0VXS6XLV C, comp. B. 14, Trdffoov] o6cov BC. si^C D, 

comp. B. 17. [idXL6xa\ -l- et -r- e corr. D^. 18. svfisd-6- 
8evxov\ -fi- et -d^ e corr. D^. 19. xi^v] om. D. TtrjXL-no- 

xr}xag] -a? in ras. D. 20. OTrcog] -n- in ras. D^ 



32 



KAATAIOT nTOAEMAIOT 



exca^EV dv£7CL6Tcct(og, alla xal dca rfjg ix r&v yQa^^av 
^sd-odLxfjg avr&v 6v6rd6£(og rbv sX^yxov i^ £vx£QOvg 
H^rax^iQitd^^^^a. xaO^okov ybivroi X9V^^^^^^ ^^^? ^*^^ 
ccQL^^Siv icp6doig xard rbv rijg i^rjxovrddog rQOTtov 
5 did rb dv^xQ^^^^T^ov rcbv ^0QLa6^G)v irL r£ rotg %oXv- 
7tla6La6^oig xal ^£QL6^oig dxokovd"ri6o^£v rov 6vv£yyL- 
^ovrog dsl xara6roxcc^6^£voL^ xa\ JcaO-' o6ov dv rb %aQa- 
X£L%6^£vov fiTjd^vl d^Lol6yG) dLacpiQfi rov jtQbg al'6d"i]- 
6LV dxQL^ovg, 

10 "E6rG) dri TtQcbrov r^^LXvxXLOv rb ABF inl dta^i- 
rQov rfjg A^F 7C£qI xivrQov rb z/, xal .dnb rov A 
rfj AF TtQbg oQd^dg ycovCag 
rix^co rj z/jB, xal r£r ^rj^d^cj 
dCxcc ri A r xard rb E^ xal 

15 i7t£t,£vx^(o rj EB^ xal x^C^d^co 
avrfi l'6ri r] EZ^ xal i7t£^£vx^f^ 
ri ZB. kiycj^ otl rj ^£v ZA 
d£xay(ovov i6rlv %k£VQd^ ri 
d£ BZ 7t£vray(x)vov. ijt^l ydQ 

20 svd^^ta yQafi^i^ rj A F rir^rjraL 

dCxci xard rb E^ xai 7tQ66x£LraC rLg avrri ^vd^^ta ri 
z/Z, t6 V7tb rcbv FZ xal ZA 7t£QL£x6^£vov OQ^oyca- 




1. i%oni8v] 'h%a)- e corr. C^. r&v] t- e corr. D. 3. ^sra- 
XtLQL^miisd^cc] fistaxsLQi^ofisd^a B, corr. in fista^SLQL^oC^sd^a D^. 

XQTiao^sd-a] corr. ex ^^pTjacb/isO-a C^. 5. srt] post s- ras. 1 
litt. D. ts] t- ins. D^ 8. diacpsQSL C. 10. Sri] eras. D. 

11. AJr] e corr. D. J (pr.)] corr. ex A D^. 13. 8l7]x^(o D. 

15. STCs^svx^co 7}] mut. in s7tL^svx^SL6T]g t^s B^; iTtL^svx^siGrjg 
T7)ff, -SL- e corr., D. xat] om. D, eras. B. 16. avf^] avlavtfji, A, 
avtrjL corr. in tavtrjL C^ otat — 17. ZB] supra scr. D^ 16. 
STts^svx^co] corr. ex STtL^svx&o} Cl 17. ZB] Z in ras. A. 

X4yci)] seq. ras. 1 litt. A. 17] in ras. D^, 18. dsKaymvov] 
e corr. D^. 19. EZ] B- in ras. BC^, ZB D. 21. E] seq. 
ras. 1 litt. C. 22. FZ] F in ras. D^ oQd-oLymvLov A. 



MA0HMATIKHS STNTASESiS A'. 33 

VLOV iisxa xov cLTto XYig EJ xexQaycovov i'0ov ecxlv 
xa ccTCo xrjg EZ xaxQaycovco [Eucl. II, 6], xovx86xlv 
xm aito xrjg BE, iTCsl terj i6xlv rj EB t§ ZE. alXh 
Tc3 aiio xr\g EB xsxqayciVGi l'6a b6xI xa ccTtb x&v 
E^ jcal ZlB xexQccycova [Euel. 1, 47]* xb aQa VTtb xcbv 5 
rZ xal Zz/ TtSQiax^iiLEVov oQd^oycovtov fiexo^ xov anb 
xfjg zlE xsxQaymvov l6ov s6xlv xotg ccTtb xmv E/l^ 
udB xsxQayavotg. Kal xoivov acpatQS^svxog xov aitb 
XYig E^ xsxQayavov XoiTtbv xb vitb xcbv TZ xal ZA 
i'6ov s6xlv xa aitb xrjg ZlB^ xovxs6xiv xa aitb rijg 10 
^F' rj Zr ccQa clkqov xal ns6ov Koyov xsx^rjxat xara 
t6 A [Eucl. VI def. 3]. STtsl ovv rj xov s^ayavov ytai 
7j xov dsxaycovov nXsvQcc xcov slg xbv avxbv xwcXov 
iyyQacpo^svcov snl xfjg avxrjg svd-stag axQov aal ^s6ov 
Xoyov xs^vovxat [Eucl. XIII, 9], i^ ^^ ^^ ^^ "^o^ i^ 
xsvxQov ov6a xrjv xov s^ayavov 7tsQLS%SL nlsvQav 
[Eucl. IV, 15 coroU.], r] JZ ccQa s6xlv l'6rj xfj xov 
dsxayavov nXsvQa. o^otcog ds^ snsl rj xov nsvxayo)^ 
vov TtXsvQa dvvaxat xr\v xs xov s^aywvov xal xriv xov 
dsxaycDvov xCov slg xbv avxbv zvxlov syyQacpoiisvcjv 20 
[Eucl. Xin, 10], xov ds BAZ oQ^oycovCov xb aitb 



1. iLEtk zov a-] in ras. C. E/J] JE D. sotlv] laxC B, 
om. D, 2. Tc5 — TovzsGttv] ins. B^, om. C. TOVTfffrt B. 

3. To5] corr. ex to C^ fTCft'] mut. in snsiSi^nsQ D^ r) EB] 
supra scr. D^ 4. to5] corr. ex to C^. iatCv D. ta] corr. 
ex TO C^ 5. tstQciycovcc] comp. supra scr. D^ 7. z/E] 

£z/ D. s6tC B. 8. zJB] V.CU JB D. tstgaymvoLg. yiaC] 
supra scr. D^ 9. tstQaymvov] ins. D^ to] seq. ras. 1 

litt. D. V7t6] V- e corr. D^. tiov] corr. ex tw C. Zz/] Z 
ins.^ C. 10. To5(pr.)] corr. ex to B^C^ 11. ZT] corr. ex ZI Cl 

aQa] aQa svd^sta D. 12. J] A. v.aC ictiv t6 fist^ov tfifjiia 
t6 z/r D. 17J supra scr. A^, ins. Bl 13. stg] e corr. C*, 
corr. ex iy, B^ 14. syyQa(po(isv(ov] pr. y supra scr. A*. 17. 
/(ffrj sGtCv D. 

Ptolemaeus, ed. Heiberg. 3 



34 KAATAIOT nXOAEMAIOT 

rfjg BZ TstQccycovov l'6ov i6tlv t^ te cctco trjg BJ^ 
ritug ietlv i^ayavov TtXevQd^ xal ta ccTtb trjg AZ 
[Eucl. I, 47], ritig i6tlv dexayavov TtXsvQcc^ ri BZ 
ccQa l'6rj i6tlv tfj roi) Ttsvtayd^vov jtXsvQa. 
5 iTtsl ovv^ cog s(pr}v^ VTtotLd-s^sd^a tijv rot» xvkXov 
dicc^stQov t^rj^dtcov qk^ yCvstai did td TtQoxsL^sva ii 
fihv jdE rjfitasia ovfSa tr\g ix tov xsvtQov t^r](idtG}v 
X xal t6 dn^ avtfjg ^, rj ds BJ ix tov xsvtQov ov0a 
t^rj^dtcov I xal tb ditb avtf^g Jy%^ tb 8s ditb trjg EB^ 

10 tovtsdtiv t6 ditb tfjg EZ^ t&v iitl tb avtb j8(p' ^tjxsl 
ccQa s6tai rj EZ t^rj^dtov ^^ d vs syy teta^ xal Xoin^ 
r[\ AZ t&v avt&v X^ d vs. r] ccQa tov dsxaycovov 
jtXsvQd^ v7totsCvov6a ds TtsQKpSQSiav toiovt C3V Ag, oXcov 
ietlv 6 xvxXog tJ, totovtcov s6tat X^ d vs^ olcov iJ 

15 dtd^stQog Iqx. JtdXiv ijtsl r] ^isv z/Z t^r^^idtcov i0tl 
Xi d 'vsj t6 df dnb ai^t fjg jatos d Ts^ s6tc ds xal t6 
dnb tfjg AB t&v avTwv jyx^ d 6vvts%'svta Ttoist t6 
dnb tfjg BZ tstQdycovov ^d%os d t£, ^tjxsl aQa 's6taL 

1. taov] supra scr. D^. 2. s^ccymvov nXsvga] in ras. A. 

3. iart B. 4. 1'67} herCv D. xov] supra scr. D^ 5. iiisC] 
inc. fol. 15 alia manu D. I^qprjv] mut. in sqiccfisv B^, sed 
euan. 8. an'] ano B. BJ] JF, zJ in ras., C^ ov6a] 

om.D. 9. ScTtoi^r.)] A, dn' BCD. 10. EZ] corr. ex ES! D. 

11. htaL] A, e6tCv BCD. 7]] ins. C^ EZ] corr. ex E^ D. 

Post Byyi6xa add. •/• C, mg. (pro scholio): */• ^ffrt ds v.ai rj 
JE X'. 12. zfZ] corr. ex z/S D. 13. xolovtcov] -cav e 

corr. C. otcav] -co- corr. ex o C^. 14. xoiovxcov] corr. ex 

xoiovxov C^. ^6xaL] comp. B, omnibus litteris mg. B^; simi- 
liter saepius; seq. ras. D. 8] ins. D^ oi'cav] corr. ex olov C^ 

15. didfisxQog] ante fi ras. 1 litt. A. ndXiv — 16. vs] BD, 
mg. A^ {■KsCfisvov) et pro scholio C. 15. snsC] ds snsl A^ 

s6xi] i6xCv D, comp. BC. 16. dno] dn D. 'is] inter i 
et s ras. A, mg. yg. x£ A^, supra s scr. 8 B^. l6xiv D. 17. 
z/£] jBz/ D. tc6i/] corr. ex tco A^. 6vvxs%svxa] alt. v supra 
scr. D^ 18. EZ] supra Z ras. D. If] supra s scr. ^ B\ 
f in ras. D. Supra fiT^xft ras. D. 



MA0HMATIKHS STXTASESiS A'. 35 

rj BZ T^rj^dtcov o^ Xp y eyyi^xa. xal rj xov iCEvxa- 
ycovov ccQa TtlsvQd^ vjtoxELVOv0a ds ^OLQag o/3, oimv 
i6x\v 6 xvxXog t|, xoiovxav s6xlv o" A/3 y, otov rj 
did^sxQog QX. cpavsQov ds avxod^sv^ oxl xal rj xov 
s^ayavov TtXsvQa^ vTtoxsCvovda ds ^OiQag |, xal i'6rj 5 
ov6a xfi sx xov xsvxQov x^rj^idxGyv s6xlv |. o^Oicog 
ds^ STtsl ri iihv xov xsxQaychvov itlsvQa^ v7toxsLvov6a 
ds fioiQag 9, dvvd^st diitXa^Ca s6xlv xrjg sx xov 
xsvxQOVf rj ds xov XQiycbvov TtXsvQa^ v7toxsCvov6a ds 
^oCQag Qx^ dvvd^si xrjg avxfjg icxuv XQiTtXa^Cov ^ ro 10 
ds dnb xrjg ix xov xsvxqov x^rj^dxcov i6xlv /yx^ ^vvax^t]- 
6sxai xb iisv dnb xf^g xov xsxQaydyvov TtXsvQag j^6^ 

a 

xb ds ditb xrig xov XQiyavov M^. C36xs xal ^TJxsi ri 
lihv xccg 9 [loCQag vjtoxsCvov6a svd^sla xoiovxcov s6xai 
7td vd T syyi6xa, oicov rj didiisxQog qx, rj ds xdg ~qx 16 
xcbv ai)xcbv Qy vs xy. 

aX8s nsv ovxog ri^lv ix TtQO^sCQov xal xad^' avxdg 
SiX7](pd-co6av., xal s6xai (pavsQbv ivxsvd^sv^ oxl xcbv 
dido^svcov svd^Si&v «| svxsQOvg dCdovxat xal aC vitb 
xdg Xsi7tov6ag slg xb ri^ixvxhov TtSQitpsQsCag vitoxsC- 20 



1. o X^\ oX ^ C. 2. 0^] supra rasuram D^. 4. ds'] 8s 

xat D. xat'] om. D. 5. yLoCqccq] [l AB, ut saepe; \l D semper 

fere. 8. ^jboiqccq] \l ABC, ft D. diiiXciGla] mut. in dLTtXccGlcov 

B^, diTtXccGLcov D. 9. xov\ xov lgotcXsvqov D. 12. roi)] om. D. 

13. Si] 8' D. xov] om. D. XQiymvov] xqi- in ras. D. 

a 01 V 

M] C, corr. ex MAB*, ^ corr. ex jt- post ras. 7 litt. D^; ccco 
add. mg. C^ 15. kyyiGxcc] -gxcc add. D^. 17. Post (ih add. 
ovv comp. C^ 18. Ante yiaC ras. 4 litt. D. saxai] corr. ex 
eaxL D^, mut. in 86X0} B^ svxevQ-sv] avxod^sv, supra avxo- 

ras., D. xoav dido^ivcov] didoiievoov x&v edd.; sed genetiuus 
reconditiore quodam modo a XsLnov6a(s TtsQLcpsQSiag pendet. 

19. at] supra scr. B^C^. 

3* 



36 KAATAIOT IITOAEMAIOT 

vov6ai dia ro r« ait^ ai^tcbv 6vvxi^i^£va jcoieiv ro 
ctTCo rrjg Sia^itQOV tetQayavov' olov^ ETtsidrj ri i)7tb 
tag Ag ^oiQag svd-Eta t^rj^dtcav idsix^rj X^ d vs xal 
t6 aTt' avtfjg at os d Ts^ tb ds ditb trjg dia^itQov 

a 

5 tiirj^dtcov i6tlv M pv^ s6tai xal t6 fihv djtb tfjg 
V7totst,vov0r}g tdg l£i7tov6ag slg t6 ri^iKvxXiov [lOiQag 

a 

QlLd tcov XoiTtcov M^yxd vs ]ibSy avtri ds ^rjxsi tcov 

avtav Qid ^ It, syyi^ta^ xal inl tcov dklcov b^oCcog. 

ov ds tQOTiov dnb tovtcov xal aC koiJtal tcbv xatd 

10 fiiQog do%"ri6ovtai^ dsi^o^sv ig^s^rlg JtQosxd-i^svoi At^ft- 
^dtiov sv%Qri6tov Ttdvv itQbg tr]v 7taQov6av jtQay- 
^atsCav. 

s6tco yaQ otvxXog iyysyQa^^ivov s^cov tstQaitksvQOV 
tv%bv t6 ABF^ ^ Tcal i7tst,svx^co6av aC AF xal B^. 

15 dsixtiovj oti t6 V7tb tcbv AF xal BA 7tSQiS%6^svov 
OQd^oydyviov l'6ov i6tl 6vva^(potiQOig ta ts \J7tb tcbv 
AB^ AF xal tco V7tb t&v AA^ BF. xsC6d-co yaQ Tg 
V7tb t&v ABF ycovicc t6ri rj V7tb ABE. idv ovv xoiv^v 
7tQo6d-S)^sv f^v i)7tb EBA^ s6tai xal rj V7tb ABA 

20 ycovCa L'6r] tfj V7tb EBF. s6tiv ds xal r] VTib BAA 



2. oiov\ corr. ex otcov B*C. 4. tf] supra s scr. ^ B*. 5. 

M?^ corr. ex jt A, ^vqi e corr. D^ 6. |u.ot^as] \i> mut. in ^ A*. 

" o of _ 

7. M\ corr. ex \i A*, ^v^t e corr. D^. j] corr. ex p D^ 

'^'^ supra scr. s B*. 8. X^ supra scr. g B^ 9. lomai^ 
-01- e corr. C^ tcov] om. B. 11. Tta.vv\ om. B. 13. Mg. 
lr\\i\i.a BC. 14. xv%6v~\ om. D. Ar\ corr. ex ABT T). 

15. devnTsov — BJ\ supra scr. D^. otl\ ovv otl D^ 

16. to5] corr. ex rd C^ 11. AB, jr\ e corr. D. to5] corr. 
ex t&v D. TiSLod-co — 18. /JBr\ supra scr. D^. 18. twv] 
om. D^ 17] supra scr. D^ Post ABE add. insl ovv tar] 
iotlv 7] (supra scr. D^) vnb JBF yojvCa tjj vnb ABE D et mg. 
pro scholio BC; /• add. C^ ovv\ om. D, del. C. 




MA0HMAT1KHS ZTNTASE^S A'. 37 

r?J vTto BFE f^rj [Eucl. III^21]* t6 yaQ avto tfiij^a 

V7t0t£LV0V6LV' L^OyCOVLOV CCQK B6tlv TO ABA tQLyCOVOV 

t(p BFE tQLydivcf). co€tE xccl 
avdloyov fVriv, cjg rj BF TtQog 
tijv FE^ ovtcog rj BzJ TtQog triv 5 
z/^ [Eucl. VI, 4]* ro ccQa vno 
Br^ AA l6ov B6t\v rc5 vno 
5z/, FE [Eucl. VI, 16]. ' Ttdhv 
ijtal l'6rj £6tlv rj vjtb ABE ycovLa 
XT} 'bno /dBF ycovLcc^ £6tLv dh %a\ lo 
«5 v7to BAE l'6r] tfi V7tb B^F^ i6oy6vLOv ccQa i6t\v 
tb ABE tQLycovov ta BF^ tQLycovG)' dvdloyov ccQa 
£6tLV^ (hg ri BA TtQbg AE^ rj Bzi itQbg z/F* ro ccQa 
VTtb BA^ ^r t6ov i6r\v rc3 V7tb BA, AE. idELx^rj 
d£ xa\ tb VTtb BF^ AA l'6ov rc5 vjtb 5z/, FE- xa\ 15 
oAov [Eucl. II, 1] ccQa ro VTtb AF^ BzJ l'6ov i6t\v 
6vva^q)0t£Q0Lg rc5 t£ vjtb AB^ ztF xa\ ta vitb Az], 

BF' 07t£Q £d£L dEL^aL. 

tOVtOV 7tQO£XX£%^£VtOg £6tG) rj^LXVxXLOV tb ABFzJ 

i7t\ dLa^itQov trjg AA^ xa\ d7tb roi) A dvo dLrJx^co- 20 



3. rw] e corr. D^ 5. trjv (alt.)] om. D. 7. BT] z&v 
FB D. ' 8. BJ] JB C, T&v Bd corr. ex t6 BJ D^ 10. 
yavLa] om. D. 11. -Ttb BJF — 12. rQLycovov] mg. B^. 

11. tcoymvLOV — 12. T^tycbvoj] mg. C^ 11. ^ffrt C^ comp. B. 

12. ABE] BAE C^ Ta5]'corr. ex no B\ ex ro D^ EFz/] 
B/ir BC^. tQLyo^va)] rQiymvmvcoL etiam in textu C. 14. Ante 
BA ins. ra>v D». J r] Tz/ D. sarL B. tw] corr. ex ro D^. 

AE] EA D. 15. To] corr. ex to5 B^C^ ' imo (pr.)] vnb 

robv B^D. BF — vno] om. C. ' BT — FE] mg. B^ in 
textu ras. 4 litt. ET, AJ] BJ, FE B^D. loov] -ov in 

ras. A'. To5] corr. ex to D^. Ez/, FE] r&v BT, AJ B^D. 

16. AF] rcav AF D. iarL D. 17. <;i;i/a^(jpoT^90/p] (7- corr. 
ex v in scrib. D. J F] FJ D. 18. BT] FB D. 19. 

rovro t6 d^smQTjiiu %a^' vTtSQOxrjv XsysruL mg. B pro scholio^ 
y mg. D. 20. A] seq. ras. 1 litt. B. 



38 KAATAIOT nXOAEMAIOT 

(Sav ai AB^ AF^ xal £6t(D axatSQa avtcbv do^Et0a tc5 
^sysd^SL^ OLCov 7] did^stQOs dod-st^a qk^ xal STts^svx^a 
ri Br. Xsycjy ort xal avtri dsdotai. S7tst,sv%%^(o6av 
yag at jBz/, F^' dsdo^svai 
5 aQa si6lv drjlovoti xal avrat 
dia tb XsiTtsiv sxslvcov stg tb 
rj^ixvxXiov. STtsl ovv sv kvkIco 
tstQccTtXsvQdv s6tiv tb ABFzJ^ 
tb ccQa vTtb AB^ FA ^sta tov 

10 V7tb tcbv Azfy BF laov s6tlv 
rc3 'bTtb AFy Bz/. xai s6tiv rd 
ts vjtb t&v AF^BA dod^sv xal tb vjtb AB^ Fz/' xal 
loiTtbv ccQa tb vnb A^^ BF dod^sv s6tiv. TiaC s6tiv 7] 
AA dici^stQog' dod^st^a ccQa s6t\v xal rj BF svd^sta, 

15 ^al (pavsQOv r]^tv ysyovsv, ort, sav dod^&^iv dvo nsQi- 
cpsQSiai xal at V7t avtag svttstai^ do%-st6a s6tai xal rj 
trjv v7tsQ0%rjv tcbv dvo 7tSQi(psQSimv v7totSiVOv6a svd^sta. 
dfiXov da, ^ti dia tovtov tov d^scoQTJ^atog dlkag ts ovx 
okCyag sv^sCag syyQccil^o^sv ccTtb t&v sv tatg xad"^ avtag 




1. avxmv] om. D. 2. ^] supra scr. D^ 4. JBz/] corr. 
ex B-4 C^ 5. ccQa daCv^ om. D. 8. xEtqd7cXEVQ0v~\ -nXsv- 
supra ras. 2 litt. D. 9. ccqo] supra scr. D. Post V7t6 add. 
r&v D^. 10. T&v] om. D. BT] B e corr. B. 11. BJ] 

BJ (/ C, JB D. KccL — 12. do&tv] BD, mg. C^ om. A. 

11. SGTLV D, comp. B. 12. rs] om. A. r&v AF, BJ] 

AB, r^ D. xat] doQ-sv kccl AC, dod-hv ds %ccl A\ AB, 

rj] AF, BJ D. 13. dod-^v sGzLv] -v del. C, sgxlv do^sv D. 

xat] ins. D^ sgxlv] mut. in sxl B^, ixl D. 14. Post 

SidfisxQog add. SoQ^slgcc B^C^ sgxlv] sgxccl D. 16. at vn'] 
corr. ex sn' D^. do&SLGu sgxccl] dod^SLoaL oiGLV sgxccl do- 

^SLca D. sGxaL] mut. in coct C^. 17. vnsQOxriv] post q 

ras. 1 litt. A. 18. oxl] oxl v.aC D. xs] mg. B^ ov-a] in 
ras. B^ 19. blCyaq] -XCy- in ras. D^ iyyQdtpoyiSv] pr. y 

in ras. D^. v.aO'' avxdg] v,ax' avxdg D. 




MA0HMATIKHS STNTASESiS A'. 39 

Ssdo^evcov vitBQOx&v koX drj xal triv v%o tag dcbdexa 
fiOLQag^ eTCSidTJTtSQ sxo[isv t7]v ts VTtb tag | xal t^v 
VTtb tag 0/3. 

Ttdkiv TtQOKSL^d-cj 8o%'sC6Yig tivbg sv^sCag sv tcvkIg) tr^v 
vTtb tb 7]^L0v tfig VTtotSLVO^svT^g TtSQLCpSQsCag svd^stav 5 
svQstv. Kal s6t€0 r^^LJcvTchov ro ABF snl dia^stQOv tijg 
AF xal do&st6a svQ^sta yj FB^ 
xal 7} FB TtSQLcpSQSLa dCxa ts- 
t^Tj^d^cj xata tb z/, xal sits- 
tsvxd'co6av ai AB^ AJ^ 5z/, lo 

;e zr ^^9 ^^^ ^^^ "^^^ ^ ^^^ "^^^ 
AF xdd^stog ^-O-co rj ^Z. Xsyco^ 

otL T} Zr Yj^C6sLd s6tL tfjg tcbv AB xal AF vnsQ- 

OXVS' xsC^&a yaQ tfl AB l'6i^ i^ -^E^ xal iics- 

t,svx%G) 7} AE. STtsl 1'67] s6tlv r] AB tfj AE^ xolv^ 15 

ds 7] AA^ dvo dri at AB^ AA 8vo tatg AE, 

A^ l'6aL SL6lv sxatSQa sxatsQa. xal ycovCa r] vnb 

BAA yovCa tfj vTtb EAz/ l'6rj s6tCv [Eucl. 111,27]' 

xal pd6Lg ccQa rj BA pd6SL tfj AE l'6r] s6tCv [Eucl. 

I, 4]. dXkd Y} BA tfi jr l'6Y] s6tCv' xal y] AT aQa 20 

T§ AE l'6r] i6tCv. sjtsl ovv l6o6xslovg ovtog tQLyco- 

vov tov AEF ditb tYJg xoQvcpfjg sjtl tY]v ^d6LV xdd^stog 

1. dsdofiivcovl dsSofiivaig D, -aig eras. dmde-na] l^ D, 

2. ju-otpag] fi, v7totsivov6ccv D. 3. Post o§ add. o D, onsQ 
fSsL Ssi^ocL D^ 4. ^ mg. D. svdstag xivog D. 6. vn6\ 
V- e corr. D. 6. xat] om. D. 7. sv&sia r) FB tiaC] ins. D^ 

FB] Br D. 10. at] om. C. 13. iazLV D. 16. AB] 

BA J). Svo] Sv6L D. AE] EA D. 17. tfeat] coit. ex 

i'6a D. s-aatiQa] seq. ras. 3 litt. B. 18. BAJ] corr. ex 

ABT D^ i6tLV — 20. i6tLv] mg. B^ 19. ^ai] om. D. 

%at — 20. i6TLv] om. C. 19. i6tLv i'67] B. 20. &Xld] 

aXla ■Aai BD. AT] FJ D. i6r} i^tCv] A, i^ttv i'6ri BD. 

Seq. 'nal i] JF aga ty JE i'6r] i^tCv mg. B^, del. B^ /^F] 
rd D. 22. JET] rJE D. 



40 KAATAIOT nTOAEMAIOT 

YjKtai 17 z/Z, l'6rj £6tlv ^ EZ tfi Zr [Eucl. I, 26]. 
«AA' ri EF oXrj r] vtcsqox^ i6tLv t&v AB xal AF 
evd-SL&v rj ccQa ZJT ri^C6sid i^tiv trjg tav avtcov 
v7t£Q0xr}g. &6t£^ STtsl trjg vjtb tijv B F n£Qi(p£Q£Lav ^vd^^Cag 
6 i)7C0}C£L^£vr]g avtod^^v didotaL xal rj X^Citov^a sig tb 
'^fiLXVKhov '^ AB^ dod^Tje^taL xal rj ZF ri^C6£La ov0a 
trig t&v AF xal AB v7t£Q0%r]g. aXl^ £7t£l ev oq&o- 
ycovCc) rco AF^ xad^itov dxd^^C^rjg rijg z/Z lcoyavLOV 
yCvstai tb A^F OQd-oyavLov t^ ATZ [Eucl. YI, 8]^ 
10 WX.C £6tiv^ hg r\ AT %Qbg r!^, r\ TA itQbg TZ, tb 

CCQa VTtb tCbV AT^TZ 7t£QL£x6^£VOV OQd-OyCJVLOV l'6ov 

£(5tlv ta ccTtb tfjg Tzf t£tQayiov(p. doO-fv d£ tb vTtb 
t&v AT^ TZ' dod^lv ccQa £6tlv ocal tb aTtb trjg T/t 
t£tQdyG)vov. G)6t£ xal ^7JX£L rj T^ svd-^ta Sod'7]6£tai. 

15 f^v r]^C0£Lav v7tot£Cvov6a trjg BT 7t£QL(p£Q£Cag. 

xal Slcc tovtov dr] 7tdlLv tov d^^oQ^ij^atog dkXai 
ts Xr](pd-'i]0ovtaL 7tl£L6taL xatd tdg r]^L6£Cag tcbv 7tQ0£x- 
t^&SLfiivcjv^ xal dr] xal aTtb tfjg tdg t/3 ^oCQag v7tot£L- 
vov6r]g svd^^Cag iq t£ vTtb tdg g xal r] V7tb tdg y xal 

20 r] V7tb ti]v fiCav 7]^l6v xal r] V7tb tb r]}ii6v titaQtov 
tf]g jiiag (loCQog. £vqC0xo^£v dl ix t&v i^tLloyL^iicbv 



2. aXld D. 4. bvQ-ECas] svdsCccg dod-eCaris ^ 5. vno- 

v.si^svTjs] del. D. Supra scr. ijroi dsdo^ivrjs B^, dsdo^svr]s 
mg. C*. ds8oxccL] corr. ex SCSoTui D. 6. Ante pr. ij ras. 1 
litt. D. xat] postea ins. D^ 7. insi] om. D. 8. tc3 

Arj] TQiyihvco Tc5 AJr D. 9. AJT] ATJ D. JTZ] 

rJZ corr. ex JZ D^. 10. Tz/ (alt.)] mut. in JT Cl 11. 
ifcov] add. D^ 12. dod^sv d^ — 14. rsTQdycovov] om. A. 

12. Ss] 6i sariv D. 13. FZ] FZ nsQisxoiisvov D. 16. rrjv] 
e corr. A. jBT] e corr. D^ nsQicpsQsCas] -s e corr. C, 

nsQicpsQsCccs onsQ sdsi dsi^ai D. 16. s mg. D. 17. nQos-n- 
nd-siisvcov D. 19. 5] s^ B. 20. ^[jnav (utrumque)] comp. 

BD. ro] vr]v D. rhccQrov] 8' D (similia posthac non 

notabo). 




MA0HMATIKHS STNTASESiS A'. 41 

tijv ^lv 'bnh tijv ^Cav rj^cav ^oiQav tOLovtcov a Xd Te 
syyi^ta^ olcov £6tlv rj dLcc^stQog qtc^ tijv ds vjcb tb 
L! d' tG)V avtCbv o fi^ Tj. 

ndliv B6t(o xvxkog 6 ABFzl %£qI didiietQov ^sv 
tijv AA^ xsvtQOV ds ro Z, xal ditb tov A aTtsiXTJq^d-o- 5 
0av dvo nsQKpiQSiai dod-st^ac xatd ro s^rjg aC AB^ 

BF^ xal S7ts^svx^(06av aC 
AB^ BF vn avt dg svd-stac 
xal avtal dsdo^avac. Xsycj^ 
ort, sdv STttisv^co^sv ti^v 10 
AF^ dod^TJestac xal avtn]. 
di7]x^(o ydQ did tov B did- 
^stQog rov xvxkov ri BZE^ 
xccl STts^svx^cj^av aC 5z/, 
z/F, FE^ J E' drjXov drj avto&sVy ott did ^sv 15 
tijv Br dod-7]6staL xal rj FE, dcd ds tr}v AB do^rj- 
6stac 7] ts -Bz/ xal rj ^E. xal did td avxd totg 
's^nQ06%'Sv y insl iv xvxXco tstQaitksvQov i^tiv ro 
BFAE.^ xal diriy^ivai slgIv aC BA, FE, ro vnb t&v 
dirjy^ivcov nsQLSxo^svov OQ^oyuiVLOv l'6ov ictlv 6vva^- 20 
(potiQOLg totg vnb tcbv djtsvavtLov w6ts^ insl dsdo- 
^ivov tov vTcb tav BA, FE didotac xal ro vnb 
t&v -BJT, z/^, didotaL aQa xal ro vjtb BE^ FA. di- 

1. Supra cc scr. ivog B^. 2. rd] rrjv D. 3. /.'] in 

ras. A. o] A, o BCD, ovdsv comp. A^D^ 7. inL^ivxd-a)- 

cccv BC; 67tL^sv\ D, -Gi add. D^ 8. sv&^scaC] corr. ex sv- 

^sCag D^. 12. Sia] ano D. 14. STiit,sv%%(iiGav BC. 15. 

^r] TA D. d?)] 8s D. avxo^sv] post -d- del. i C. 8ia\ 
in ras. D^. 16. 8o%-r\6sxai (alt.)] do4i]6ovxai D. 17. xd] corr. 
ex X D». 18. iv] -v in ras. D^. 19. BJ, FE] in ras. A. 
20. s6XLv] -V eras. D. 21. vno] v- in ras. D^ 22. Bz/] 
BT C. dsSoxai] corr. ex dCSoxai Dl 23. BF] mut. in Bz/ C*; 
BE, rj supra scr. D^. dfdorat (pr.) — FJ] om. D. -Soxai 
— 8s-] mg. A^ SsdoxaL (alt.)] dsSovxai D, sed v eras. 



42 KAATAIOT nTOAEMAIOT 

dotac ds xal ri BE dLa^srQog, xal loLJtij r] T^ Idxai 
Ssdo^svrjy xal dca xovto xal rj k£i%ov0a sig xb rj^Lxv- 
xXlov ri FA' co6X8^ iav do%-cb6iv dvo neQLCptQSLaL xal 
at VT(! avxag svd^staL^ dod-T^^sxaL xal rj 0vva^g)oxsQag 
6 xag 7CSQLq)SQSLag Tcaxa avvd^s^LV v7toxsLVOv6a svd^sta 
dLo: xovxov xov d^scoQijfiaxog. 

cpavsQOV df, oxL 6vvxL%'svxsg asl ^sxa xcbv tcqosk- 
xsd^SL^svcjv 7Ca0cbv xrjv v%h xriv a C ^otQav %a\ xocg 
6vva7txo^£vag STtLXoyL^o^svoL 7tcc6ag ccTtX&g syyQd^o^sv, 

10 o0aL dlg yLVo^svaL xqlxov p^SQog £%ov6lv^ zal ^ovaL sxl 
TtSQLXsLcpd^T^^ovxaL at ^sxa^v xcjv dva d L! ^otQav 
dLa6xrj^dxc3V dvo xad'^ sza^xov s^o^svaL^ S7tSLd7]7tSQ 
Kad'' rj^L^OLQLOv 7tOLOv^sd-a xijv syyQacpriv. cj6xs, sdv 
xiiv vTcb xb rjiiL^OLQLOv svd^stav svQco^sVy avxrj Ttaxd 

15 xs xrjv 6vvd-s0iv ocal xr^v v7tSQ0%riv xrjv 7tQbg xdg xd 
dLa6xrj^axa 7tsQLS%ov0ag %al dsdo^svag svd^sCag xal 
xdg XoLTcdg xdg ^sxa^v 7td6ag rj^tv 0vvava7tXr]Qd)6sL. 
STCsl dl dod^SLdrjg XLvbg svd^SLag cjg xf]g V7tb xrjv d /.' 
^OLQav rj xb xqlxov xrjg avxrjg ^tSQLcpSQsCag v7toxsCvov6a 

20 dta xG)v yQa^u&v o\) dCdoxaC TCcog' sl ds ys dvvaxbv 
rjv^ sl'xo^sv dv avxod^sv %al xijv 'bTcb xb rjfiL^oCQLOV 

1. Se] corr. ex di D^. AotTrrjJ ij Xoimfi A. Deinde add. 
oLQa D^ i]\ BC, 17 vnb xriv AD, vno v^v eras. D. 3. FA] 
AT onsQ bSsl dst^aL D. 4. vno D. $od'^6staL'] corr. ex 

dod"^GovtaL D^ 6. tovtov] tov\tovtov C, om. D. tov] tov 
xoLovtov D. 7. r°T mg. D et in textu D^ 8s] mut. in ^r/ 
B^D^. nQ0sv.xL%-s^sva}V D. 9. evvantoiLivag] -n- in ras. D^ 

syyQatpoiisv] pr. y in ras. D^ 10. ocrat] corr. ex 06 at C^D^ 

ysv6(isvaL D. 11. nsQLXsL(pd"rj6ovtaL] corr. ex nsQLlT]q)d"ri- 
covtaL C^D^ x&v] post ras. 3 litt. D. 13. ■nad''] v,al xa-O'* D. 

14. avtri] BC^, avtfi A et corr. in avtri D, avrij C. 15. 
xdg] corr. ex ra A. 16. dsdoiiivaq] -(is- supra scr. A*. 

17. Tag(alt.)] xat Tccg corr. ex xara D. 19. fiOLQav] sic AC. 

7] to] corr. ex ijtoL D. tfjg avtjjg] corr. ex tiig D^ 20. 
SCdotaL] dsdotai corr. ex dsScotaL D. 



MA0HMATIKHS STNTASEiiS A'. 43 

TtQotSQOv ^ed^odsv^o^sv trjv vjtb tijv a ^olqccv icTto ts 
tfjg vTcb trjv d L! ^oiQav xccl rijg vnb C ^' vJtod-e^svoL 
Xrj^^dtLOV^ 0, Tcdv ^rj TtQbg ro xad^oXov dvvrjtai tdg 
TtrjXiocotrjtag 6ql^slv^ sitC ys tmv ovtcog sXa%C6t(x)v tb 
TtQbg tdg G)QL6^svag aTtaQdlXaKtov dvvaLt dv 6vvtrjQstv. 5 

ksyco ydQj ort, sdv sv xvxXc) dLax^G)6LV dvL60L 
dvo svd^staL^ rj ^sC^cov ^Qbg tijv iXd66ova sXd06ova 
koyov s%SL 7]7tSQ rj STtl tfjg ^sC^ovog svd^sCag TtSQLCpsQSLCC 
TtQbg tfjv STtl trjg sXd60ovog. 

s6tcj yaQ xvxXog 6 ABF^^ xal dLYii^^co^av sv avtw 10 
dvo svd-staL avLdOL sXd66cov [isv r] AB^ ^sC^cov ds 'fj 
BT. Xsyco^ otL fj FB svdsta 
TtQbg tfjv BA svd^stav sXd6- 
0ova Xoyov s^sl r]7tsQ rj BT 

TtSQLCpSQSLa TtQbg tfjV BA TtSQL- 15 

(psQSLav. tst^rjad^co yaQ rj vTtb 

ABF ycovCa dC^a vTtb tfjg 

Bz/, xal s7tst,svx%-co6av i] ts 

^ AET xal ^ Azf xal fj Tz/. 

xal sjtsl f} vTtb ABF ycovCa dC^a tst^rjtaL vTtb 20 

trjg BE/i svdsCag^ l'0r} {liv s6tLV r] TA sv^sta r§ 




1. /Ltf-O-o^fvffOftfr] corr. ex fied-odevGa^sv C^. 2. fioiQavl 

om. D. -uTrd] vno x6 D. 3. XT][i^dxt,ov\ -xi- in ras. A. ft^] 
corr. ex jLtot C^. 4. 7triliv.6xr\xoig\ corr. ex TtrjXrjyitioxTixag C. 

iX(xx^6xcov~\ corr. ex iXdxLGxov C^. 5. mQLafiivag] «(njoftfVag 
corr. ex oiQLGfiEvag A^. _ dvvaix' dv'] dvvaxai J). 6. ifnnia 
mg. BC. aviGoi 8vo\ (3 dviGoi D. 7. iXaGGova (^r.)] ante v 
ras. 2 litt. A. iXdaGova (alt.)] AD, om. BC, add. C et mg. B^ 

8. ^LEL^ovog] -g in ras. D^ 9. inC] ait6 B. iXdxxovog D. 

11. avLGoi Evd-ELai D. 12. FB] BT J). 13. 7tQ6g — 15. 
TCEQLcpEQEia] mg. B^C^ 13. Evd^ELav] om. B^D. iXdxxova C. 

14. i]7t8Q] 7] C^ Br] rS B^D. 15. TCQOg TtSQLCpSQBLav] 

et in textu C et in mg. C^. 16. ? mg. D. 17. dL^a ycovLa D. 
20. xal insi] iTtsl ovv D. 



44 KAATAIOT nXOAEMAIOT 

A/1 [Eucl. III, ^2^, 29], ^ffctav d\ ^ TE tijg EA 
[Eucl. YI, 3]. ^x^f^Gj d^ ccTtb tov z/ xdd-srog stcI 
tijv AEF rj AZ. eTtsl tOLVvv ^h^cdv i6tlv rj (isv 
AA tr\g EA^ rj ds EA trjg z/Z, 6 ccQa xsvtQG) ^ev 
5 tca A^ dua^tri^ati ds tw AE yQacpo^svog xvxkog 
t^iv ^lv AA ts^st, 'i)7CSQ7Cs6sttac ds tijv z/Z. ysyQci- 
(p^c3 dij 6 HE&^ xal SK^s^lri^d-G) rj AZ®. xal iTtsl 
6 ^isv AES to^si)g iisl^cov s6t\v rov AEZ tQLychvov, 
t6 ds ^EA tQLycovov ^st^ov tov AEH to^scog, tb 

10 ccQa AEZ tQLycovov TtQbg tb AEA tQiycovov sXd6- 
6ova Xoyov sxsl i^TtSQ 6 AE& to^svg TtQbg rdv AEH, 
dXX' G)g ^sv tb AEZ tQLycovov JtQbg tb AEA tQLycj- 
vov, ovtcog rj EZ svd^sta TtQog tijv EA [Eucl. VI, 1], 
d)g d^ 6 AE® to^svg itQbg tbv AEH to^sa^ ovtcog 

15 't] V7tb ZAE ycovLa TtQbg tijv vjtb EA A' rj ccQa ZE 
svd-sta TtQbg tr^v EA ikd^^ova Xoyov s^sl rJTtsQ 17 
vTtb ZAE ycovLa TtQog tijv vTtb EAA. xal ^vvd^svtc 
ocQa r] ZA svd^sta TtQog ti^v EA skd66ova Xoyov sxsi 
T^jtSQ i] vTtb ZAA ycovia jtQbg tijv vnb AAE' xal 

20 r«v riyov^svcov td dLTtXdOLa^ rj FA svd^sta TtQbg ti^v 
AE iXd66ova loyov s^sl iJTtSQ r] vitb TAA ycovCa TtQbg 



4. 6 &Qa] 6 cc~ e corr. D^ fisv'] om. D. 5. diaGri^^atL 
St] xal diccGtrjaati D. 6. tsfist] corr. ex tifivsL D. z/ Z] 

corr. ex AZ B\ AZ C. 7. HE@] corr. ex E& D, supra 
ras. 1 litt. y.al ineL] intl ovv D. 8. iatLV — 9. [1£l^ov] 

supra scr. D^ {ictC). 10. Tb dEZ aga tQLycovov TtQog tbv 

JE& tonia iXdttova Xoyov i%SL iJtcsq tb JEA tQLycovov TtQbg 
tbv JEH tofiia • ivaXld^ mg. pro scholio B et nonnullis uerbis 
recisis C. JEA tQLyavov] a? atQLycovov D. 11. Ante Xoyov 
ras. 1 litt. A. 12. t q Ly cov ov (sdt.)] om. D. 13. EA] AE B, 
corr. B^ 14. rofiia] om. D. 15. Post pr. vno ras. 1 litt. C. 
16. 1^] add. D^. 17. ZJE — vno] supra scr. D^ EJA] 
E^A ycovCav D. 20. TA] FA aQa D. 21. FJA] seq. 

ras. 1 litt. A. 



MA0HMATIKHS STNTASESiS A'. 45 

T^v vTcb E^ A' Ttal dLskovn 1] FE svd^sta TtQog tijv EA 
iXd06ova koyov eiei i^tcsq yj vTtb FzlE yavCa TCQog tr^v 
vTcb E^A. aXV dyg ^sv r} FE evd-eta TCQOg tijv EA^ 
ovtog 7} FB ev^sta jCQbg triv BA [Eucl. VI, 3], cjg de 
7} VTcb FAB ycovCa iCQbg triv vicb BAA.^ ovt&g r\ TB TceQi- 5 
fpSQeia iCQbg tr\v B A [Eucl. VI, 33] * r\ TB aQa evd-eta 
^Qbg tijv BA eldaGova Xoyov e%eL r\7CeQ rj FB TceQC- 
<peQeia JCQbg tijv BA TceQKpsQSLav. 

rot^rov 8ri ovv vTCoxec^evov 
e6t(o KvxXog 6 ABF^ xal di- 10 
?J%0'G5^ai' ev avtcp dvo evd^etac 
ri te AB ocal r\ AF^ v7COKeC0d-o 
de TCQ&tov ri ^ev AB vtco- 
teCvov6a ^cag ^oCQag C 8\ r} 
de AF ^otQav d. enel rj AF 16 
evd-sta TCQbg tijv BA sv^stav 
eld06ova loyov s%si ^tcsq rj AF TCSQKpsQsca TCQbg tijv 
AB, rj ds AF icsQLipsQSLa STcCtQLtog s6tLv trlg AB^ ri 
FA ccQa svd^sta trjg BA sXd66c3v s6tlv i^ STcCtQctog. 
aXXd r\ AB sv^sta s8sCjpr\ tOLOvtcov o ^^ r\^ otcjv 20 
s6tlv r\ dLd^sTQog ^* r\ ccQa FA svdsta sXd66c3v 
s6tlv tcjv avtcbv d p v' ravra yaQ sjcCtQLtd s6tLV 
iyyL6ta t&v o ^^ rj. 




1. EJA] AJE D. disXovtL 07] disXovtTqi D, t supra 

scr. D^ 3. E/JA] A e corr. C^ svd-Eta] om. D. 4. 

tvd-etcc] om. D. 5. 7} (pr.)] om. C. BJA] -B e corr. D^. 

6. rrjv — 7. tzqos] mg. B^ 6. 17 — 7. BA] add. C*. 8. 
^SQicpiQSLccv onsQ dsL (sdsL D^) SsL^aL D. 9. ^ mg. D. ovv] 
om^ D. 13. 7] }isv] pLsv ij D. 14. fiL&g] supra scr. D^ 

15. a] mut. in a^ D^ 17. 17] supra scr. A^, om. C. Mg. 

t6 Xfifxiia pro scholio BC. 20. 0] o C, ut saepius. 21. FA] 
AF I). 22. sitLXQicta. C. 23. ?j] supra scr. D^ 



46 KAATAIOT nTOAEMATOT 

ndXiv inl tijg avtrig ocatayQatpfjg ij ^lv AB 
sifd^sta v7Cox6L0d-(D v7totsCvov6a ^OLQav a, i^ <^^ ^^ 
ILOiQav a i\ ocata xrft; avta dij^ sicsl ii AF TtSQicpSQSia 
trjg AB s6tcv rnLioXCa^ tj FA aQa svdsta tijg BA 
6 sXd66(DV s6tlv i^ rj^ioXiog, dXXd tr\v AT d7Csdsi%a^sv 
toiovtcjv ov6av d Xd is^ olcov s6tlv rj did^stQog ^* 
17 ccQa AB sv&sta ^sC^cjv s6tlv tcbv avtcjv a ^ v' 
tovtcov yaQ rj^idXid s6tiv td TCQOxsC^sva a Xd Ts, 
&6ts^ STCsl tcbv avtcbv sdsCx^yj xal ^sC^cav xal skd66cov 

10 ri trjv iiCav ^otQav v7CotsCvov6a svd^sta^ xal tavtrjv 
drjXovoti s%o^sv toiovtov d p v syyi6ta^ Oicov s6tlv 
7] did^stQog ^, Tcal 8id td 7CQodsdsiy^sva xal trjv 
{)7cb tb 'fi^i^oCQiov, ijtig svQC6xstai tcbv avtG)v o Xa xs 
iyyi6ta. xal 6vvavaTcXriQC3%"ri6stai td Xoi7cd^ cog sq^a^isv^ 

15 6ia6t7]^ata sk ^sv tijg 7CQbg trjv ^iCav 7]^i6v ^otQav 
Xoyov svsxsv cjg S7cl tov 7CQG)tov dia6t7]iiatog 6vv- 
d^s6sc3g Tov rj^i^oiQCov dsizvv^svrjg trjg vTcb tdg /3 
^oCQag, SK ds tijg v7CSQ0%^g tijg 7CQbg tdg y ^oCQag 
xal trjg V7cb tdg /3 /.' dido^svrjg' co^avtcog ds xal stcI 

20 t&v Xoi7Ccbv. 

r] ^sv ovv 7CQay]iatsCa tcbv sv ta xvxXco svd^si&v 
ovtcog dv oi^ai Qa6ta ^staxsiQi^d^sCrj. Xva ds^ cog s^prjv^ 



3. TCSQicpiQSia — 5. ^r^ mg. D^ {'ntLfiivov). 4. rjiiLohos 
icTiv D^. FA aga] AF D\ BA] ABD^ 6. ovcav] supra 

scr. D. 7. AB] BA D. 8. a Xd Ti] corr. ex ^ dls D^ 

9. &6t' D. 12. TCQOVTcodedsiy^Eva D. 14. ag erpa^BV tu 
Xomd D. 16. TcqmTOv] corr. ex a D^. gvv^^soscqs] D (-? e 
corr.), T^g GvvQ^EGsoiis ABC. 19. xat (pr.)] eras. D. 22. 8s] 
8' D. ^cpr^v] corr. ex Btpr} C*, scpr} B. 



MA0HMATIKH2 STNTASE^iS A'. 47 

i(p exd^trjg tav xqblcov £| itOL^ov tag jcrjhxdtritag 
81(0 ^ev tG)v svd^SLcbv ixxsi^avag, xavovia vTtotd^o^sv 
ava 6tiiovg jis di« tb 6v^^etQ0v ^ d)v ta ^sv TtQcota 
^iQTj TtSQii^SL tdg nrjXixotrjtag t&v TCSQKpSQSLUiv xa%^ 
rj^L^OLQLOv TtaQrjv^rj^ivag^ td ds dsvtSQa tdg tcbv 5 
jtaQaxsL^ivcov tatg TtsQLtpsQSLaig svdsL&v TtrjlLXotrjtag 
cog trjg dLa^itQOv tcbv 'qx t^rj^dtcov VTtoxsL^ivrjg ^ td 
ds tQLta t6 A' ^iQog tfjg xa^ sxa6tov rj^L^OLQLOv tcbv 
svd^siGiv jcaQav^7]6scog, Xva s%ovtsg xal trjv tov svhg 
i^rjxo6tov y.i6rjv iitL^ol^v d8Lacp0Q0v6av TtQog atd^riGLV 10 
tr]g dxQL^ovg xal tcov ^sta^v tov rj^L^ovg ^isq&v s% 
itOL^ov tdg i7tL^aXkov6ag JtrjXLXotrjtag iitLXoyL^s^d^aL 
dvvco^s^a. svxatavorjtov d\ otL d^d tcov avt&v xal 
jtQOxsL^ivcov d-scoQrj^dtcov^ xdv iv dL6tay^a ysvcofisd^a 
yQa(pixfjg d^aQtLag tcsql tLva t&v iv tw xavovCc) TtaQa- 15 
xsL^ivcov svd^SLav^ QadCav JtOLrjao^sd^a ttjv ts i^ita0LV 
xal trjv iTtavoQ^co^Lv rjtOL dito tfjg 'bjtb tfjv dL7tXa6Cova 
tfig iTtL^rjtov^ivrjg t) tf]g TtQbg dXXag tLvdg tcbv dsdo- 
[livcov vTtSQOxfjg rj tfjg tfjv ksC7tov6av slg tb rjiiLXvx- 
Xlov jtSQLcpiQSLav v7totSLVOv6r}g svd^sCag. xaC i6tLV rj 20 
tov xavovCov xatayQatpf] toiavtr]' 



1. XQSi&v] mut. in xQV^^foav D^. 3. avd~\ ins. D^. ctLxovg] 
ccGZLxovg, -L- corr. ex o, D. 6. ijiiifio^^QLov D. 6. neQi- 

(pSQSiccig] -tg e corr. C. 8. >l'] X ABC, TQicaioGtov D. fj^i- 
(lo^QLOv D. 9. ivcc txovtsg'] bis D, sed corr. 10. aSicccpo- 

Qovaav] mut. in aSiacpoQOvg av A^. afad-rjaLv] -aiv in ras. B^. 
11. i^ stOL(iov] om. C. 12. e7tL§aXlovaag'] -tcl- in ras. B^ 

13. dvvdiiEQ^a BC. d'] 8e D. 14. yevoiisQ^a C. 16. ttjv] 
tfi extr. lin. A, triv A*. 20. %aL sativ] satLv ds D. 21. 

v,atayQa(pfi\ diayQacpfi D. TavT?] D. 



48 KAATAIOT nXOAEMAIOT 

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1. la'] om. ABCD. 



i'] U o D. 12. /lis] fiE^ D. 



13. fis (alt.)] ^d' D. 14. }id] (ly'' D. 17. fia] nd" D. 20. 
^8] vd BC. voc] vd D. 22. Xs] mut. in W Bl 23. ly] 
U^ D. 24. 1] a AD. 28. Is] ly D. 29. xy] %|3>' D. 

32. \i^] corr. ex |* A^, ^'i D. 33. is] -s in ras. C. 37. 
t^alt.)] ^ D. 39. Tia] %d'^ D. 40. xa] x5" D. a (alt.)] |3 C, 
corr. C*; §" D; item lin. 41—47. 42. va] vd" D. 43. 

ta] mut. in lB B^. 44. g] tg D. 46. vy] v8 D. 47. %8] D, 
corr. ex xa A\ xa BC, corr. B^ 

Ptolemaeus, ed. Heiberg. 4 



50 



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51 



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8. ta] id D, mg. ta. 9. tj] v BC. 12. a(pr.)] l D. 14. 
(iS'] S e corr. A, (la D. 16. Z (alt.)] Xcc D. 17. Xy] Xz^ D. 

18. 8] d^ D. 20. Mg. s D. 21. XS] ia BC, corr. B*. 

23. a(alt.)] inras.A. 26. «(pr.)] ^s D. 27. Xt (alt.)] Xs^ D. 

a] d D. 29. ;i^] -t eras. A. 30. v&] -d- e corr. A. 31. 
Xr}] -rj in ras. A. 32. Xd^] X C. 33. Xd^] in ras. B^ (i C. (i?] 
mut. in (i^ B\ (is^ D. 36. Xy] Xy^ D. 38. Mg. s D. 39. 
X] a D. 42. p,y (alt.)] (l8'^ D |:a^] ^B? D. 43. «] a" D. 



44. (1^8 (alt.)] |Ltf^ D. Mg. y D. 45. Mg. tg D. 



46. ^a-] i-a* D. 
4* 



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vs 


xd 


Ag 


o 


o 


vs 


^ 


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vs 


v^ 


xg 





o 


vs 


h 


V? 


v<5 


K 


./J 


o 


o 


vs 


xs 


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vsr 


^? 


vd 


o 


o 


vs 


^l 


25 vt, 


vi 


VS 


ky 


o 


o 


vs 


^ 



MAOHMATIKHS STNTASEiii: A'. 



53 



vtC 


vt 


(lY 


5 





o 


VB 


a 


vri 


VI] 


l 


^ 


o 


o 


vd 


vy 


VTjL' 


vr, 


xn 


' 


o 


o 


vd 


ILE 


V» 


V» 


i 


oct 


o 


o 


vd 


K 


!/«■/.' 


V» 


A/S 


il6 


o 


o 


vd 


71%' 30 


1 


1 


O 


O 


o 


o 


vd 


na 


1/.' 


1 


^t 


la 


o 


o 


vd 


iP 


1« 


1 


v8 


li 


o 


o 


vd 


d 


^aL' 


1« 


xa 


L^ 


o 


o 


vy 


vg 


ip 


1« 


firj 


li 


o 


o 


vy 


fit 35 


i^' 


tP 


iS 


i 


o 


o 


vy 


1% 


%7 


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iiP 


o 


o 


o 


vy 


X 


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iy 


V 


lie 


o 


o 


vy 


kP 


1* 


ir 


Xs 


KS 


o 


o 


vy 


ly 


iSL' 


is 


P 


P 


o 





vy 


d 40 


%B 


%s 


7t7l 


M 


o 


o 


v^ 


VE 


$«/.' 


is 


VE 


a 


o 


o 


v^ 


/t*sr 


Is 


is 


xa 


itd 


o 


o 


v^ 


A? 


i?L'- 


1* 


^y 





o 


vfi 


xri 


u 


Is 


iy 


v% 





o 


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1. TtSQLcpsQSiaL D. 3. vy] xy C. 6. i-O"] in ras. A. 9. jlwj] 
-7} in ras. B^ 11. i; (alt.)] seq. ras. 1 litt. D. 12. trj] trj- B, 
mg. ■9' B^ 13. i;a(alt.)] corr. ex v§ D. 15. t?] ts" B, mg. 
^BK 20. vd (alt.)] VE^ D. 21. [i] fia D. 22. ve (sec.)] vs* D. 
24. V? (alt.)] vt^ D. 25. vt (alt.)] vtj^ D. 26. v^ (alt.)] 

vri^ D. 27. VT] (alt.)] v^'? D. 28. rr; (alt.)] v-^'? D. 29. X^] -^ 
in ras. C. 30. vd- (alt.)] vd^ D. 33. |] |" D. 37. o (pr.)] 
ILE D. 38. [ie'] h^ D. 39. ;if] as? A. ne] |3 D. 40. 

p (alt.)] Xa D. 43. ^e] in ras. A. 44. |f] in ras. A. 45. |g] 
m ras. A. v^] corr. ex ^ A*, X^ D. 46. |s] in ras. A. 



54 



KAATMOr nTOAEMAIOT 



nsQupB- 




svQ^eL&v 




S^7\V.06t&V 




QSl&V 
















In 


it 


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c^ 


o 


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15 


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1* 


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vri 


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o 


va 


(ly 


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iv 


xy 


Vd' 


o 


o 


va 


ly 





In 


ii^ 


^e 


o 


o 


va 


■ 7cy 


or 


i» 


ts 


«e 


o 


o 


va 


Ld 


Ott 


l» 


(la 


d 


o 


o 


va 


d 


oaL! 





S 


Ag 


o 


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fie 


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vt 


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vg 





o 


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vp 


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o 


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o 


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ly 



MA0HMATIKHS LTNTABESiS A'. 



55 



JC 


ol 


V 


e 


O 


o 


m 


y 


^L 


0? 


x^ 


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o 


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Tta 


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vg 


P 


o 





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01? 


Ld- 


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o 


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X 30 


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iri 


o 


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ny 


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X 


vp 


o 





f*ff 


^ 


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v6 


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o 


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^^ 


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lia 


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sr 


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1. TcsQKpsQSicit D. 2. 1^] |- in ras. A. 4. vrj] fitj D. 

1]] in ras. B^ v C. 10. S] D, y ABC, cfr. p. 122, 4, 10. 

11. v^] va BC. Xs] X- corr. ex tj A*. 14. o§] o- euan. C. 

17. vT]]Xri D. 18. v§] x^ D. 19. t^] in ras. Bl 23. 
x^] x£ D. 30. n§] seq. ras. 1 litt. A. 31. n§] -§ e 

corr. A. 32. ny] seq. ras. 1 litt. A. 33. nyi'] e corr. A. 

38. fi£] -« in ras. D. 39. ty] t^ C. 43. (iS] -S in ras. D, 
ut hoc loco complura. 



56 



KAATAIOT nXOAEMAIOT 



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S^r}%06t&v 




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X% 


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MA0HMATIKHS LTNTASESiS A'. 



57 



Q^L' 


^y 


-Xs 


la 


o 


o 


1%' 


ly 


W 


9Y 


vd 


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id 


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9d 


Xy 


lia 


o 


o 


xn 


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vp 


vn 





o 


Xrj 


xa 30 


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cp 


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3. fiy'] vy D. 
euan. C. 16. jital euan. C:' * 27. tif] X^ B"d. 29. Xd] Xy 
BC. 37. rs] i;£ D ■ ~ ~ 

X8-\ Xb BC. 



13. %%•] nri D. 15. x^ %^ D. ^a] 

. C. 27. ft^] Xt BC. ^ . 

44. ti\ -E in ras. C. 46. [i^] X<5 D. 



58 



KAATAIOT nXOAEMAIOT 



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ev&eLm 


, 




£|7]xo<yrcov 




Qei&v 
















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MA0HMATIKH2 STNTAgEiiS A'. 



59 



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2. Xd(pr.)] yicc D. ;i* (alt.)] D, corr. ex Xa A, Xa B et 

in ras. C 3. Id] Xa D. x] in ras. C^. 4. s] in ras. Cl 

6. xf] -s e corr. A. 8. ta] i^d D. 13. o (tert.)] 0^*6,« 
eras. 14. Xa] -a in ras. D. fts] fiy D. 18. ^] (i8 D. 

23. pxy] Q- postea ins. A. 24. ity] xij D. 27. ^l^] -# e 
corr. A, 29. >t^] x- in ras. A. 46. v§] v- e corr. A. 



60 



KAATAIOT rrrOAEMAIOT 



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MA0HMATIKHS STNTAgjEiiS A'. 



61 



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7. cc] i c. 8. v-e-] v c. »]] v c. 

^a D. 16. 8] Kd B. 17. xg] vg D. 

id D. 28. TiQ'] x£ D. 30. ^8] k§ D. 

(id] corr. ex (xa A^, (la D. 35. 8] fi 

43. ft] e corr. Bl 46. (icc] va D. 



QLu] corr. ex qi^ C^ 

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27. xa] %8 D. ta] 

31. rj] V CD. 32. 

BC. 40. ^] vp A. 

li] l^' D. 



62 



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14. X^] Xy C. 16. x£] -« in ras. C. 22. X8'\ corr. ex 

id C. 29. ^oa] -o e corr. A. ty] -y e corr. A. 31. /Ltd] B^, 

fitt ABCD. ^f] X^ D. 35. va\v8 D. 36. i] «• D. 42. 

vb] vd J). 



64 KAATAIOT nTOAEMAIOT 

i^\ UsqI tilg ^eta^v tcbv tQOTCLTCQbv TtEQicpeQeCaq, 

'ExtEd-SL^svrjg d'^ trjg Tttj Xtxotrjt og t&v iv t(p xvxlo) 
svd^Siav TtQcbtov av etri^ xad^aTteQ el'7to^sv, dei^at, Tto^ov 
6 lo^bg xal dta ^e0(ov tCbv t,G)dC(ov Tcxmkog eyxexlttat 
5 TtQog tbv L6Yj^eQtv6v, tovteattv tCva Xdyov e^et 6 dt 
a^ifOteQCDV tCbv exxet^evcov TtoXcov ^eyt^tog xvxlog 
TtQbg tijv ditoXa^pavo^evrjv a^btov ^aTalv tcbv TtoXcov 
TteQttpeQetav^ fi l'0rjv ccjtexet drj^ovott xal tcov tQoittxcbv 
exateQov 0rj[ieCcov tb xatd tbv Carj^eQtvdv. avtod^ev 

10 ^' 'fj^tv tb totovtov oQyavtx&g xataXa^ipdvetat dtd 
totavtrjg ttvbg djtXrjg xata0xevrjg, 

7totrj6o^ev ydQ xvxXov %d}.xeov Cv^^ietQOv tat ^sye- 
d^et tetoQvev^evov dxQt^cbg tetQaycovov tijv eitttpdv etav^ 
& XQV^Ofied-a fie6rj^PQi,v^ dtelovteg avtbv eCg td vTto- 

15 xeC^eva tov [leyCetov xvxlov t^rj^ata t^ xal tovtcov 
exaetovy eCg o6a eyxcoQet ^eQrj' eTtetta eteQOv xvx- 
XC6X0V XeittdteQOv vitb tbv etQi^^evov evaQ^66avteg 
ovtcog^ G)6te tdg ^ev TtkevQdg avtcbv enl ^tag ^evetv 
eTtttpaveCag^ iteQtdyedd^at de dxcoXvtcog {)7cb tbv iieC^ova 

20 dvva0d-at tbv eld66ova xvxkov ev ta avt^ eTttTtedco 
TtQbg aQxtovg te xal ^e6rj^pQCav, TtQodd^rjao^ev eTtl 
dt^o ttvcbv xatd dtd^etQov t^rj^dtcjv tov eld66ovog 
xvxXov xatd tYjg eteQag t&v TtkevQcbv 7tQt6iidtta fitxQd 



1. t^'] om. AD. rfjg] corr. ex t&v D^. 3. EinofiEv] 

corr. ex El7tco(iev B. 4. t&v] om. D. iyn^y.XritccL C, corr. C . 
8. fj'] 7] A. 9. ro] mut, in td D^. 10. dLdXuiL^dvstai, D, 
12. Tts qI 'KataGiisvfig mg. B, v.ataav.Evfig mg. C. 14. w] e 
corr. B, tfig nsQKpsQsCag tp D. 18. ^iv — jLitag] bis C, sed 
corr, Post (livsiv del. — B. 22. ■nata] t&v yiatd D, t&v 
ins. B^ 23. nvtiXov] 'av%XC6v,ov D. TtQiafidtLa] mut. in 

Tcrjyiidtia C^, Ttr^yfidtia corr. ex 7tQLy(idtLa D', 



1 



MA0HMATIKHS STNTASESiS A'. 65 

i!6a vs^ovtcc TtQog ccXXrjXd xe xal tb xevtQOV tcbv 
xvkXcjv ccKQL^cbg TtaQad^svtss xata fis6ov tov TCldtovg 
avtG)v yvcj^ovca ls%td 0vvd7ttovta tfj tov ^si^ovog 
xal dLfjQrj^svov xvkIov %ksvQa. ov dri xal svag^o- 
6avtsg dotpaXag snl tcbv TtaQ^ sxa6ta %QSLcbv STtl 5 
6tvlL6K0v 6v^iistQ0v xal xata6t7]6avtsg sv VTtaLd^QCt 
tijv tov 0tvXL6KOv pd6LV sv aKhvsL TtQog tb tov 6ql- 
^ovtog STtLTtsdov sddcpSL TtaQacpvM^o^sv^ oitcjg tb STti- 
Ttsdov tcbv kvkXcjv TtQbg ^sv tb tov bQL^ovtog OQd^bv 
^, Td5 ds tov ^s6ri^^QLVov TtaQdXkrjXov rovtcov ds tb lO 
lisv TtQotSQOv dtd xad^stLOv ^sd-odsvstaL KQrj^va^svov 
Hsv aTtb tov Katd KOQvcprjv s6o^svov 6r]^SL0v^ tr^Qov- 
lisvov ds, scjg dv sk trjg tcbv 'bTtod^s^dtcov dtOQd^co^scDg 
STtl t6 xatd dtd^stQov 7toL7]6rjtaL tr]v 7tQ66vsv6Lv, tb 
ds dsvtSQOV ^s6r]^PQLvr]g yQa^^rjg sv67]^cog sikr]^^svr]g 15 
iv ta V7tb tbv 6tvkL6Kov STtLTtsdco Kal 7taQaq)SQO^svc3v 
sig td TtXdyta tcbv kvkXcov, sog dv 7taQdlXr]kov tf] 
yQa^i^f] t6 STtLTtsdov avtcov dL07ttsvr]taL. tOLavtrjg d?) 
trjg d^s6scog yLVO^svr]g str]QOv^sv rrjv TtQbg aQKtovg 
Kal ^s6r]^PQLav tov rjXiov 7taQa%G}Qr]6Lv TtaQacpSQOvtsg 20 
sv tatg [is6r]^pQLaLg rbv svrbg kvkU6koVj ecog dv t6 
v7tOKdtco 7tQL6^dtL0V oAoi' vq)' oAov tov VTtSQaVCO 

1. iGo] v,cu laa. D. 2. ftfffoi;] corr. ex [leaov D^ 3. 

yvconovia IsTttcc gvv-'] supra scr. D^ 4. ivagfioaavTsg] corr. 
ex ivaQfio^ovtsg D^. tcsqI Q-86soog mg. BC. 6. xaraGrifffa»'- 
xsg] ■na&LGzdvtsg D. 7. ayiXLVSL ^ et mg. >jW ^. e. naQ- 

aXXriXoi) B. 9. t6] supra scr. D^. 10. Post ^ ras. 1 litt. D. 
11. x^rjju-vorfifVov] B^D^, v.Qvybvaiisvov ABCD. 12. GrnisCov'] 
corr. ex G7](istov C^ 13, av] a extr. lin. A, corr. A*. vno- 
^s^atLcav BD, corr. B*. 15. svG^fi^cog C. slXr\iLHvrig D. 

16. naQacpsQoiLsvaiv'] CD, 7tSQiq)SQO(isvcov A^B. 18. nsQl 

XQ-nGsoog mg. BC. 21. fisGT^fi^QivaLg D, sed corr. 22. TtQiGfid- 
TLov] mut. in 7tr]y(idtiov C^; 7tr]y(idtL0v, 7] e con*., D. tov] 
corr. ex to D^ 

Ptolemaeus, ed Heiberg. 5 



ee KAATAIOT nXOAEMAIOT 

axicced-y, xal rovtov yLVOfievov disarniaivev rj^tv ta 
tG)v yvco^ovicov axQa^ 7t66a tfiyj^ata tov xata xoqv- 
(priv ixdetots tb tov rjXiov xevtQov d(ps6trjxsv ijcl 

XOV U£6rj^PQLV0V. 

5 stL ds £v;up?^0TdT£()Ov iTtOLOVfisd^a trjv toiavtrjv 
7CaQati]Qrj6iv xata0X£vd0avt£g dvtl tcov xvkXcov Xl^C- 
vrjv 7] ^vXLvrjv jcXLvd^Hda t£tQdycovov zal ddLd6tQO(poVy 
b^aXrjv fiivtOL xal d7tot£ta^£vrjv £xov6av dxQL^ag trjv 
it£Qav tcbv 7tX£VQcbVy i(p '^g nivtQG) xQV^d^£V0L GrjusLot 

10 tLvl TtQog tfj ^La tcbv ycovLcbv iyQdipa^£v xvxXov 
t£taQtrj^6QL0Vy ijtL^si^^avt^g dTtb tov xatd t6 xivtQOv 
erj^SLOv ^£%QL tfjg y£yQa^^ivrjg 7t£QL(p£Q£Lag tdg trjv 
VTtb t6 t£taQtrj^6QL0V dQd-rjv ycovLav 7t£QL£%ov6ag 
£v^£Lag xal dL£l6vt£g o^OLCDg trjv 7t£QL(piQ£Lav £Lg tdg 

15 9 fiOLQag xal td tovtcjv ^iQrj. fi£td ds tavta i7tl 
liLdg tG)V Evd^ELcbv tijg ^£XXov6rjg OQd-fjg t£ £6£6&aL^ 
7tQbg t6 tov OQL^ovtog i7tL7t£dov xal 7tQbg ^£6rj^PQLav 
trjv d^i^LV £%£LV i^7toXL6avt£g OQd^d xjoI L'6a 7tdvto^£v 
dvo xvlCvdQLa fiLXQd xatd t6 o^olov t£toQV£v^iva^ t6 

20 ii£v iTt avtov tov xatd t6 xivtQov 6rjii£Cov 7t£Ql avtb 
t6 ^i6ov dxQL^cbg^ t6 ds 7tQbg ta xdtcj 7tiQatL tfjg 



1. 6v.icc6%'^'\ 6- euan. A. du^riiiccvsv corr. in di86i]fir}- 

v£v D^. 2. yvcofiovcov D. 5. tcsqI xaraGxsvTjg tiXlv&lScov 

mg. BC. evxQri6Tor£Qav D. 6. Xid-^^vriv B. 7. nXrjv^ida 
BCD, corr. D^. ccdLcc6tQocpov'\ A, add. iv (om. D) ^vyniizQcp 
nXcczsL ytaL ^ccd^SL nQog tb ps^rjyievccL v,atd ■HQOtacpov BD, et mg. 
pro scliolio C {oifiaL 6(po:X^a add. eadem manu). 8. ccTto- 

t£\tsta^8vrjv D. 10. iyQccipaii£v~\ iyQ- in ras. A. 11. yisv- 
tQov D. 12. 6r]fisiov] corr. ex ^rjfisiov C. tds\ supra 

scr. A^ 14. SL£X6vt£g] corr. ex. disX&ovt^g B^C. 15. ini] 
yiatd D. 16. fisXov^rjg D. ts s^sed-aL] tCd^s^&aL D. 17. 
3r^dg(pr.) — xaef] om. B, mg. C^. 18. i(i7toXi6avtsg] mut. in 
iv£7toXL6a\tsg B^, ivs7toXi^6a^sv D. 19. -iivXLvdQLa] post v 

eras. x D. bfioLov] b- ins. D^ 



i 



MA0HMATIKBS STNTASES^S A'. 67 

Evd^SLccg, STCSLta L6tdvteg tavtrjv trjv xatccyeyQafi^svrjv 
tfjg nkivd^idog nXsvQav TtaQa triv iv rco vtcoxsv^svg) 
STtiTtidc} dirjy^ivrjv ^sdrj^pQivriv yQa^^rjv^ co6ts xal 
avtrjv TtaQaXXrilov s%siv tr^v d^icvv rc5 tov fis6rjfL- 
Pqlvov iTtiTtido}^ xal xad^stLCJ dLcc t&v xvkLvdQLCov 5 
aKhvrj ts nal dQd^rjv TtQog ro ijtLJtsdov tov oQL^ovtog 
trjv Sl' avtcbv svd^stav axQt^ovvtsg VTto^s^atC&v TtdlLV 
tLvcbv XsTttcov tb ivdiov dLOQd^ov^ivcov itrjQovfisv 
G)6avtG)g iv tatg ^sdrj^^QLaLg tijv djtb tov TtQbg ta 
xivtQG) xvXlvSqlov yLvoiiivrjv 6KLdv jtaQattd-ivtsg tc 10 
TtQbg tri xataysyQa^^ivrj jtSQLcpSQSLCc itQbg tb Tcatadrj- 
XotSQOv avtrjg tbv tOTtov (pccLvsdd-aL %al tavtrjg tb 
lii6ov 6rj^SLOv^svoL tb xar' avtov t^rj^a tr]g tov 
tstaQtriiLOQLOv TtSQLfpsQsCag iXa^^dvo^sv dLa6rj^atvov 
drjXovoti trjv xatd itldtog inl roi) ^s^rjfiPQLvov JtdQodov 15 
tov iikCov. 

ix drj t&v toLovtcov 7raQatrjQ7j6sG)v xal ^dXt^ta 
tG)V TtSQl tdg tQOTtdg avtdg ri^tv dvaxQLVO^ivcov ijtl 
TtXsLOvag jtSQLodovg td l'6a xal td avtd t^^tj^ata tov 
^s6r]^PQLvov xvxXov Tcal xatd tdg d^sQLvdg tQoitdg xal 20 
xatd tdg ^SL^SQLvdg trjg 6r]^SLG)6sG)g G)g i^Citav djtb 
tov xatd xoQvcpijv d7toXa^pavov6rjg 6rj^sCov xatsXapo- 
fisd^a trjv ditb tov poQSLOtdtov jtiQatog iitl ro votLcj- 
rarov TtsQlcpiQSLav^ rjtLg i6tlv rj ^sta^v tcbv tQOTtLX&v 

1. nsQi ^^ascog mg. BC. 3. yqa^riv C. 5. v,vXLvdQaiv D, 
deinde del. ax^t^cr xe Y.aL. 6. av,Xivfi'\ dv.XLVst" D. xs] 

postea ins. D. 7. ndltv" xlv&v B. 8. XsTtxibv'] in ras. D, 
Xsnxov BC. neql xqtigscois mg. BC. 9. mGavxaig] dfiOLoos D. 
xb v,ivxQOv D. 10. wXLvdQOv D. 13. avxov] a-uro seq. 

ras, 1 litt. D. 14. diaarnLatvov] 8- in ras. A, 17. 8ri\ postea 
ins. B. 20. v.axd'] supra scr. A^. 21, cbg] supra scr. A. 22. 

6r]^SLov\ corr. ex crjiistov C, supra scr. D^, 24. nsQicpiqsiv A. 
S6xt A. 17] supra scr. A^ xQOTttvcbv] x- postea ins. C. 

5* 



68 KAATAIOT nTOAEMAIOT 

t^rjlidtcov^ jtdvtots yivo^svrjv ^^ Tcal ^Si^ovog ^ev tJ 
difiOLQOv tfiTJ^atog^ sXdd6ovog ds 'fj^i6ovg tEtccQtov, 
di ov avvdystai ^xsdbv 6 avtbg koyog rd5 tov 'EQa- 
toCd^Bvovg^ a Tcal 6 "I^TCaQxog 6vv£%Qri6ato' yCvstai 
5 yaQ toiovtcov rj [ista^v tcav tQOTtixcbv Td syyi&ta^ 
oXg)v s6tlv 6 ^s6rj^PQivbg %y. 

svXrjTCta ds avtod^sv soc tfjg TtQOKSi^svrjg TCaQatr^Qrj- 
escog yCvstai %a\ td tcbv oiTcrj^scov^ sv alg dv jcoid)- 
^sd^a tdg trjQr]6sig^ syxXC^ata Xa^^avo^svcov tov ts 
10 ^sta^v 6ri^sCov t&v dvo TCSQdtcov^ 6 yCvstai Tcatd tbv 
i6rj^SQiv6v, Tcal trjg ^sta^i) tovtov ts xal tov Tcatd 
xoQvcprjv 6rj^sCov jcsQicpSQsCag^ i] l'6rjv drjkovott Tcal ot 
7c6koi tov oQC^ovtog dcpsatijxaeiv. 

iy\ nQola^pav6^sva sCg tdg 6(paiQi7cdg dsC^sig. 

15 'Axokovd-ov d' ovtog dTCodst^ai xal tdg xatd fiSQog 
ycvo^svag TCrjhx^trjtag tcov aTCoXa^pavo^svcov icsQicps- 
QSicbv ^sta^i) rov ts i6r]^SQivov Tcal tov did ^s6cov 
tG)v t^GidCcov kvkXov t&v yQacpo^svcov ^syC6tcov xvxXcov 
did tG)V tov i6riiLSQiV0v jcolcov TCQOSxd^rj^o^sd^a kr]^- 

20 ^dtia ^Qa^sa xal svxQrj^ta^ di^ g)v tdg jcksC6tag 6xs8bv 
dsC^sig tcbv 6cpaiQiXG)g d^scoQov^svcov^ cog svl ^dXi^ta, 
d7Ckov6tSQOv xal ^sd^odix^tsQOV TCOirj^^^sd^a, 

sCg dvo drj sv^sCag tdg AB xal AF diaxd-st^ai 



2. di] 8s i] B. 3. rc3] t6 C. 5. fisra^v] -|- postea 

ins. C. 13. TtoXoi] noXloC C. 14. ly'] C, yt B, om. AD. 

15. ovtog] -V- ins. D^. 17. (isaov D. 21. 6(pccLQL%a)v 

'd-8a}Q7]}idr(ov D, supra scr. 6(p8QLV.a)s ^sajQovfiiva^v D^. 23. 

8lg dvo d^q] postea ins. D. a' Xrjfi^ix svd-vyQau^ov %atcc 6vv- 
^S6LV mg. BC. 



MAeHMATIKHS STNTAgESiS A'. 69 

dvo svd^etaL rj ts BE xal rj Iz/ ts^vst(o6av aXk7]las 
xata To Z drj^stov. 

^.syco^ oti 6 trig FA jtQog AE loyog ^vvYiiitai sx. 
ts roi) tijg F^ TtQog z/Z xal tov tfjg ZB TtQog BE. 

^X^Gi y^Q ^i'^ 'fov E tri Pz/ itaQaXXriXog rj EH. 5 
STtsl TtaQaXXriXoC sl6iv aC FJ %al EH^ 6 trjg FA 
TtQog EA Xdyog 6 avtog s6tiv ta 
trjg rj TtQog EH [Eucl. YI, 4]. 
slco^sv ds rj ZA' 6 ccQa trjg FA 
TtQog EH Xoyog 6vyxsi^svog s6tai 10 
SK ts tov trjg FA TtQog AZ xal 
roi) trjg AZ JtQog HE' S6ts zal 
6 tijg FA JtQog AE X6yog 0vy- 
Tcsitai SK ts tov tfjg FA TtQog 
AZ ocal tov tijg AZ TtQog HE, 15 
s6tiv ds xal 6 trjg AZ TtQog HE Xdyog 6 avtog t^ 
trjg ZB TtQog BE [Eucl. YI, 4] dia to TtaQaXlriXovg 
TtdXiv slvai tag EH xal ZA' 6 aQa tijg FA TtQog AE 
^,6yog 6vyKSitai sx ts tov tijg FA TtQog AZ xal tov 
tijg ZB TtQog BE' ^TtsQ itQosKSito dsi^ai. 20 

xata ta avta ds dsixd"t]6stai^ oti xal xata SiaC- 
QS6iv 6 tijg FE TtQog EA X6yog 6vvij7ttai sx ts tov 
tijg rZ TtQog AZ xal tov tijg AB TtQog BA^ dicc tov 
A tri EB TtaQaXkriXov dxd^sC^rjg xal TtQO^sxpXrjd^sC^rjg 
STt avt^v trig TAH. STtsl yaQ TtdXiv JtaQdXXr^X^g 25 




1. rj] z/r D. 7. EA\ AE D. 9. e^a^sv ds'] xai 

s^ood-sv D. 10. TtQog] corr. ex nQo Dl 11. dZ] ZJ D. 

12. JZ] ZJ D. HE] EH D. 15. HE] EH D. 16. 
HE] EH D. 17. ZB] BZ B. 20. ZB] EZ D. 21. §' 
Xfjlilicc yiata SiaCqiGiv mg. BC. 23. z/Z] Zz/ D. z/B] Ez/ D, 
z/B mg. D^ 24. T^] seq. ras. 1 litt. B. nuqaXXriXov] 

TtaXXrjXov D. 25. Fz/H] corr. ex Tz/ D^ 



70 



KAATAIOT nTOAEMAIOT 




iatcv rj AH rfi EZ^ s6rt,v^ cjg 7] FE JCQog EA^ i^ 

rZ TtQog ZH [EucL VI, 2]. aX^A xrig ZA '^m^ev 

Xa^^avo ^Evrjg 6 rfig FZ TtQog 

ZH k6yog evyxeircn ex rs rov 
5 rfjg rz TtQog Z/1 xal rov rf^g 

AZ TtQog ZH £6riv dh 6 rfjg 

/IZ TtQog ZH /,6yog 6 avrbg 

ra rfjg jdB itQog BA dia rb 

sig TtaQakXfiXovg rag AH %al 
10 ZB difii^&aL rag BA xal ZH' 

6 aQa rfig FZ TtQbg ZH k6yog 6vvfj7trai, sx re rov 

rf^g rZ TtQog z/Z xal rov rfjg AB TtQbg BA. alXoc 

Tc5 rfjg rZ JtQbg ZH X6y(p 6 avr 6g i^rcv 6 rfjg FE 

TtQbg EA' ocal 6 rfjg FE ccQa ^Qbg EA X6yog 0vy- 
15 ocsLtm £x rs rov rfjg FZ TtQbg AZ xal rov rfjg AB 

TtQbg BA' OTtSQ sdsc dst^ai. 
jtdXtv s6r(X) TtvxXog 6 ABF^ 

01) KBvrQOv rb A^ nal siXrjcpd^co 

iitl rfig TtsQicpSQsCag avrov rv- 
20 j(^6vra rQua ^r^^sta ra; A, B^ F^ 

m6rs £xar8Qav r&v AB^ BF 

TtSQLfpsQSLGiv iXd66ova sivai rj^i- 

TcvxXiov xal iitl r&v s^fjg ds 

Xa^Pavo^sv(ov 7tSQi(psQSi&v rb 
25 o^Oiov v7taxov£6^(xi' xal iTt^^^vx^Gi^av aiAFKal AEB. 

1. T^] zfig BC. 2. nQos] bis D. 3. Xccfi^avofiivrjs] corr. 
ex Xcc(i§a(io^svr}s Bl ngo" D. 6. JZ] ZJ D. 12. JZ] 
Zd D. /^B] Bz/ D, zfB mg. D^ 14. v.aC — E^] om. 

BC. Eyi (alt.)] corr. ex A D^. 15. TZ — xf]s] mg. A^ 

VZ] Zr D. z/Z] Zz/ D. 16. OTiBq 8Sei dsbica] om. D. 

17. y' Xiififiu v.vaUv,6v mg. BC. 20. xd] om. D. 24. locyir- 
§avofisvcov] X coiT. ex s D. 25. Ofioiov] avto corr. ex avro) D, 

ai] bis C. 




MA0HMATIKHS STNTASE^S A'. 71 

Afyo), 6tL iexCv^ cog rj vtco trjv dvnlfiv rijg AB 
jtSQLq)SQSLag JtQog xriv vtco xijv dLTClrjv xr]g BF^ ovxcog 
rj AE svd^sta TCQog xijv EF svd^stav. 

r]x^G>0av yaQ xdd^sxoL ocTcb xav A xal F 0r]^SL<ov 
STcl x^iv ^B 7] xs AZ xal i^ ^^* ^'^^^ TCaQdklrjXog 5 
i6XLv rj AZ xfj FHy xal dLrJKxaL slg a\}xag si^d^sta i] 
AEF^ s^XLv^ (og r] AZ TCQog f^v FH^ ovxcsg i] AE 
TCQog EF [Eucl. VI, 4]. dW 6 avxog s6xlv Uyog 6 
xfjg AZ TCQog FH xal xfjg vtco xf]v dL7cXf]v xrjg AB 
TCSQLcpSQsCag TCQog xr]v vico xrjv dL7cXf]v xfjg BF' '^^C- 10 
6sLa yaQ sxaxsQa sxaxsQag' xaX 6 xf]g AE aQa %Qog 
EF Xoyog 6 avx6g sdxLv x(p xf]g ijTCo xi]v 8L7ckf]v xfjg 
AB TCQog xf]v 'bicb xijv diJcXfjv xfjg BF' otcsq sdsc dst^ai, 

TCaQaKoXovd-st d' avxod^sv^ 
oxL, xdv dod^&^LV f] xs AF oXrj 15 
TCSQLcpsQSLa Tcal 6 X^yog 6 xfjg 
vTcb xijv dLTcXrjv xfjg AB JCQog 
xf]v i)7cb xf]v dLTcXrjv xr]g BFj 
dod^rj^sxaL xal sxaxsQa xcov AB 

Xal BF TCSQLCpSQSLCbV. SKXSd^sC- 20 

6r]g yaQ xfjg avxf]g xaxayQacpfjg 

STCs^svx^co r] AA, xal "^^O-aj 

aTcb xov A xd%sxog stcI xf]v AEF r] AZ. oxl ft^v 

ovv xf]g AF TCSQLCpSQsCag dod^sCarjg r] xs vicb AAZ 




1. T^s — 2. Bri mg. BC^ rrjff ET etiam in textu BC. 
._ j)r - - - _ 



3. TT^dff] supra scr. Dl 6. Bv%iia\ corr. ex Bv&emg D. 8 

r] rrjv Er D. 6 (alt.)] om. D. 9. r^s (pr)] corr. 63 

rr) D^ 10. TtsQicpEQsiag] supra scr. D. 12. EF] trjv EF D 



EF] trjv Er D. 6 (alt.)] om. D. 9. r^s (pr.)] corr. ex 

n D^ 10. TtsQicpEQsiag] supra scr. D. 12. EF] trjv 

13. BT] FB D. OTtsQ sdsi dsL^ai] supra scr. D^ 14. S'] 



comp. ins. Dl 15. AT] corr. ex FA D^ Post oXri del. 

Tj B\ 17. trjv] t- e corr. C. 18. BF] corr. ex FB W. 19. 
xat] ins. Dl 23. AEF] corr. ex zJEF BC*. 



12 



KAATAIOT nTOAEMAIOT 



yavta triv rniC^SLav avxriQ VTtoxdvovCa dsdo^evrj s^tai 
xal oXov t6 AAZ tqiyfovov^ dijXov' SJisl ds trig AF 
si^d^SLug ^Xrjg dsdo^svrjg vnoxsitai xal 6 trjg AE TtQbg 
EF Xoyog 6 avtbg cov ta tfjg VTtb f^v diTtkriv trjg 
5 AB TtQbg trjv vnb trjv diJtXrjv tfjg BFj rj ts AE 
s6tat dod^st^a [dat. 7] xal koLTtr] r] ZE, xal did^ 
tovto xal tfjg AZ dsdo^svrjg dod^yjastaL xal iq ts vitb 
EAZ ycavCa tov EAZ OQd^oycovCov xal oXrj r] vjtb 
A^B' cS6ts xal i] ts AB TtSQicpSQSLa dod^rj^staL xal 
10 koLTti] ii BF' OTtSQ sdsL dst^aL. 

TtdkLV s6t(o Tcvxlog 6 ABF ^sqI xsvtQOv tb z/, 
xal STtl tfjg nsQLtpsQsCag avtov slX7]cpd^(X) tQCa arj^sta 
%a ^, B^ ri, &i6ts sxatsQav t&v AB^ AF 7tSQLg)SQSicov 




iXd66ova slvaL r]^LXvxXCov' xal sjtl tcbv s^f]g 8s ka^- 

15 ^aVO^SVCOV TtSQLCpSQSLGiV tb O^OLOV VTtaxovsdd^cj' xal 

ijtL^svx^steaL rj ts AA xal r] FB sxps^kr]0%'co6av xal 
6v^iL7tL7ttsto6av xata ro E 6r]fiSL0v, 



1. dsdofiivT]] seq. ras. 1 litt. D. 2. tQCyoavov'] xQiycovov 

dQd^oyoavLov D. ds] ds %ai D. 3. 6] supra scr. D^. ^E] 
seq. ras. 3 litt. D. 5. BT] FB D. 6. ZE] EZ, E in 

ras., D. 7. dsdoiihrig] alt. d supra scr. D^ 8. ycovCa tov 
EJZ] om. D. 10. onsQ sSsl dsL^ai] om. D. 11. ABr] 

ATB D. Mg. xQLtov t&v y.vnXiK&v B^ 12. 6ri(isia] Gr}\iiSLcc, 
post 7] ras. 1 litt., A. 13. m6ts — 15. vnay.ovs 6^-00] om. D. 
13. Supra AT scr. BT C\ 16. STtitsvx&SLGu D. TB] 

BTB. 



MA0HMATIKHS STNTAgESiL A'. 73 

Xeyco^ oti i6xvv^ cog 7] vtco tijv dLTtXfjv tijg FA 
7t£QC(p€Qeiag TtQog tijv vnb tijv diTtkfiv trjg ABy ovt cog 
7] FE ev^eta TtQog ti^v BE. 

bfiOLCog yccQ t(p TtQoteQG) Xrj^^atLG)^ eav airb tcbv B 
xal r dydyco^ev xad^etovg enl trjv AA t^v te B7j 5 
v,a\ trjv FHj e6tat dcd tb xaQaXXyjXovg ai)tdg elvac^ 
cog r] FH TtQbg trjv BZ^ ovtcog r} FE JtQbg trjv EB 
[Eucl. VI^ 4] • co6te %aC^ hg r] vnb trjv dtTtXrjv tfjg FA 
TtQbg f^v VTtb trjv dLTtXrjv tfjg AB^ ovt cog r] FE TtQbg 
tf}v EB' OTteQ edet detiat, 10 

xal ivtafjd^a de avtod-ev JtaQaxoXovd^et^ dcdtt^ xdv 
r] FB 7teQt(peQeia [lovr] dod^^j xal 6 Xoyog 6 tfjg vjtb 
tf]v diitlfjv tfjs FA TtQbg tf]v vjtb tr]v di%kY]v tf]g 




AB dod^fj^ xal r] AB neQitpigeia dod^rj^etai. Ttdliv 
yaQ ijti tfjg bfioiag xatayQacpfjg ijti^evxd^ei^rjg tfjg zlB 15 
xal xad-itov dx^ei6r]g ijtl tf]v BF tfjg AZ f] fiev 

1. rA] AF D. 2. ovtcog] corr. ex ovtco A^ 4. yccQ 

om. BC. 6. sgtul] om. D. 7. cbg] yivhxcci mg D. 1? (pr.) 
ins. D^ BZ] ZB D. Tcgbg rr\v] TtQog corr. ex nqo D 

8, cb?] supra scr. D^ 10. onsQ tSti dft^at] o>: AC, 

7i£Qicp8QSiccv comp. B, om. D. 11. g' mg. A. di] S' D. 

12. 7}] 7] t£ D. do^ji] Sod-SLT} D. 6 (pr.)] om. D. 13. 
T^S (pr.) — dmXfiv] ins. B^ FA] -A in ras. A. FA — 

14. ^B(pr.)] supra scr. C^ 13. nQog t7\v] corr. ex tiq cp D^ 

14. ^E(pr.)] etiam in textu C. 80%'^ del. B^, 8o%r\GstoLi D. 

8o%r\Gsta.i] om. D. 



74 KAiATAIOT nTOAEMAIOT 

vTtb B^Z ymvta tijv rjnL^ecav vTtotSLVOvda tTjg BF 
TtBQKpBQeCag £6tat dsdo^svrj' xal okov aQa tb B^dZ 
OQd^oycovtov. STtel ds xal o te rijg FE TtQbg trjv EB 
Xdyog didotau ocal eti rj FB evd^eta^ dod-7]6£tat xal i] 
5 te EB xal ett oAt^ rj EBZ' &6te xaC^ eitei r\ /IZ 
dedotat^ dod^TJ^etat xal i] te i)Jtb EzlZ ycovCa tov 
avtov oQd-oycjvCov xal XotTtri 17 vTtb E/IB. co6te ;c«l 
rj AB TteQLfpeQeta ^6tai dedo^evr]. 

tovtcjv TtQokrjcpd^evtcov yeyQacpxf^o^av ijtl 0g)aLQiKfjg 

10 BTtLcpaveCag ^eyCotcjv tcvkXcov TteQLfpeQeiaL^ caGte etg dvo 
tag AB %al AF dvo yQaq^eCaag tag BE xal FA 
te^veLv aXXr^Xag %ata tb Z 6r]^etov' e6tc3 de exd6tr] 
avtG)v eXd66c3V rj^LKvocXCov tb dl avtb Tcal iTtl %a6G}V 
tcbv KatayQacpcjv 'b7ta}cove6%'co. 

15 leyco dif]^ ott 6 trjg vnb tr]v dL7tXr]v tr]g FE jteQL- 
(peQeCag itQbg tr]v 'bTto tr]v dtTtXrjv tfjg EA Xoyog 
6vvf]7ttaL eK te tov tfjg 'bnb ti^v diTtXfjv tf]g FZ 
JtQbg tf]v vTtb tf]v dL7tXf]v tfjg ZA Kal tov tfjg V7tb 
tf]v dL7tXf]v tf]g z/-B TtQbg tf]v vTtb tf]v dL7tXfjv tfjg BA. 

20 eiXr^cpd^co yccQ tb KSvtQov tfjg 6cpaCQag Kal e6tco tb 
H^ Kal iqxd^co^av d7tb tov H e7tl tdg B^ Z^ E to^dg 
tcbv kvkXcov 7] te HB Kal f] HZ Kal f] HE, Kal e7tL- 
^evxQ^et^a f] AA eK^e^kr]6d-co Kal 6vu7tL7ttetco tf] HB 
SKpXr^d^eC^T] Kal avtf] Katd tb & 6r]^etov, ofioCcog de 



2. aQo] supra scr. D^ 3. oQd^oymviov] tqlycovov D, 5. 
a>6te y.aL, stcsC] mGr' snsl v.ai D. 7. oQ^^oycovlov] XQiytovov D. 

9, Q^smQiqiia Kata diaCQSGiv mg. B. 11. yQacpsCaa^s] corr. 

ex yQacpQ-siGag Cl 12. ernLsiov'] om. D. 13. sXdrtcov D. 

^^j d' D. 14. vTtayioviGd^co] vTtWAOviaQ^ca rjiiiv D. 16. r^g 
— 17. diTtXfiv] D, mg. A^BC^, ^sCfisvov add. B^. 16. EA] 

EJ B, yQ. sa B^ 18. vnb T^v(pr.)] bis A. 21. ccTtb xov H] an 
ainov D. B,Z,E]BEZ D. 22. i] (pr.)] om. BC. xat'(tert.)] 
g v.ai D. 



MA0HMATIKHS srNTASEaS A'. 



75 




i7tL^£vx^£t6aL at ^ F xal AF xs^vEtG)0av tag HZ Tcal 
HE xata tb K xal A 07]^etov' ijcl ^idg dij yCvstav 
svd^SLag ta @, K^ A erj^sta dia tb iv dv6lv «fia 

sivat iTtiTtiSoLg tw ts 
tov AF/l tQtycovov 5 
Tcal t(D tov BZE 
Kvxkov 5 rjtig ini- 
t,svx%-SL6a Ttoisl slg 
dvo svd^stag tag SA 
xal FA dLTjy^ivag lO 
tag ®A Tcal jTz/ 
ts^vov0ag aXX-riXag 
xata tb K ^ri^slov' 6 aQa ti]g FA TtQbg AA Xoyog 
6vvfJ7ttaL SK ts tov trjg FK TtQbg K^ xal tov 
tfig A@ TtQbg @A [p. 69, 21]. aW hg fisv rj FA 15 
jtQbg AA^ ovtcog ^i vjtb tijv dLTtXrjv tfjg FE TtQog tiiv 
VTtb tijv dLTtkfiv tfjg EA TtSQLtpsQsCag^ hg dh 1] FK JtQbg 
K^^ ovtag r] vitb ttjv dLTtXfjv tfjg FZ TtSQLCpSQsCag itQbg 
trjv VTtb tijv dLTtXfiv tfjg ZA [p. 70, 17], hg ds rj ®A TtQog 
QA^ ovtog rj vjtb tijv dLTtlfjv tfjg AB TtSQLcpsQsCag JtQbg 20 
tijv VTtb tijv dLTtXijv tfjgBA [p. 72, 11]" xal 6 Xoyog aQa 6 
tfjg VTtb ti^v dLTtlfjv tf}g FE TtQbg tijv vitb tijv dLJtXfjv 
tfjg EA 6vvfi7ttaL sx ts tov tfjg vTtb ti^v dL7tkf]v tfjg FZ 

1. at] supra scr. C^ AF] corr. esi J F C^ 2. to] 

ra D. arifieicc D. ev&sCag yCvetcci D. 3. 8ia\ comp. B, 
8i B^ 7. eTti^evx&eioa'] ante g ras. 2 litt. A. 11. GA] 

corr. ex OA D^. 15. TA] corr. ex Tz/ D. 17. vno\ supra 
scr. D. TTjv] supra scr. D^ EA] EA corr. ex EJ B, 

EA mg. B\ 18. Kd] corr. ex KA B^C^. 19. Z^] 

z/Z D. @d] AC, corr. ex z/0 B^ z/6> C^D. 20. JB — 
21. rf]g] om. B, mg. C^ (^^ mg. B^. 20. neQtcpeQeCag] om.C^. 
21. rfjg] corr. ex tt) D^. rf^g BA] mg. C^ alio atramento. 22. 
rrjg (pr.)] om. D. vno (alt.)] e corr. D^. 24. Ante EA 

ras. 1 litt. A. 



76 



KAATAIOT nTOAEMAIOT 



JtQog rriv vjtb zijv dLTtXfjv rijg Zz/ zal rov rfjg VTtb rrjv 
diTtXriv rrjg z/JB Jt^bg rrjv VTtb rr^v diitkriv rr^g BA, 
xara ra avra drj xal &67t£Q STtl rrjg ETtiTtidov 
xarayQaq)rlg rcjv svd^SLCov [p. 68, 23] dstxvvraty on 
5 Tial 6 rfig v%b rijv dL%kf]v rfig FA TtQbg rrjv vitb rrjv 
dLTtXfjv rfjg EA X6yog 6vvf}7traL ^x rs rov rfjg vitb 
r^iv dLTtXfjv rfjg F^ nqbg rijv 'bitb rijv dL7tXf]v rfjg 
jdZ, Tcal rov rfjg VTtb rrjv dLTtXfjv rfjg ZB JtQbg rfjv VTtb 
xiiv dLTtXfjv rfjg BE' aitSQ TtQomsLro det^aL. 



10 Ld\ JIsqI ra)v fifralv rov t^rjiiSQLvov xal ro\> 

koi^OX) ZVXIOV 7t6QL(pSQ£LCbV. 

Tovrov dfj rov d^scjQij^arog ^tQo^xr^d^^L^svov 7toLrj66- 

lisd^a 7tQ(Qrriv rrjv rav 7tQox£L^£VC3v 7t£Qiq)£Q£Lcbv a7t6- 

8£L%LV ovrGig. 
15 £6rcci yaQ 6 ^t' diiq)or£QCOv 

rcbv 7t6Xc3v rov r£ t6rj^£QLvov 

xal roi) Slcc ^£6c3v r&v ^adLCjv 

xvxlog 6 ABFzf xal rb ^£v 

rov i6rj^£QLvov rj^LXvxXLov rb 
20 AEF^ t6 dh rov Slcc ^£6cov rcbv 

t^GidCcov rb BEA^ rb 81 E 6riii£tov 

rj xara rfjv iaQLvijv L6rj^£QLav 

avrcbv ro^T]^ co0r£ rb ^lv B %£Liii£QLvbv rQ07tLxbv ^lvaL^ 

t6 d£ A ^£QLv6v.^ £lXrm)%Gi 8\ i7tl rfjg ABF 7t£Qi(p£Q£Lag 




2. xfis JB — 8inXfiv] supra scr. D^. Tr]v vtco] postea 

ins. A^ 3. di]'] ds D. ■kccl coc-] in ras. A. 4. ort] corr. 
ex dwTi D^. 7. diTtlfiv (alt.)] -l- corr. ex ?] A. 8. z/Z] Zz/ D. 

9. nQoiv,SLz6\ corr. ex nqoyiBLxaL xo D^ 10. td'] C, dt B, 

om. AD. UEQL — 11. nBQKftQELOiv] mg. D^ 10. Toi) (pr,)] xov 

XE D^, 12, 8ri] om, D, 13. xriv] om. D, 23, xo] Tial x6 D. 

elvaL xQOTtLyiov D. 



MA0HMATIKHS 2TNTASESi2 A'. 77 

6 7c6Xog tov AEF t^r^^SQLvov ;cal £6ta) tb Z ^rjiistov^ 
xal ocTtSLXTJcpd^cj ^ EH TteQLCpiQEia tov dia ^s6(ov t&v 
^cjdccov TcvxXov t^rj^dtcjv ijTCoxELfievrj A, olcjv idtlv 6 
^8yL6tog TcvxXog t|, dt« ds t&v Z, H ysyQcccpd-G) ^eyC^tov 
tcvkXov TceQLipEQeLa rj ZH&^ xal TCQOxeL^d^cj tr^v H@ 5 
drjlovotL evQelv. jCQoecXrjcpd^c^ drj zal evtav^a xal 
xad^oXov eTcl 7Ca6cov t&v b^OLCov dec^ecov, Xva fiij xad'' 
exd6trjv tavtoXoyco[iev^ otL^ orav tdg TcrjkLXotrjtag 
leyo^ev JceQLcpeQeLcbv rj evd^eL&v^ o6cov ei^lv ^olqcov 
rj tfirjfidtcov^ ejcl ^ev tcbv TCeQcg^eQeLcbv tOLOvtcov (pa(iev^ 10 
OLCov r] tov ^eyC6tov xvkXov TCeQLq^SQeLa t^rj^dtcov 
t|, ejcl de tcov e^dd^eLcbv toLovtcov^ oXcov rj tov xvkIov 
dLa^etQog 'qk. 

eicel toCvvv ev KatayQacpfj ^eyC6tcov xvxXcov eCg 
dvo tdg AZ xal AE TceQLcpeQeCag yeyQa^i^evaL el6l 15 
8vo 7] te Z0 xal rj EB te^vov6aL dXXrjlag xatd tb 
Hj 6 trjg vTcb tr^v dLTCkrjv trjg ZA loyog TCQbg tr^v 
VTcb triv dLTckfiv trjg AB 6vvYi7CtaL sx te tov trjg i)7tb 
tr^v dLTcXfjv tfjg @Z TCQbg triv vTcb f^v dLTclrjv tfjg 
®H xal tov tfjg vjcb tijv dLicXfiv tfjg HE TCQbg tr^v 20 
vTcb trjv dcTcXfjv tfjg EB [p. 76, 3]. aAA' 17 ^ev tfjg 
ZA TceQLcpeQeCag dLTcXfj uoLQcbv e6tLv ^ xal r] vjc 
avtrjv evd^eta t^rj^dtcov 'qx^ ri de tfjg AB dLJcXfj xatd 
tbv 6v^7Ce(pcovrj^evov [p. 68, 4] rjfitv tcbv ny TCQbg td 
Td X6yov ^olqcov ^^ fi/3 Jl^ rj d' 'bic avtijv evd^eta 25 
t^rj^dtcov ]irj Ka ve^ xa\ TcdUv rj ^ev tfjg HE TCeQL- 



6. drf] Ss D. 9. elaCv] M in ras. 1 litt. B^. 10. ri\ 
supra scr. D^. 11. 17 — t(ir}^cctcov] 6 [isyiatog ■Kvtilos D. 

(isyLatov] mg. B, om. C. 15. sIol] comp. B, stoCv D. 16. 
£B] BE D. 17. TCQbg rrjV] TtQolajrjv D, post 6 add. o D^ 

19. 0Z] A, Z0 BCD. 24. TtQog] corr. ex TCQth C\ 



78 KAATAIOT nTOAEMAIOT 

q)£Q£tag diJtXfj ^^oiqcjv | nal ri vti avxriv svd^eta tfirj- 
(jidtcov ^^ fj dh t7]g EB diTtXfj ^olq&v Qjt xal rj vn 
avtrjv evd^eta t^rjfidtcjv ^' iav ccQa djib tov tav 
QX TtQog td ]irj Xa v£ X6yov dtpElca^sv tbv tav | TtQbg 
5 td QXy xataXsCitEtai 6 Xoyog tfjg vjtb trjv diTtXrjv trjg 
Z@ JtQog tr^v vTtb trjv dLTtXijv tfjg &H 6 t&v 'qtc 
TtQog td xd Ls vt,. TtaC iattv rj ^sv diJtXfj tfjg Z& 
JtSQKfSQsCag ^otQcbv ^y rj ds v% avtrjv svd^sla tfirj- 
fidtcDV Q7C' Tcal rj vjtb tijv dcTtXfjv aQa tfjg SH tmv 
10 avtcbv iettv xd Ts vt,. cS6ts xal r] fisv diTtXfj tfjg SH 
nsQLfpSQsCag fiotQcbv i6tLV xy l^' vd'^ axftfj ds rj SH 
tmv avt&v Td ]JL syyL6ta. 

Ttdhv VJtOXsC6d'CJ rj EH JtSQLipSQSLa flOLQCbV I, &6ts 

t&v dkXmv fLSvovxcDv tcbv a^t&v tfjv fisv dLJtXfjv tfjg 
15 EH yCvsa^aL ulolq&v ^, triv ds V7t' avtfiv svd-stav 
tfirjfidtcov ^ vs '%y. idv aQa TtdlLV ditb rov t&v p;c 
TtQbg td ]irj Xa vs Xoyov d(psXc3fisv tbv tcbv Qy vslcy 
TtQbg xd ^, xaxaXsLg^d-ij^sxaL 6 Xoyog 6 xfjg vjtb xi^v 
dLTtXfiv xfig Z0 TtQbg xijv VTtb xrjv dLTtXfjv xfjg 0H 6 
20 x&v ~QX TtQbg xd fi^ d ]ir]. xaC icxLV r] vitb xfjv dLTtXfjv 
xfig ZS xfirifidxcov q%' &6xs xal rj vjtb xr^v dL7tXf]v 
xfjg @H xcbv avxcbv sOxaL fifi a ]irj. Tcal rj fisv dLJtXfj 
ccQa xfjg SH TtSQLCpSQsCag fiOLQcbv i6XLV ]JLd o Trjj '^ ds 
®H xcbv avx&v ^ X ^' djtSQ sdsL dst^aL. 

2. 0^1 Q- corr. ex o D^. vtt'] vno D. 3. t^rijjLdTcov] -v 
supra scr. D^. 5. %ataXEC7tBtocv\ iBCnBtai D. 6. Z0] corr. 
ex S'® D. 7. li r^] corr. ex tv rs D^ 8. nsQicpBQECaq] -g 

supra scr. D^. ^i] d' D. 9. tayv] tov C. 10. <] m^ BC, 
mg. V B. 11. vd'] rrj D. 12 Ji] Xd' vd^ in ras. D^ syy leta] 
in ras. D^. 15. df] d' D. 18. 6 (alt.)] corr. ex v C. 19. 
@H] @- e corr. D^ 20. nQog td] con-. ex nQo aya D^ 21. 
^j sv.atcov simai mut. in snatbv sho6t D^ 24. X] in ras. A. 



MAeHMATIKHS 2TNTASESi2 A'. 79 

tbv avtbv dij tQonov xal enl t&v xata ^isQog 
%EQi(pSQEiG)V B7tikoyLt,6^£voL tccg TtrjXixotrjtas SKd^rj^d- 
lisd^a xavovLOv t&v tov tetaQtrj^oQLOv ^olq&v 9 Ttaga- 
xei^svag e%ov tkg TtrjXLxdtritag tcbv bfiOLCov tatg aito- 
dsdsLy^svaLg nsQKpSQSLcbv' %aL s6tLV tb xavovLov 

tOLOVtOV 



2. sniXoyLGdiisvoi, sec. -i- corr. ex -rj-, D. 5. nsQicpB- 

QSL&V^ TtEQlCpEQSLKig A. 



80 



KAATAIOT nTOAEMAIOT 



B 

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MA0HMATIKHS STNTAHESiS A'. 



81 



SS2 


gV^ 


2SI. 


^V2 


^\5-< 


»<a.<o. 


S^S 


* U» >i 


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!« ?i >S J4 }« }4 


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... _ . . pq 
^.r . *o Qo. "2 

in M w? O S=" ^i — I 
Ptolemaeus, ed. Heiberg. 



82 KAATAIOT nTOAEMAIOT 

L(5\ IleQl t&v «V 6Qd-7Jg trjg 6q)atQag avafpOQ&v, 

^Ei^rig d' av sl'rj ^vvaTtodst^aL r&v tov L6rj^sQivov 

7isQi(pSQSLG)v tag yLvo^svag TCrjXLKOtrjrag 'bm tav 

yQa^pofisvcov oivkXcov dLci ts t&v Tcdkcjv avtov xal t&v 

6 dL^o^svcov tov 2.0I0V Tcvxkov t^rj^dtcjv' ovro) yaQ 

s%oiisv^ sv OTcd^OLg XQOvoLg t^rj^sQLvotg ta tov dLa 

lis6(ov rcbv Jcodtov r^rj^ara dLsXsv6sraL rdv rs fis^rj^- 

Pqlvov TCavraxrj xal rbv stc' OQd^rjg rrjg atpaCQag 6ql- 

tfivra dLo: rb xal avrbv rors ^dvov dia rcbv jtoXcov 

10 yQd(ps6d-aL rov L6rj^sQLvov. 

SKXSL^d^cj roLVVv ri TCQodsdsLy^svri TtarayQatpr] ^ xal 
dod^SL6rjg jcdlLV rrjg EH TCSQLtpsQsCag rov kolov xvxXov 
yCQorsQOv r^rj^drcjv A dsov s6tco 
rrjv E® rov l6t^^sqlvov tcsql- 

Ib (pSQSLaV SVQStV. 

Tiard rd avrd drj rotg ^^- 
TCQO^d^sv 6 rrjg vTcb rrjv dLTckfjv 
tr\g ZB TCQbg tr^v vicb trjv Sl- 
Ttkrjv tfjg BA koyog 6vvf]7CtaL sk 

20 ts tov tf]g vTcb ri]v dLJClfjv rfjg 

ZH TCQbg rfiv VTcb rf]v dcTcXfjv rfjg H® xal roi) rfjg 
'bnb rijv dLTtlfjv rfjg ®E JCQbg rf^v 'bjcb rijv dLTcXfjv 
rfjg EA [p. 74, 15]. dlX' r] ^sv rfjg ZB %SQL(pSQsCag 
dLTtXf] iLOLQGiV s6rLV qI^ l^ % jcal r] vTcb avrf]v svd-sta 

25 r^r]^drc3V Qd" (id vy^ i] ds rr]g BA ^olq&v ^^ ^/3 'Ji 

1. c?'] st B, om. ACD. cvvavacpoQ&v T>. 2. tGr^^sgivov^ 
BCD, larifiSQivov v,vv.Xov A, v.vvXov mg. pro scholio BC. 5. 
ovTcog D. 6. -V iv OTT-] postea ins. A^ 19. loyog] -g in 
ras. D^, seq. ras. 4 litt. owrintca'] GvynEtrca D. 20. r?)? (alt.) 
— 21. H@] supra scr. C^. 21. ZH — H@] mg. B^ TtQog 
xriv'] vccl T^s C^. rfjg H&] etiam in textu C, H@ in textu B. 

TiccC] vccl Ix D. 22. 0E] E0 D. 24. -67^0] A, i^n BCD. 

25. BA] BA SinXr) D. jx] corr. ex t, D. 




MA0HMATIKHS STNTAlEjESJS A'. 83 

xal rj VTth avxriv avd^eia t^rj^dtCDV Jirj Xa vs' xal 
TtdXiv rj ^sv tfjg ZH 7i8Qi(paQeCag dcTtXfj ^olq&v qv<s ^ a 
xal rj vTcb avtrjv sv^sta t^rj^dtcov qc^ Aa Ti, rj ds 
trjg H0 fioiQ&v %y id' vQ" Tcal ri vtco avtijv sijd^sta 
t^rj^dtcDv xd Ts vj. sdv aQa dno tov tcov Qd^ ^d vy 5 
TtQog td Ji^ ka vs kdyov d(pslG)^sv tbv tcbv qi^ Xa ts 
XQbg td xd Ts vj, xataXsLq)d-7]6stai rj^tv 6 tfjg 'bjtb 
tijv dL7tkf]v tfjg ®E TtQbg triv vjtb trjv dtTtXfjv tfjg 
EA loyog 6 t&v vd v^ scg ^Qog td ^tj Xa Ts' 6 
d' avtbg loyog s0tlv xal tav vg a xs TtQbg td qx. 10 
xc^fc s0tLV rj ^sv diitlf] tfjg EA iioiQmv QTty rj d' 'bn' 
avtiiv svd^sta t^rjfidtcjv qz' xal rj vjtb tijv dtTlXfjv 
ccQa tfjg 0E t^rj^dtcjv tcov avrwv scjttv vg a xs. 
co0ts xal ri ^sv dtJtXfj tfjg ®E 7tSQL(pSQSiag s6taL fioi- 
Qcbv vs Ji syyL^ta, rj ds ®E tcyv avt&v k^ v. 15 

Jtdhv VTtOKSLed^CJ rj EH 7tSQL<pSQSLa ^OLQcbv I, Sdts 

ta)v dXkcjv ^svovtcov tcov avtcbv triv ^lsv dLTtXfjv rfjg 
ZH TtsQLcpsQSLag yCvsad^aL ^olq&v QXri vd' ^p Kal trjv 
V7t avtfjv svd^stav t^rj^dtcov ql^ Ky vg^ tfjv ds 8L7tkf]v 
tfjg H& 7tSQL(pSQSLag ^olq^v ]id o Ttj Kal tfjv V7t 20 
avtr]v svd-siav t^rj^dtcov ^^ d ]irj. sdv ccQa aTlb tov 
ttbv pO" ^d vy TtQbg td Jirj la vs l6yov d(psXco^sv tbv 
tcbv QL^ %y vg TtQbg td ^^ d Jirj., KataXsL(p%"ri6staL 6 
tfjg V7tb trjv dt^tXfjv tfjg 0E koyog TtQbg t^v V7tb tfiv 

1. V7t6] A, V7t' BCD. 2. QV? ft a] B, ^ s jta A, qvz Jl ^ 
B^ Qv^ jxa C, Qv^ {ig§ D. 3. vno] AC, corr. ex vn' B, vn' D. 

4. iI0] H& 7t£QL(p£Q£Lag dLTcXaaLcov D. vjrd] AC, V7t' BD. 

5. idv] bis D, sed corr. Qd''] corr. ex qo D^ 7. 6] in 
ras. C. 10. %at] yiccl 6 D. xf] corr. ex vy D^, vy in ras. B^ 

11. -uTc'] corr. ex a7t' C. 13. r/xrj/Ltarcov] supra scr, D^. yTs] 
corr. ex vy Dl 15. Post JL ras. 1 litt. D. 20. H@] AB^C^D, 
ZJf BC. 7t£QLq)£QSLC(g] om. D. 21. aQCi] ccQa TtdXLV D. 22. 
Xa] corr. ex l^ D^ Xoyovc, 6 eras., D. 



84 KAATAIOT nTOAEMAIOT 

dLJClrjv tfjs EA 6 tcov 9f ^ jil TtQog ta ql^ %y vg' 6 
d^ a-dtbg tovtG) X6yog 66tlv xal 6 t&v ^ xt] % TCQog 
tcc 'q%. TcaC B(5tLV rj vico f^v diJt^v tfjg EA tisql- 
(psQeLag sv^sla t^rj^dtcav qx' G)6ts xal ij {jjcb tiiv 
5 dLTckfiv tfjg &E t&v avt&v s6tLv qcc xrj z. Tcal rj ^sv 
dLTcXfj ccQa tfjg @E jcsQLCpSQSLag s6taL ^olq&v qTs xrj 
syyL^ta^ avtrj ds r} @E t&v aift&v vj ftd. 

acal dsdsLXtaL^ otL ro ^sv a' dicb tov l^rj^SQLvov 
6rjiiSL0v dcodsxatrj^dQLOv tov d^d ^s6g)v tG)v t,Gi8LG)v 

10 xvxXov 6vy%Q0vsL totg tov L6rj^sQLvov xatd tbv ix- 
xsL^svov tQOJCov t^rj^a^LV x^ v, tb ds dsvtsQOv t/lm{- 
fia6LV xd' vd, S7CSLdi]7CSQ d^(p6tSQa djcsdsLxd^rj ^olqcov 
vt, ^d' xal tb tQLtov ds drjXov6tL dodsxatrj^^QLOv 
6vy%Q0VL6SL tatg XoLicatg slg tb tstaQtrj^oQLov ^OLQaLg 

15 A/3 7g dLd tb xal oXov tb tov 2.o^ov xvxXov tstaQ- 

trjfl6QL0V oXg) tG) tofj L6rj^SQLV0V 6vy%Q0VLt,SLV G)g TCQbg 

tovg dLa tcjv 7c6Xg)v tov L6rj^SQLvov yQatpo^svovg xvxXovg. 
tbv avtbv dij tQ^icov tfj TCQOXSL^svrj dsL^SL xat- 
axoXovd^ovvtsg STCsloyL^diisd^a xal tdg s%d6trj dsxa- 
20 iiOLQL(f Tov Aojoi) xvxkov 6vy%Qovov6ag TCSQLtpsQsCag 
tov i6rj^SQLVov dLd tb tdg hL tovtcov ^L%Q0^SQ66tSQag 
^rjdsvL d^LoX6yG) dia(psQSLv t&v TCQbg o^aXrjv jcaQav- 
%rj6LV 'h7CSQ0%G)v. i^d^rj^^^ed-a ovv %al ravrag, Lva 
xatd tb 7Cq6%6lqov s%g)^6v^ iv 660Lg %Q6voLg avtcbv 



2. i6Tiv~\ -V del. C^. x] D, supra scr. A\ in ras. B^, 
P C. 5. tiav — 6. 0E] D, om. A, mg. BC. 5. icxiv] 

^Gxai D. 6. ocQo] D, ix BC. 8. 8i8eiyLxcci\ corr. ex ds- 

dsKxai C^ x6] supra scr. C^ 10. Totg'] om. D. 11. ds] 
om. BC. 14. Gv/xQo^f^Cosi] BC, 6vv%qovi6si A, 6vvxQovrj6Si A^, 
ovyxqovT^^si mut. in 6vy%Q0ViEi D. Xoinccig] l8i7iov6cag corr, 
ex XiTtovociig D. 15. xov] corr. ex x6 C^ 16. 6vyxQovEiv BC. 
19. dsyicc^oiQicc] corr. ex dsy.aTrjfiOQicc D^ 22. TCQog] corr. ex 

7tQb\g D^. 24. TtQOXSiQOXOV D, TtQOXSiQOXCCXOV D^. 



MA0HMATIKH2 STNTAtElESiS A'. 85 

ixcc6t7} t6v te ^s6r]^pQLv6v^ cjg £(pa^svj jcavtaxri xal 
tbv S7t OQd-rjg trjg efpaiQag OQt^ovta disksv^stai^ trjv 
aQxrjv aTCo trjg TCQog ta ierniSQUva 6r]^SLC3 dsxa^OLQiag 
7toiri6d^svoi. 

rj ^sv ovv TCQcbtrj jtSQiSxsi XQ^^^ovg d" T^ rj ds dsv- 5 
tSQa ;u()(5i/ov^ d' ls^ ri ds tQitrj xQ^^^ovg d' xs, &6ts 
tovg STCi tb avtb tov a dcjdsxatrj^oQiov ^vvdys^d^ai 
XQ6vovg Tc^ V' ■rj ds tstaQtr] XQovovg d' jij rj ds TCsiiTttrj 
XQovovg d" vrj^ rj ds sxtrj xQ^^^ovg l Ig, a6t£ xal tov 
dsvtSQov dcodsKatr]^oQiov rovg xd- vd XQ^^^^^S 6vv- 10 
dys^&ai' rj ds s^d6^r] xQOVovg T Xd^ r] ds 6yd6rj xQOvovg 
T fij, rj ds svdtrj xQOvovg T vs^ Sg TcdXiv 6vvdys6^ai 
xal tov ^sv tQitov ical JCQbg totg tQOTCixotg 6rj^si0ig 
dcodsxatrj^OQiov tovg A/3 Zg XQ^'^^'^^') okov ds tov 
tstaQtrj^OQiov tovg 9 6v^(pG)vcjg. 15 

xai s6tiv avt^d^sv (pavsQ6v, oti xal r] tav XoiTCcbv 
tstaQtr]^OQicov td^ig rj avtrj tvyxdvsi ot)6a^ ndvtcov 
xa%^ sxa6xov t&v avtcov 6v^paiv6vtcov dicc tb tijv 
6(paiQav OQd-ijv vTCOKst^d^ai ^ tovts6tiv tbv i6r]^SQivbv 
dvsyxXitov JCQbg tbv oQi^ovta. 20 



3. t6 l6riii£QLVov 6r]fiSL0v D. Ss-nccfioLQLag'} post pr. -cc- 

ras. 1 litt. D. 5. 7csql4x^T\ seq. ras. 1 litt. D. l rf] L'\f) 

corr. ex \i7j D^. 9. xQOvovg (Blt.y] -ov- ins. D^ tg] corr, ex 
tc D. coffrf] Gjg D. 12. svdtr)] & C, v supra add. D^ 14. 
8(o8s%utr]iLOQiovg, -g eras., D. tovg~\ om. D. 17. ov6u\ 

om. D. 19. tovt^6Tiv] -v del. C. In fine: KXavdCov 

IltoXsfiaLov nad-rjfiati-A.mv {-bv C) a' ABC, tsXog tov TtQthtov 
mg. sup. D^ 



B'. 

Tdda sve6tiv iv ta /3' tijg IltoXsiiLaCov ^ccd^rj- 
fiatLKTJg avvtd^sog' 

a, tcsqI tfjg xad^oXov d^s^sog trjg xad'' 'fifiag otxov^svrjg. 

5 p\ JC&g dod^svtog tov trjg ^syC^trig rjiiSQag ^sysd^ovg 

aC dTtoXa^^avo^svai, tov d^C^ovtog 7CSQi(psQSiai 

VTto ts tov i6rj(iSQLV0v xal tov Xo^ov kvkXov 

dCdovtai. 

y' , %G}g tcbv avtcbv VTCoxsifisvcov tb s%aQfia tov 7c6lov 

10 dCdotai xal tb dvdicakiv. 

d\ Tccbg iTCiXoyiOtsov^ tCdv xal 7c6ts xal TCo^dmg 6 

r]Xiog yCvstac xatd TcoQvcpTJv. 
s\ TC&g aTcb t&v STcxsi^svcov ot X6yoi tcbv yvc3^6vG)v 
jCQbg tdg i0r]^SQivdg xal tQOTCizdg iv talg 
15 ^sdrj^^QCaig axidg la^^dvovtai. 

b'. SK%^s0ig tcbv xatd TCaQdXXrjXov idicj^dtcov. 
%' . jcsQi tcbv ijcl trjg iyxsxXi^svr^g 6(paCQag tov did 
fie6cDv tcbv ^cjdCcov xvkXov xal tov Cerj^sQivov 
0vvava(pOQcbv. 
20 ri'. sxd^s^ig xavovCcjv tav xatd dsxa^oiQiav TCaQallrjXov 
dvacpoQcbv. 



_ 1. B'] om. ABC; KXavdCov UtoXsfiaCov (locd^r^fiocTiytcav D, 
§ add. D^. 2. tfjg — 3. avvrd^scog] ^L§Xi(p x&v ThoXsn,a.Cov 

(lad^ri^ari-iimv D. 6. OQL^ovtogl OQLlovtog %al tov D. 11. 

tL6L D. 15. iisGri(i§QLvaLg <7xtatg D. 17. syyisy,XLG(iiv7]g AC. 
20. "AavovCov D. ds-Ka^LOLQLav] om. D. naQdXXTjXov] -Xov 
comp. in ras. B. 



KAATA. nXOAEM. MA0HMATIKHS STNTASESiS B'. 87 
d'\ TtSQi tG)v Tiaxa ^EQog rats dvaq)OQatg TtaQaxolov- 

d^OVVTCJV. 

L . TtSQl tG)v V7tb tov dia fis6c3v tG)v ^a^dcov TcvxXov 
Tcal tov ^s6r]^^QLV0v yivo^svov ycDVLobv. 

ta'. TtSQL tcbv V7tb tov avtov Xo^ov KvxXov xal tov 5 
bQL^ovtog ycvo^svcjv yayvLCJV. 

L^'. TtSQL tcbv TtQbg tbv avtbv kvkXov tov dta tcbv 
jtoXcjv tov bQL^ovtog yLVO^svcjv ycovLcov xal 

7tSQL(pSQSLG)V. 

Ly\ SKd's6Lg xatd TtaQalXrjXov t&v TtQOXSL^svov yovLGiV 10 

Tial TtSQLCpSQSLCbV. 

a. UsqX tr\g na^^^Xov d^sasog tijg xad^' ri^ag 
OLXov^svrjg. 

^LS^sX&ovtsg iv ta TtQcotc) tijg dvvtd^sog td ts 
jtSQL tfjg rraz/ oAoi/ <3%s6sog xatd tb 7CS(paXaLodsg 15 
h(pSLXovta TtQolrjcpd^fjvaLy Tcal o6a dv tLg Td3i/ stc OQxi^rig 
tfig 0(paiQag XQ7]6L^a TtQbg trjv tov vTtoxsL^svov 
d^soQLav riyri^aLto^ TtSLQaao^sd^a Katd tb s^rjg ml r«i/ 
TtSQL trjv syxsxlL^svrjv 6(paLQav 6v^^aLv6vtov td 
xvQLotSQa TtdUvy og svl /laAt^ra, %atd tbv svfista- 20 

XSLQL6tOV tQOTtOV S(po8sv6aL. 

xal svtavd^a dii ro (isv bXo6%SQog dcpstXov itQO- 
Xrj^pd^rjvaL tovto i^tLV^ otl tfjg yrjg slg tscf6aQa dLaLQOv- 



1. 7taQa'iiaXovd'6vTcov D. 7. tcoj; (pr.)] tov B. 8. ■kul'] D, 
xal t&v ABC, z&v del. A^ 10. kcctcc] x&v •accxd A. yco- 
vLcbv] T&v yoovLaiv A. 11. In fine add. xeqpaXata Ty D. 12. 
fiad^rj^cctLK&v § supra scr. B. a'] B, om. ACD. 14. ts] 

om. BC. 17. toiv vTtdisifiivcov] vTto-nELfiivriv D. 18. rjyij- 

caTo D. 22. To] t- in ras. A. oloaxsQSS B. 23. rovro 

BotLv] T0VTE6TLV D. tsoaaQa] tiaCEQa A, a D. 



88 KAATAIOT nTOAEMAIOT 

lisvrjg xstaQTrj^OQLa rcc yivo^eva vtio ts tov Kata tbv 
L6rj^SQLvbv xvTcXov Tcal ivbg tcbv dLa tav tcoXcjv 
avtov yQa^po^svcov tb tYJg xad'' ^i^ag OLXOviisvrjg ^sysd^og 
vTcb tov itSQOv tcav ^oqslcov syyL^ta s^TtSQLsxstaL. 
5 tovto d' av ^dlL&ta ysvoLto (pavsQbv [sTtl ^sv tov 
TiXdtovg^ tovts6tLV tfjg djtb [is6rj^PQLag JtQbg tdg 
aQJttovg TtaQodov^ dtd tov 7tavta%fi tdg sv tatg i6rj- 
fiSQLaLg tcbv yvc3fi6va)v yLyvoybSvag ^s^rj^^QLvdg 6XLdg 
XQbg aQKtovg aisl TtOLSt^d^aL tdg 7tQ0<3vsv6SLg xal 

10 ^rjdsTtots TtQbg fis^rj^PQLav^ STtl ds tov firjKOvg^ tovts6tLV 
tfig dnb dvatoXmv TCQbg dv6^dg jtaQodov^ did tov tdg 
avtdg sxXsLtpSLg^ ^dXL6ta ds tdg CsXrjvLaxdg^ TtaQa ts 
totg STt^ dxQcov tcjv dvatohK&v ^sq&v trlg xa^ rj^dg 
oixov^svrjg oixov6L xal TtaQd totg s% dxQcav t&v 

15 dvtLKcbv ocatd tbv avtbv %q6vov d^smQOv^svag ^rj 
TtXsov dcodsKa jtQOtSQstv rj vGtSQStv coQcbv i^r^iSQLVcbv 
avtov xatd ^rjxog tov tstaQtrj^oQLOv dcodsxdcoQov 
dLd6trjiia 7tsQLS%ovtog ^ STtSLdrJTtSQ vcp ivbg tcbv roi) 
iOrj^SQLvov rj^LXVxXLCov dcpOQLt^staL. tcbv ds xatd ^iSQog 

20 dipsLXovtCDV d^scjQrjd^rjvaL ^dkL6t dv tLg rjy7]6aLto 
TtQbg tfjv JtQoxsL^svrjv TtQay^atsCav aQiibt^SLv td xa%^ 
axa6tov tcbv ^OQSLOtSQCov tov i6r]y.SQLVov xvxlov 
TtaQaXkrjkcov avt& xal tatg VTtoxsL^svaLg oixrj^s^L xatd 
td xvQLcbtSQa tcbv idLO^dtcov 6v^7tL7ttovta' tavta 



5. i7tL~\ e corr, D^ 7. TtuQdSova D, 6 eras. 8. yivo- 
(levag C. 9. cc£l D. 10. fis6r](i§Qiccv~\ -v e corr. D^ 11. 
itno'] kn D. 12. \iaXi6xoL\ /i- in ras. A. rag] om. D. 

15. 8vxi-Aiav'\ 8v- e corr. A; avti-Kobv C, S supra scr. C^. 16. 
OQcbv C. 17. Post rov ins. tfjg y^g mg, pro scliolio BC. 

r6taQtr}fi0Qi0v\ tstaQtrjfiOQiOV tfjg yfjg A. Scodsy.dcoQov^ corr. 
ex ds-adcoQOv A*. 20. (idXiet' dv\ (idXiata D, 21. td\ corr. 
ex ro BC^ 22. yiVKXcov D. 23. 'nard] corr. ex xa C^, xa 

corr. ex y.ai B^. 



MA0HMATIKHS STNTASESiS B'. 89 

d' i6ttv, o6ov ts 01 TColoL trig TCQCjtrjg (poQdg tov 6qc- 
t,ovtog ag)e6t7}xa6LV^ i) o6ov tb xata xoQV(prjv 6r}^stov 
tov L6rj^SQLvov Ttata tbv fis6rj^PQLvbv xvxkov^ xaC^ 
olg 6 i]XLog xata xoQV(priv yCvstaL^ Tcots xal 7C06ccxLg 
t6 toLovto 6v^paCvsL^ xal tCvsg ou koyoL tav C6r]^SQLvcov 5 
xal tQOTCLX&v iv tatg ^s^rj^^QCaLg 6XLcbv iCQbg to^bg 
yva^ovag^ xal jcrjkCxaL t&v ^syC6tcov rj iXa%C6tGiv 
rj^SQcav TCaQcc tag C6rjfiSQLvag aC v7CSQ0%aC^ xal o6a 
aXXa tcsqX tag xata [isQog av^oy^SL(x)6sLg tCbv vv^d^rj- 
liSQcov 'stL ts tcsqC ts tccg 6vvavatoXotg xal 6vyxa- 10 
tadv6SLg tov ts i6r]^SQLvov xal tov Xo^ov xx)xXov xal 
tcsqI ta LScco^ata xa\ tcc ^syi&rj t&v yLvo^ivcov 
yc3VLG)v VTcb tcbv xvQLC3tiQC3V xal ^syC6tc3v xvxXcjv 
ijCL^v^paCvovta d^scoQsttaL. 

p\ Ilcjg dod^ivtog tov trjg ^syC^trjg rniiQag 15 
^syid^ovg at ccjcola^pavd^svaL tov bQC^ovtog 
TCSQLCpiQSLaL V7c6 ts tov C6r]^SQLvov xal tov 
Xo^ov xvxkov dCdovtaL. 

IIqoxsC6^(o drj xaO^dAov t&v VTCodsLyficctcov svsxsv 6 
dia ^Podov yQa(p6iisvog jcaQccXkrjXog ta i6r]^SQLV^ xvxXog^ 20 
07C0V ro ^sv s^aQ^a tov 7c6lov ^olqcov i6tLv Ag, ri ds 



1. d'] 8s D. Tf] om. D. tov\ ano tov D. 3. Post 

u, 

yiviiXov add. a.(piGtT\v.EV mg. A\ acf)EGtr\ mg. B, ^ acp£Gtriv.aGiv 
mg. C. 4. yCyvBtai D. xat'] xal nov v,aC D. 5. toiovtov D. 

tivsg\ tLvsg te D. 9. av^oyLSimGsig] -v- supra scr. C^, pr. f 
ins. A*. vv%Q-rniiQ(iiv\ corr. ex vvxQ-ri^BQLviov D^. 10. gvv- 
avatoXdg] corr. ex GvvavatoXLV.d.g C^_ 12. TtEqi'] oGa tcsqL D. 

Post naL del. yiatd D^. 15. j3'] ^ B, om. ACD. 16. at] 
a- in ras. C. 19, va&oXov] mter duas ras. 8 et 3 litt. D. 

20. ^Podov] 'P- inras. A^ naQdXXTjXog] naQdXXriXog v.vv,XogT). 

v,vvXog~\ vvvXcp D. 21. ^iOLQ&v'] ras. 3 litt. A. 



90 



KAATAIOT nTOAEMAlOT 



lLeyC6tri ti^sQa g}Qcov l07]^sqlvcjv idi^ xal s6tG} ^sefrj^- 
^QLvbg iiEV xvxXog 6 ABF^^ oQL^ovtog ds dvatoh- 
Ttov tj^lxvxXlov ro 
BE/l^ xal L6riiiSQL- 

5 VOV ^SV tJllLTCVKhoV 

o^OLCjg ro AEF^ 
6 dh votLog avtov 
7c6Xog tb Z. v7to- 
71sl6%'G3 8s roi> dLa 
10 ^s6c3v tav ^cjdLcov 

KVkXoV rO XSL^SQL- 
vbv tQOTtLTcbv 6r]- 
^SLOv dvatsllov dLcc 
tov jE/, xal ysyQag^d^cj 
15 dLa tav Z, H ^isyC^tov kvkXov tstaQtrjnoQLov tb 
ZH@. dsdo^d^co ds TtQ&tov ro ^sysd-og tfjg ybsyC6tyig 
rj^sgag^ kol TtQoxsC^d^co ti^v EH tov bQC^ovtog tceql- 

(pSQSLaV SVQStV. 

sjtsl toCvvv rj trjg 6(paCQag 6tQ0(pri tisqI tovg tov 
20 l6ri^SQLvov TtdXovg dTtotsksltaL^ cpavsQOv^ otL sv tco 
avt(p XQOvfp rd ts H 6r]^SL0v xal ro & xata tbv 
ABFzi ^s6rj^PQLvbv s6taL^ xal 6 ^sv dit dvatoXrjg 
^sxQL tijg VTtsQ yfiv ^s6ovQav7]6scjg tov H XQOvog 6 
TtSQLSXo^svog s6tLv 'bitb tijg @A tov L6rj^SQLvov jtSQt- 
25 cpsQsCag, 6 d' d^tb tY}g vitb yrjv ^s^ovQaviij^sog ^sxql 




4. %at — 6. AEF] supra scr. D^. 6. AEF] -F e corr. C. 

13. avathXlaiv C. 17. EH — TtEQicpiQSKxv'] HE nsQicpBQSiuv 
xov oQi^ovTog D. 18. svQSiv] add. B^C^ 20. ccTtotsXsttai] 
-si- corr. ex s A*. 22. ABFJ] corr. ex FJ, AB D^. 

sGtui] S6tai drjXovoti y.ivovfiEVTjg zfig acpaiQag D. an'] 

ano D. avatoXfig] -Xt]- renouat. D^. 23. xQOVog] comp. B, 
mut. in XQovovg C^ 



MAGHMATIKHS STNTABESiS B'. 91 

rfjg dvatoXfig 6 jteQLSxo^evog 'i)7tb rflg FS. ccKdXovd^ov 
ds EdXLV^ otL xal 6 ^sv tijg rj^sQag ;t(>o^o? o dLiclaGiov 
s6tlv tov i)7cb rijg 0A tcsqlsxo^svov^ 6 ds tijg vvxtbg 
6 diTtka^Ccov tov VTtb tfjg F® jtSQisxo^svov^ STtsidriTtSQ 
ocal XG)Qlg td ts VTtsQ yfjv xal td vjtb yfiv tiiYiiLata 5 
tciv naQalXTJXcov t<p Ldrj^SQtv^ kvxXcov Jtdvtcov dLioto- 
^sttaL VTtb tov ^s6r]^pQLVov. 

dLa ds tovto xal ri ^sv E® TtSQLcpSQSia rjfiL^SLa 
ov6a tov dLacpoQOv tfjg ska%L0trig r) ^syL^trjg rj^SQag 
TtaQd tfjv i^rj^sQLV^v fiLdg ^lv S^ag xal d' yCvsraL 10 
xard rbv vTtoxsCfisvov JtaQdXXrjXov^ XQOvmv 8s dr^Xovort 
Trj Jis^ rj ds koLTtfi sig rb rsraQrrj^oQLOv r] ®A rcbv 
aifrcbv od Ts, STtSLdrj ovv xard rd avrd rotg s^jtQoad^sv 
aTtodsdsty^svoLg sCg dvo ^syC6rov xvkXcjv TtSQLCpSQsCag 
rdg AE xal AZ dvo ysyQa^^svaL sl6lv at EB xal 15 
Z@ rs^vov6aL dXXrjXag xark rb H^ 6 rfjg VTtb triv 
dLTtXfjv tfjg @A jtQbg ti^v vitb tijv dtTtXfjv tfjg AE 
Xoyog 0vvfJ7ttaL sx ts tov tfjg VTtb tfiv dLTtXfjv tfjg 
®Z TtQbg tfiv 'bitb tf^v dLitlriv tfjg ZH xal tov tfjg 
vTcb tfiv 8L7tXf]v tf]g HB TtQbg tf^v 'bjtb tf^v dLTtXfjv 20 
rfjg BE \j^. 76, 3]. dXXd ri fisv rfjg ®A jtsQLcpSQsCag 
dLJtXfj liOLQcbv s6rLv Q^^ X xal 'fj 'VTtb avrfjv s^vd^sta 
r^ri^drcov QLy Ag vd, i^ ^^ '^^? -^^ ^olq&v QJt xal f] 



2. xqovog] mut. in %q6vovq C^. 4. Post TtSQLSxoii^vov del. 
ETCitSr] TiEQiE%oiiivov A. 5. xyiriybata] corr. ex t^rj^dtcov D^. 

6. t&v'] om. D. yivnXcoL D. 15. AZ] corr. ex ABZ D^ 

16. Z0] corr. ex ZH@ D. 17. &A] -A supra ras. 1 

litt. Dl T^g(alt.) — 19. dinlfiv] supra scr. D*. 17. AE] 
Ey4 CD*. 21. cclV B. Post nsQLcpsgsiccs una litt. (t?) ma- 
cula del. C. 22. vno] ABC, vn' C^D. 23. t^rificitcov — 

p. 92, 1. Q>i] bis C, corr. C^ 23. X^] in repet. corr ex 

^^ C. AE] AE SLnXfi D. 



92 KAATAIOT nTOAEMAIOT 

V7t avxriv Ev^eta t^rj^dtcov ^, xccl jcdhv rj ^ev tijg 
@Z diJtXrj [lOLQav ^ xal r] vtco avtrjv evQsia t^rj- 
lidttav QX^ rj de trjg ZH fiOLQcov qI^ tj x %al rj vjtb 
avf^v evd^sta tnrj^dtov Qd' ^d vy' idv aqa ajtb tov 
5 koyov tcbv QLy XC, vd JtQog td q% dcpskaiiev tbv t&v. 
Qx TtQbg td Qd" ^d vy^ %ataXsLg)d"i]0etaL rj^tv 6 trjg 
vTtb tijv dLjtXfjv tfjg HB JtQbg trjv vitb f^v d^jrAijv 
tfjg BE Kbyog 6 t&v 'oy ve %y TtQbg td qx. %aC e6tLV 
r] vjtb trjv dLTtXfjv tfjg BE TteQLcpeQeCag^ eitel tetaQtrj- 

10 iloqCov tvyidveL^ t^rj^dtcjv qtc' xal rj vitb trjv dLTtXfji 
aQa tfjg HB tcbv avtcbv edtLV ^ ve Tcy' co6te xal ij 
^ev dLitXfi tfjg BH jteQLcpeQeCag e6taL ^olqg)v qx ey- 
yL6ta^ avtrj de rj BH tcbv avtcbv |* xal loLTtfj aQa ij 
HE toLOvtcov xatakeCTtetaL A, olcov e6t\v 6 oqC^g)! 

15 rj* oTtSQ edeL det^aL. 

y' . n&g t&v avtcbv vTtoTceL^evov tb e^aQ^a toi 
7t6Xov dCdotaL zal ro dvdjtaXLV, 

HQOKeCGd^cj dfj Ttdktv tovtov dedo^evov xal tb s^aQiit 

tov Ttolov ka^etv^ tovte6tLV tfjv BZ TteQLcpsQeLav tov 

20 fieOrj^PQLvov. yCvetaL toCvvv enl tfjg avtfjg TcatayQacpfjg 

6 tfjg vTcb tfiv dLTtXfjv tfjg E0 itQbg tfjv vTtb tfjv dLJtXfiv 

1. T^rjfidtcov Qyi] etiam mg. C^ xfig] corr. ex t^ D^. 2. 
vTCo] A, V7t' BCD. 3. qX§] corr. ex Qa^ A. vno] AC^, 

vn' BCD. 6. Qiy] -L- supra ras. 1 litt. D. vd] corr. ex 
vX D^ 7. tfis HB] supra scr. C. 8. oy] post q ras. 1 

litt. D. xy] B, xy^ A, k<5 CD; sed cfr. p. 93, 10. 11. xy] 
xy^ A, X? BCD. 12. BH] HB D. fiOLQai, D. 13. ytaQ 
corr. ex f} D^. 14. 6ql^(ov] -v supra scr. C*. 15. dneQ] supra 
scr. D^ 07C8Q MsL dsL^uL] o):oo ABC. 16. y'] 7 B, om. 

ACD. 18. di] ndXiv] corr. ex drinXriv C. dsdo^ivov] dso- 
[I8V0V D. 19. JBZ] ZB D. 21. E@] @E D. 



MA0HMATIKHS STNTASESiS B'. 93 

tfjg ®A Xoyog 6vvrj(i^evog 6k xe tov tfig 'bito trjv di7tli]v 
trig EH TtQog tijv vjtb tijv dcTtXijv trjg HB xal tov trjg 
VTtb f^v dcTtkrjv trjg BZ TtQbg tijv vTtb trjv dtJtXrjv 
tfjg ZA [p. 74, 15]. «AA' r\ \i\v diTtXrj trjg E® fiotQ&v 
ietiv AJ X xal 7] 'bitb avtijv evd^sta t^rj^dtcov Xrj Xd ;c/3, 5 
ij de dtTtXfj tfig 0A ^olq&v q^l^ X xal rj vTtb avtrjv 
evd^eta t^rj^dtcov Qtty Ag vd, xal itdXiv ri fiev dtTtXf] 
tfjg EH yLOiQcbv | Ttal ri vjtb avtijv evQ-eta t^rj^dtov 
I, i^ df dLTtXfj tfjg HB ^otQ&v qtc xal rj vitb avtijv 
evd^eta t^rj^dtcDv Qy ve 7iy' iav ccQa ditb tofj Xoyov lo 
tG}v Xrj Xd xfi JtQbg td ^ly Xt, vd dipeXco^ev tbv t&v 
f TtQbg td oy ve xy^ xataXeLq)d'rj0etat 6 tfjg vitb tijv 
di7tXf]v tf]g BZ TtQbg tijv VTtb tijv dLTtXfjv tfjg ZA 
Xoyog 6 t&v o Xy eyyi^ta TtQbg td q%. %aC iotiv 
jtdXtv rj 'bitb tijv dtTtXfjv tfjg ZA TteQLCpeQeCag t^rjfid- 15 
tmv 0%' xal ri 'uitb tijv dtTtXfjv aQa tfjg BZ tav 
avtcbv i6tLV o Xy G)6te Tcal 17 ^ev dLTtXfj tfjg BZ 
%eQLcpeQeCag e6taL ^olqCov o^ a^ ij de BZ tav ai)t€bv 
X<5 eyyL6ta, 

TtdXtv iitl tfjg a^dtfjg 7tatayQag)fjg dvdTtaXtv 'fj ^ev 20 
BZ 7teQL(peQeLa tov i^dQpLatog tov jtdXov dedded^io 



1. 6vv7}fi[i£vog] 6 6vvr}yfiivog D. 2. EH] HB yiccl tov xrjg 
vnh X7]v dinXfjv tfjg EH BC, corr. B^ TtQog — HB] del. C^ 

4. Tf)ff(pr.)] bis D, 5. X^] -Jinras. A^ vn' D. uvtr^v] 
corr. ex tif^v C. svQ^sta] in ras. C. 6. vno] mut. in vn C*, 
vn D. 8. Ante f ras. 1 litt. A. vno'] mut. in vn C*, 

i^n' D. 9. Post 1 del. H D^. HB] -B in ras. B; HM C, 

corrigere uoluit C^. vn' D. 10. idv dQo] bis D, corr. D^ 

13. BZ] ZB B. 14. i6tLv] -v del. C*, comp. B. 18. e6tat 

lioiQcav] (X iatLv D. 0/5 a] cc in ras. A, corr. ex o §a D^. 

20. n&g tov s^ccQfiatog tov noXov Sod^ivtog tb [isyE&og tfig 
(LifytffTTjs rjfiBQag dCdotai mg. pro scholio B, 21. EZ] -Z in 
ras. A, ZB D. 



94 KAATAIOT nTOAEMAIOT 

XExriQriiidvri iiolqCov Ag, nQ0KeC<5%^(o ds svqslv ro Slk- 
(pOQOv rrlg i^axL^trjg i) ^eyC^trig rj^SQag TtaQcc rriv 
L6r}^SQLV7]v^ rovts6tLv trjv dLTtXfjv tijg E® 7tSQL(psQsCag, 
yCvstaL toCvvv Slcc ta a\)ta [p. 74, 15] 6 rrjg vno rijv 
5 dL7tkr]v rfjg ZB TtSQLcpSQsCag TtQog ri}v 'i)7tb rrjv dL7t^>rjv 
rfjg BA Xoyog 6vvr}^^svog sx rs rov rrjg vTtb rfjv 
dLTtlfiv rfjg ZH 7tQbg f^v 'bitb f^v diTtXfjv tfjg H0 
Tcal sx rov rfjg VTtb 'pfjv dL7tXfjv rfjg ®E 7tQbg rijv ij^tb 
rfjv dLTtXfjv rfjg EA. dXX^ rj fihv dL7tXfj rfjg ZB 

10 ^OLQCov s6rLV op Tcal rj V7tb a^drrjv svd^sta r^rj^drcov 
o kp y^ r] ds dL7tkfj rfjg BA ^olq&v qT] >cal rj vTtb 
avrfiv svd^sta r^rj^drcov qj ^ vs', Tcal TtdUv rj ^sv^ 
8L7tkfj rfjg ZH ^olqgjv s6rLv pA/3 tf y. Tcal r] V7tb 
avtfjv svd^sta t^rjfidtcjv Qd' ^d vy^ r] ds dL7tkfj tfjt 

15 H@ ^OLQcov ^J ^p ji xal rj V7tb avtijv svd^sta t^rjfid- 
tcov Jirj ka vs' sdv ccQa aTtb tov tav o k^ y 7tQbg, 
9? ^ vg koyov dcpskco^sv tbv tcbv Qd' ^d vy TtQbg th 
'iiri la vs^ xataksLcpd^TJ^stai rj^tv 6 tf]g V7tb tfjv dL7tkf]i 
tfjg 0E 7tQbg tf]v V7tb tf]v dL7tkf]v tfjg EA kdyog 6 tcoi 

20 ka Td icy 7tQbg td 9^ d vg. Tcal S7tSLdf] 6 avtbg koyog 
s6tLV syyL0ta Tcal tcbv kr] kd 7tQbg td qk^ r] ds {f^th 

6. Xoyog] Xoyog 6 D. 8. SiitXfiv'] Sl- in ras, A. 10. ol 

sGziv D. vn' D. vTth avtrjv'] vn avTrjv corr. ex vnb f^v U 

11. y] seq. ras. 1 litt. B, corr. ex a J)\ y d AC, 8 del. C 

vno\ mut. in vn C^, vn AD. 12. fifV] -i- in ras. A^. 13, 

Igziv] om. D. ^X^] Q- e corr. D^. vno] mut. in vn' C* 

vn' D. 14. fiS] corr. ex jTv Dl 16. ii§] -§ e corr. D^. Ji 

^ D, ft add. D^. vn6] mut. in vn C^, vn D. 16. 7] corr 
ex A D^, y^ ABC, sed S punctis adpositis del. AC^, eras. B, 

nqoq] ngbg xd D. 17. S] postea ins. C. [lS] corr. e3 

vS D^ 19. 0E — tfig] mg. A^ 20. xy] supra scr. ^ C*. 

%al snsiSri] inel S' D. 21. r&v] 6 x&v D. XS] Xu seq. 

ras. B. Si] S' D. 



MA0HMATIKHS STNTABES^S B'. 95 

rijv dLJtXrjv trjg EA T^rjiidtcjv i6tlv qk, 6vvdy£taL 
xal 7] v7to triv dntkfiv trjg E@ tcov avt cbv Xrj W' 
w6tE xal r] diTclr] tfig E@ 7teQL(psQ£Lag ^olq&v ^£v 
itStaL Af k iyyLGta^ cjq&v dh LGrj^SQLV&v /3/.'* 07t£Q 
id£L d£t^aL. 5 

xatd td avtd dh 8o%"ri6£taL xal ri EH tov oql- 
t,ovtog 7t£QL(p£Q£La dLa ro xal tbv tfjg VTto trjv dLTtkfiv tfjg 
XA TtQog trjv V7tb tfjv dL^tXfjv tfjg AB koyov d£do^£vov 
evvfjcpd^ac [p. 76, 3] £x t£ tov tfjg VTtb trjv dL^tXfjv tfjg 
Z® 7tQbg tfjv vTtb tfjv dL^tXfjv tfjg @H d£do^£vov xal 10 
avtov xal ix tov tfjg VTtb tfjv dL7tlf]v tfjg HE 7tQbg 
tfjv V7tb tfjv 8L7tlf^v tf]g EB^ &€t£ xal tyjg EB d^do- 
fiivrjg xataK£L7t£6d^aL Tcal tb tfjg EH ^iyEd^og. 

(paVEQOV d\ Ort, xdv ^f] tb X£Lll£QLvbv tQOTtLKOV 

6rjfi£tov v7tod^c)^£d-a ro H^ tav dXXcov di rt rov dLa 15 
[i£6a)v t&v ^codLCOv xvxkov t^rj^dtcjv^ xatd td avtd 
^dkLV ixatiQa tcbv E® xal EH 7t£QL(p£Q£LC3v dod^rj- 
6£taL ^tQOExtLd^E^ivcDv t£ rj^LV d^d tov tfjg Xoi66£C3g 
xavovLOv t&v d^toXa^pavo^ivcov tov ^£6r]^PQLvov 
7t£QL(p£Q£LG}v v(p £xd6tov t^rj^atog tov dLa ni6cov 20 

t&V ^CjdLCOV XVXIOV Xal tOV i6r]ll£QLV0V^ tovt i6tLV 

tmv b^OLCov tf] H& 7t£QL(p£Q£La^ xal ^taQaxoXovd^ovv- 



3. ftfV] om, D, 4, 07t£Q edsi dsi^ccL] om. D. 6. n&g 
8o&ivrog xov s^dQHccrog xov nolov 8C8oxai r] (isxa^v xov lari- 
[iSQLVOv yiccl xov lo^ov STtl xov dgL^ovxog nsQLcpsqsia mg. B. 

9. -nlfiv — 11. 8l-'\ mg. Q\ 10. Z0] 0Z D. Z0 — 11. 
TTjff (alt.)] om. B. 10. rijg] om. A. Ssdofisvov yial avxov] 

om. C^ 11. fjt] om. Cl Trjg (alt.)] om. A. HE] corr. 
ex NE Cl 12. EE(alt.)] BE J). 13. KaxalsLnscd-aL] mut. 
in yiaxaliniGd-aL D. ■>tat] om. D. 15. dXXoov'} -v add. D^ 

18. 7tQ0S'iiXLQ'siiivaiv'] -l- mut. in s C^, nQOSKXs&SL^svoav D. 

xs] ys D. 20. vcp'] vno corr. ex vtc' D^ xov] om. B, 

add. C^ 22. xjj] xfjg C. nsQLCpSQSLa] nsQicpSQSLmv at D, 

at del. D3. 



96 



KAATAIOT nTOAEMAIOT 




tog [i£v avTod-sv xov xh vTib rCbv avt&v jtaQcc^lijXcov 
yivoiisva tiirniata tov dca ^e^cov^ tovtB6tiv ta l6ov 
aitiiovta tov avtov tQOTtcKOv 
67jfi6Lov, tag avtag xal STtl 
5 ta avta iieQri tov L^rj^SQLvov 
TtoLSLV tag tov dgL^ovtog to^ag 
xal ta tcov vv%%iriiiEQG3v ^sysd")] 
l'0a eKatSQa sxatSQOLg tG)v 
dfiOLCDV^ 6vva7todsLXvv^svov ds 

10 tov xal ta vjtb tcbv 1'6g}v TtaQ- 

aXXTJXcov yLvd^isva^ tovts6tLV tcc l'6ov aitsjjovta xov 
avtov L6rj^SQLVov 6rjii£L0v^ tdg ts tov bQL^ovtog TtSQt- 
(pSQsCag l'6ag szatSQcod^sv tov L6ri^SQLvov TtOLSlv xal t&v 
vvx^r}^SQCOv svaXka^ l'6a ta [isysd-rj t&v dvo^OLCov. sdv 

15 yccQ STtl trjg sjcxsL^svrjg xatayQacpfjg VTtod^^^sd^a xal tb K 
6ri^SL0v^ xad'' o ts^vsL tb BE^ tov OQL^ovtog rj^t- 
xvxIlov 6 l'6og xal jtaQdXXrjlog ta dtd tov H yQacpo- 
lisvG), xal 6vvava7tXrjQco6o^sv td HA xal KM tcbv 
7taQaXXt]Xc3v t^yj^ata ivaXkdlE, xal t6a drjXov6tL yLVO^sva 

20 dtd ts tov K xal tov ^oqslov TtoXov tb NKS yQdipc^nsv 
tstaQtrj^oQLOv^ l6av fisv ^6ovtat i} filv &A TtSQLCpsQSLt 
tri ISjr dLa tb sxatSQav sxatSQo, t&v AHxal MK b^OLai 
sivat^ xataXsLq)d"rJ6staL ds xal XoLTtrj rj E& XoLTtf] t| 
ES ^'»^^5 ysv7]6ovtaL ds xal dvo tQLTtXsvQOv b^iOLCOi 



1. fiiv'] om. D. 2. yivofisvcc] ysvofisva D. 7. Ant 

fisysd-r} del. ra D^ 15. xat] supra scr. A. 16. BE. 

om. D. 17. xat] om. D. ypagjoftsVo)] corr. ex ygaq^ofiivov D* 

20. Ante did ins. %at comp. C^ tb NKlSj] corr. ex roi 
KS A, corr. ex ro KlSl B^; tbv KS C, mg. tov; v mg. add. C*. 

21. tWt] corr. ex fog Bl fiiv (-pr.)] om. D. @A] A& D. 
nsQtq^EQSLocL C. 22. r^] "nccl i) Halma. syiatSQoc] corr. ez' 

sv.cctsQug D. 23. tfj] corr. ex r^g D^. 24. l'6r]] corr. ez 

iGrjg D^ v.ai] om. D. 



MA0HMATIKHS STNTASESiS B'. 97 

rwv EH& xal EK^El ai 8vo {ihv TtXsvgal ratg dv0lv 
l6ai, ^ iiev E® xf] ElHl, {] de H® r^ KS, oq^ ds 
£xat6Qa t&v TCQog totg xal ^ ycjvicov^ aats ical 
^ddLv tr]v EH ^d6sc rf; KE ycvs^d-ac farjv. 

S\ Hcjg STCikoyi^tsov^ tC6iv Kal jcots xal 7Co6dxLg 5 
6 ijXiog yCvstai xatd }C0QV(p7]v. 

Hqoxsiqov 8s iatcv tovtcov dsdo^svcov tb 0vvstcl- 
XoyC^sad^aL^ tC6L xal jcots xal TCoediCLg 6 ijXLog xatd 
xoQvcprjv yCvstaL, (pavsQov yaQ bvtog avtdd^sv, ott 
rotg psv VTcb tovg TcXstov dicsxovtag tov L6rjpLSQLVov 10 
7caQakX7]lovg tcbv trjg oXrjg aTCo^td^scog tov dsQLvov 
tQOTCLXov 6r]fisCov iiOLQcbv xy vd 7c syyL6ta ovd' oXcjg 
■6 i]XLog yCvstaL xatd xoQV(p7]v, totg ds vjcb tovg avtb 
t6 toaovtov dcps^t&tag aTCa^ sv avtfj tf] dsQLvf] 
tQOTCf].) df]lov yCvstac xaC^ otL totg VTcb tovg skd06ovag 15 
t&v sxxsL^svcov [lOLQav djcsxovtag dlg yCvstau xatd 
%OQV(pr]v' xal tb nots ds 7Cq6%slqov TCOLSt rj tov xavo- 
vCov tfjg ko^co6scog sxd^s^Lg. o6ag yuQ dv 6 S7CL^r]tov- 
(isvog 7caQdXkr]log dTCsir] tov L6r]^SQLVov ^oCQag^ tcov 
ivtbg 8r]kov6tL tov ^sqlvov tQOTCLxov^ tdg to0avtag 20 
€L0svsyx6vtsg sCg td dsvtSQa fiSQr] tcbv 0sXl8Ccov tdg 
jcaQaxsL^svag avtatg ix tov tstaQtr][ioQCov ^oC^ag iv 

1. EH@] E- e corr. C. 2. ES] E- e corr. C^ mg. I^. 

H0] corr. ex HB Dl _3. Post Toav del. totg D\ 0] e 
corr. D^ %at £7] corr. ex o^ D^ 5. S'] om. AD. zlgl D. 

6. yCvBtai] yCvE C. 7. iati D. 8. tLGi] corr. ex tCciv D^. 

9. ydq] del. C^ 10. tov] tovg A. 12. xl supra scr. 

AD^ 13. Totj?] -i- supra scr. D^. 14. rd] ins. U^D^. aqp- 
eGt&aiv D. 15. SriXov] D, drjXovott, ABC. xat] D, xara 

^oQvcprjv -KaC ABC. iXXdaaovag D. 16. 8Cq] corr. ex 8l6 D^ 

17. to] supra scr. AD^. 18. av] D, Bav ABC. 19. naQ- 
M,XXr]Xog] pr. X e corr. A. 21. asXCScov D. 

Ptolemaeus, ed. Heiberg. 7 



98 KAATAIOT nXOAEMAIOT 

totg 7tQ(x)tot,g ^sQB6i, tav ^eXLdLcov e^ofisv^ odag anixcov 
6 TJUog dq)' BxateQOv tcbv i^rj^EQLV&v Grj^SLCOv ag 
XQog tb d^EQLvbv tQOTCLxbv xata TioQVip^v tolg vit^ 
ixsLVOv tbv SKXSL^svov JcaQaXXrjlov yCvstaL, 

5 s'. Il&g djtb tav ixxsL^svcov ot XoyoL tcov yvco- 
[lovcjv JtQbg tdg l6riiLSQLvdg xal tQOTCLxdg iv 
tatg fis^rjii^QLaLg 6xLdg la^pdvovtaL. 

"OtL ds Xal 01 TtQOXSL^SVOL XoyOL tCOV 0XLCbV JtQbg 

tovg yvco^ovag ditXov^tSQOv Xa^pdvovtaL dod^ivtcov 
10 djta^ trjg ts ^sta^v tcbv tQOTtLXcov 7tSQL(psQSLag xal 
trjg ^sta^v tov oQL^ovtog xal tcbv ndXcov^ ovtcog dv 
yivoLto drjXov. 

s(3tco yaQ ^sarj^^QLvbg xvxXog 6 ABFzl TtSQL xiv- 
tQov t6 Ej xal 'bTtoxsL^ivov tov xatd xoQvg^ijv (frj^sLOV 
15 tov A dLTJx^co y] AEF dLa^stQog^ fj itQog OQd-dg yo- 
vCag rixd^co iv tm tov ^s6rj^PQLV0v iitLJtidco r] FKZNj 
jcaQaXXrjXog drjXovotL yLvo^ivrj tfj xoLvfj to^fj tov ts 
bQCt,ovtog xal tov ^s6rj^PQLV0v. xal insl olrj rj yfj 
6rjiisCov xal xivtQov Ibyov s%sl TtQbg at6%"ri6Lv TtQbg 
20 t^iv tov r]lCov 6q)atQav^ co6ts ddLacpoQStv t6 E xivtQov 
tfjg tov yvco^ovog xoQvcprjg^ vosCad^co yvco^cov ^sv 6 
PjEJ, ri ds FKZN svd^sta^ icp^ riv iv tatg ^s^rj^^QCaLg 



1. asXidLcov^l corr. ex aeXCdcov D. ansxoav] corr. ex Sitc- 

i%ov C^ 2. 6 riUog] in ras. A, seq. ras. 2 litt. arjfiSLOv C. 

4. iv.nsCfiBVOv'] supra scr. D^ 6, f'] om. AC. 7. [isar}^- 



V 



^Qiatg D. XccfJL^dvovtag BC. 8. oi] dia t&v D. ngo- 

TiSLfisvoLl -fisv- supra scr. A, TiQoyiSLfisvoov ot D. 12. yCvoLto D. 
15. AEF^ A- in ras. B^ corr. ex ^EF C^. 16. TAZiV] 
-N corr. ex H A. 20. adLa(pOQSLV~\ (li] dLacpiQSLV D. Post 
E eras. N A. 21. yva^icov] corr. ex yvm^ov C^ 22. xaLgJ 
taig rj- D. 



MA0HMATIKH2 STNTASESiS B' 



99 



7Ce6ettccL xa cckqcc tcjv 0XLav^ xal dL7lxd'cj6av dia tov 
E 7] te iarj^eQLvij xal at tQOTCLxal ^e^rj^PQLval axttveg. 
e6tC3 de L6r]^eQLvii ^ev rj BE^Z^ d^eQLvii de r} HE®Ky 
XeL^eQLvrj de rj AEMN^ ca6te xal trjv ^ev TK d^eQLvijv 

yLve6d-aL 6XLciv^ tijv 5 
-" — de rz l^rj^eQLv^v^ 

tijv de FN xeLiieQL- 
vrjv. eTtel toCvvv rj 
fihv Fz/ TceQLcpeQeLa^ 
fi ti}v l'6r]v eifJQtaL 6 lO 
PoQeLog TCokog tov oql- 
Jovrog, ijcl tov V7C0- 
xeL^evov xXC^atog toi- 
ovtcov e6tlv Ag, otcjv b ABF ^e6rj^PQLvbg t|, exateQa 
de t&v 0z/ xal jd M t&v avtcbv xy va x^ cpaveQov^ 15 
Ztc xal XoLTcij ^ev ij F® TceQLcpeQeia t^rjfidtcjv e^tac 
t/3 rj ^^ okrj de rj TM t&v avt&v vQ' va x. a0te xal 
t&v VTcb avtag yovLcbv^ oXov ^ev el^LV at d dQd^al 
t|, rotovrcov rj ^ev vjcb KEF ycovCa e6tlv l^ ri Ji^ 
r} de VTcb ZEF tav avt&v Ag, ri de vTcb NEF b^oCcog 20 
vd' va x^ oXc3V de aC dvo OQd^al tJ, tOLOVtcov ij ^ev 
VTcb KEF ycovCa xd t^ Jc, ri 8e 'bicb ZEF tcbv 
avtcbv o^, ^i de 'bicb NEF b^oCcog qlQ' fi/3 ^. xal 




.K 



1. SirixQ^mattv] -%- in ras. A. 2. rpojrtxat] zQ07Ciyia,l g C. 

4. AEMN^ D, A- in ras. A, corr. ex JEMN B^Cl 5. 
yCyvBGQ^ai D. 10. I^^^rat] D, s^TJQTrjzat, ABC. 11. ^OQLog A. 

12. vTto-nsifiivov'] 7tQoy.£Lfiivov D. 14. egtC D. 15. zmv @J'\ 
zo) N@J C, iV e corr. C^; zmv J& J). xy] corr. ex xa C*. 

17. vd^ va x] corr. ex ^ ^ B\ 18. vn6] BC, vn' C^D. 

vTto avzdg] vn avzdg corr. ex vno Tcig A^. 19. ymvia 

BGTLv] om. D, T-L supra scr. D^. 20. ds (pr.)] ds 17 D. NEF] 
corr. ex NT Dl 21. di] 8' D. at] supra scr. Dl 22. xj 
seq. ras. 1 litt. D. 

7* 



100 KAATAIOT nXOAEMAIOT 

r&v yQa(po^EVG}v dga xvkXcjv tcsqI rk KEF xal i 
ZEr xal NEF XQiyGiva OQ^oycivia 7} fisv inl 
rr}g FK svd^etag TCSQKpsQeLa fioiQ&v s6rLV xd i^ k 
xal rj eTtl rfig FE^ lei7Cov6a de elg rb rj^LKvxXLOv^ 
5 r&v avrcbv Qve ^^ ji, r} de e%l rf^g FZ ^olq&v o/3 
xal rj eTtl rfjg FE o^oLcog r&v avrSiv Qrj^ 17 de iTtl 
rfjg FN ilolq&v QLd' fi^ ]i xal r] iiti rfjg FE rcov 
XoLTtcbv TtdXLV etg rb rj^LXvxXLOv ^ l^ x, &0re xal 
rcjv v:t avtag evd^eLav ri FE 6vvdyeraL^ oHcjv ^sv ri 

10 FK i6rLv xe lS ]iy^ roLOvrcov ql^ T^ va^ olcov de ^ 
rZ TtdlLv ip d^ roLOvrcDV 9? ^ vg^ olcov d\ rj FN 
OfiOLCjg 'oy ]ig Jg^ roLOvrcov | Te fip, xal oicjv ccQa 
i6rlv 6 FE yvco^cov |, roLovrcov xal ri ^ev FK 
d^eQLV^ 6xLd 0vvaxd"i]6etaL l^ iTe^ r] de FZ L6rj^eQLvii 

15 Jiy Xg^ rj ds FN %SL^eQLvrj Qy % eyyLara. 

(pavsQbv de avrod^ev^ otL xal dvaTtalLVj xav di^o 
^ovoL XoyoL dod^a>6LV bitoLOLOvv ditb r&v ixxeL^evcov 
rQLcbv rov FE yvco^ovog TtQbg rdg 6xLdg^ ro re rov 
Ttolov elaQaa dCdoraL xal r] ^era^v rcbv rQomxcbv^ 

20 ineLdrJTteQ xal 8vo dod^eL^cbv bitOLCovovv TtQbg r<p E ^ 
ycovLcbv dCdoraL xal rj XoLTtij dLa rb L6ag eivaL rdg 
0z/, ^M jteQL(peQeCag. rov ^ievroL jteQl rdg rriQij- 



2. xat NEr tQCyoiva] om. D, g NEF Jj mg. Dl 4. 8i] 
om. D. 5. qve\ seq. ras. 1 litt. A. r^?] yfig D. 6. 17 (pr.) j 
add. A^ ^] -T] e corr. A, corr. ex QTt C^D^ di'] d' D. 

7. QiQ"] QTiy D, '9' supra scr. D^. r]] om. D, 8. |] seq. 
ras. 1 litt. A. 10. vcc] vd" C. 11. v?] corr. ex vy D^ 

12. i^] corr, ex x^ D^ xai] seq. ras. 3 litt. A. a^a] 
supra scr. A. 15. Qy x] supra scr. D^, 9 ^ x D. syyi^ata] 
-yiGta eras. propter figuram insertam et in mg. add. B^. 18, 
TE] supra scr. D^ 20. rc5 E] xb Ty D. 22. @^] 0A C, 
SJ %ai D. 



MA0HMATIKHS 2TNTASESiS B'. 101 

6sig avrccg dxQiPovg svsTcev ixstva ^sv adi^xdKxcog dv 
Xa^pdvoLXOy xad"' ov {)7ted£L%a^£v xqotcov^ ol dh xav 
ixx£L^£VG)v 6xiG)v TtQog xovg yvw^ovag Xoyoi, ovx 
ofiOLCog dtd xb xcbv ^lv i0rj^£QLv&v xbv xq6vov doQiCxov 
Ttcog xad-' avxbv £tvac^ xcbv d£ %£L^£Qivcbv xd xCbv 5 
X0QV(pG)V dxQa dvadidxQLxa. 

%, "Ex^^^^ig xcbv xaxd TtaQaXXrjlov idicjfidxcjv. 

Tbv avxbv 8rj XQoitov xovxoug xat iitl x&v dlXcov 
TtaQaXXrjXov Xa^6vx£g xd bXo6%£Qi] x&v ixx£Lfi£vcov 
Idicjfidxcov X£xdQxcp fiidg S^ag i6r^fi£Qivrjg cog avxdQX£i 10 
xdg v7t£Q0xdg xav iyxXC^^cov 7taQavir]6avx£g 7tOLr}66- 
fi£&a xijv ^xd^^^iv avxcbv xijv xad^^Xov TtQb xrjg x&v 
xaxd fi£Qog i7ti6vfipaiv6vxc3v xrjv dQxr^v d7tb xov {)7t 
avxbv xbv (6r]fi£Qivbv TtaQaXXrjXov 7tOir]6dfi£voi^ bg 
d(poQi^£i fi£v iyyi^xa xb TCQbg fi£6rjfiPQiav fiiQog xov 15 
oAov x£xaQxrjfioQiOV xrjg xa^ rjfidg oixovfiEvrjg, fi6vog 
d£ £X£i tdg rifi£Qag xal xdg vvxxag 7td6ag l'6ag dXXij- 
Xaig 7tdvxG}v xcbv iv xfi 6(paiQa 7taQaXXr]Xc3v rco L6rj- 
fi£Qiv^ xvxXg) x6x£ fi6vov dixcc VTtb xov bQi^ovxog 
diaiQovfiivcjv^ g)6x£ xd V7t£Q yr]v avxcbv Xfirjfiaxa Ofioid 20 
x£ dklrikoLg £ivaL xal l'6a xotg V7tb yfjv xad-^ €xa6xov^ 
xov xoLovxov fi^i 6vfi^aLvovxog i7tl firjd£fiidg xg)v 
iyxXi6£G)v^ dXXa \i6vov filv TtdXiv xov i6rjfi£Qivov 
Ttavxaxf} dixa x£ VTtb xov OQi^ovxog diaiQovfiivov xal 



1. ic8iBxa,v.x(oq BC, corr. B. Mg. xovxo xb Q^^mqi Sicc xb 

fil jjopta 0) k'yQag£ 6 n/ D. 5. ;ffi.|u.fptrco»'] jjftfispivcov xqo- 

Tt&v D, XQon&v del. D^; T(>07rtxwi/ Halma. 7. g'] om. AD. 

8. u mg. D. 12. yiuQ^oXov] -X- in ras. A. 14. og] corr. 
ex wg Cl 15. x6] corr. ex xd D. 17. 8s] 8' D. 18. r^] 
xfii corr. ex xf^ A. 



102 KAATAIOT nTOAEMAIOT 

rag xar' avtbv rj^8Qag xalg vv^v i6ag Ttoiovvxog TCQog 
al0d-'r}6LV^ BTtel xal aifxbg x&v ii£yC6x(x)v £6x1 kvxIcov^ 
xmv de XoLitGtv £Lg avL6a dLaLQOv^evcov xal xatcc xb 
xijg rjfi£t£Qag OLXOV^£vrjg £yxXL^a xcbv ft£v voxlcjx£qg)v 
6 avxov xd x£ v7t£Q yrjv x^rniaxa x&v vjcb yfjv iXdxxova 
xal xag rj^iQag xcbv vvkx&v ^Qa^vxiQag TtOLOvvxcav^ 
xcbv §£ ^oQ£LOX£QCov dvdTtaXLv xd x£ V7t£Q yr]v x^rniaxa 
^£L^ova xal xdg ri^BQag 7tokv%QOVLCox£Qag. 

^6XL dh xal dficpL6KLog ovxog 6 TtaQaklriXog xov 

10 rjXLov dlg xaxd xoQVCprjv xotg vjt avxbv yLVo^ivov 
xaxd xd xov L6riii£QLvov xal xov Xo^ov xvxXov r^ij- 
^ata^ G)6t£ x6t£ ^ovov tovg yva^ovag iv tatg ^£6ov- 
Qav7]6£6Lv d6xLovg yLV£6&aL, xov d£ rjlLov xb fihv 
P6q£lov rj^LXvxXLOv dLa7toQ£vo^ivov xdg x&v yvcD^6vcov 

15 6xLdg d7toxXLV£Lv TCQbg ^£6r]^pQLav^ xb d£ v6xlov 7tQbg 
xdg ccQxxovg. xai i6XLV ivxavd^a^ oicov 6 yvco^cov 
S, xoLOVxcov ixaxiQa fj x£ d-^QLvij xal rj x^L^^QLvrj 6XLd 
x^U £yyL6xa. 

XiyofL£v d£ xad-^Xov 6xLdg xdg iv xatg ^£6r]^PQiaLg 

20 yLvo^ivag xal ag ^rjd^vl d^LoX6ya) dLacp£Qov6ag dia 
xb ^ri Ttdvxcog iv avxatg xatg ^L£6riii^QiaLg xdg x£ i6rj- 
^£Qiag xal xdg XQ07tdg dxQL^cbg d^tot^X^t^d^aL. 

totg d£ vTtb xbv L6rjii£QLvbv xaxd xoQvg)rjv ^£v 
yivovxaL x&v d^xiQcov^ o6ol xax avxov xov i6ri^£QLV0v 



2. iwft] -si in ras. 1 litt. A^. 4. votslotsqcov, -sl- e 

corr., D. 6. vvyiTmv] bis C, sed corr. 7. di] corr. ex ts D^ 

9. ^6Tiv D. ovTog^ ovTcog C, avTog D. nuQdXXriXoGi B. 

10. Toig'] corr. ex tt)? D*. 11. ra] ins. B^, supra scr. C^ 
Supra T^riiiuTcx. add. %oivd D*. 15. nqog — 16. v.ai~\ 

mg. A^ 16. svTavQ^a] -a postea add. D. 17. v.al 17 xsiiis- 
qivri] om. BC, post 6v.id add. C^ 20. alioXoym] -0- e corr. B*, 
corr. ex to C^. 21. lerniSQLag] -a- e corr. A. 23. terjfiSQL- 
vov] l- ins. A^. 



MA0HMATIKHS STNTAgESiS B'. 103 

TCOLOvvtai, rag TtSQLtpoQccs^ Tcdvxeg de xal dvarsXXovtss 
xal dvvovtsg (paCvovtai tcbv tfjg 0(paLQag TtoXcjv cV 
ccvtov tov ^QL^ovtog ovtcov ocal ^rjdeva xvxXov itoiovv- 
Tcov ^TJts t&v TtaQaXXTJXcov dsl (pavEQOv t) dsl dcpavfj 
^rjts ta)v ^s07]^pQi,VG)v k6Xovqov. oCxTJasLg ds slvac 5 
(isv VTtb tbv L6rj^SQLvbv svdsxs^d^aL (pa6Lv ag Ttdvv 
svxQatov dtd tb tbv ^Xlov ^t^ts totg xatd xoQvcprjv 
6rj^SL0Lg syxQOVL^SLV taxsCag yLVO^svrjg tfjg jtSQl td 
i6r]^SQLvd tiLrinata xatd itldtog TtaQaxcoQtjascjg^ od^sv 
av t6 d^^Qog svxQatov yCvoLto^ inrit iv tatg tQOitatg lo 
TtoXi) d(pC6ta6d-aL tov xatd xoQV(p7]Vy ag ^irjds tbv 
XSLiLcbva 6(podQbv TtoLstv tCvsg ds sl6lv aC oCxTJasLg^ 

OVX dv SXOL^SV 7tS7tSL6^SVC0g stltStV' dtQLTttOL yaQ 

si6L ^sxQL tov dsvQO totg ditb tfjg xad^' rj^ag olxov- 
^svrjg^ xal sixa6Cav iiaXlov dv tLg ri L6tOQCav rjyTJ- 15 
6aLto td Xsyo^sva TtSQl avt cbv. td ^sv ovv 1'dLa tov 
vTcb tbv i6rj^sQLvbv TtaQaXXtjXov 6vvsX6vtL siTtstv 
ravta dv strj. 

TtSQl ds tcov XoLTt&v^ d(p G)v xal tdg oixrJ6scg 
tLvlg olovraL xarsLXfj^pd-aL^ 7tQ06d^7]6ofisv ixstva xolv6- 20 
rsQOV^ Lva ^fi xad'' sxa6tov tavtoloycb^isv^ otL ts tcbv 
iq^s^flg sxd6tov xatd xoQv^pf^v yCvovtaL tcbv d6tsQcov^ 

060L tflV t6riV TtSQLCpSQSLaV d(ps6t7]xa6LV tov i6rj^SQLV0V 



1. noLovvxai] -vxoci ins. in spatio uacuo 2 litt. D^. rag] 
g xdg D. nsQiq^OQdg'] corr. ex nsqicpsQBCcig D^ 3. >tvM>loj'j 

corr. ex 'Avv.Xcav C^, v.vv.Xcov D. 4. /Lityrf] ^iiidi D. cpuvsqo^ D. 
iccpavfi] 6c- supra scr. D^. 5. x&v fiEcsria^QLvdbv'] x fiecrjii^Qiv 

mut. in 'x (i£a7](i§Qi,v^ B^. 10. fit^xe D. 13. ovv.] o- in 

ras. A. 7ce7teiG(ievcog] ne- corr. ex nex- C^. 14. (iexqC] (i- 

inras. D. 15. ijynoaixo] fjyi^cjaxo C^ 16. xov] xa^^ D. 17. 
naQaXXriXovg C, -g del. C^. 22, e%ck6xov] eyidaxrjg D, ev,daxov D'. 



104 KAATAIOr nTOAEMAIOT 

STtl tov dicc t&v Ttolav avtov xvxkov^ ijv xal avtbg 
6 VTtOKSLnsvog TtaQalXrikog a<p60trjxs^ xal oti, g^avsQog 
fisv dsl TtvTcXog yCvstai 6 7t6X(p ^isv ta ^oqsCo) TtoXc» 
tov i6ri^SQLVov^ dia€triiiLatL ds tco tov itokov s^ccQ^atL 
5 yQag)6^svog^ xal oC Sfi7tSQLXa^Pav6^svoL vjtb tovtov 
a6tSQsg asl (pavsQoC^ asl d' aq^avijg xvxXog 6 TtoXe^ 
fisv Tc3 votCc!) 7t6l(p^ dtaetrifiatL ds t<p avta yQa^p^- 
fisvog, xal ol svtbg tovtov d6tSQsg dsl dcpavstg. 

p\ dsvtSQog yCvstaL TtaQaXXrjXog^ xad^' ov rj fisyC6tr} 

10 rjfiSQa s6tlv cjQcov lcrnisQLvcbv l^ d\ ovtog ds ditsyst 
tov L6rjfiSQLV0v fioCQag 6 d\ xal yQacpstaL dLa TajtQO- 
pdvrjg trjg viJ6ov. s6tL ds xal ovtog tcbv dfi(pL6xCc3v 
Tov rjXCov jtdXLv dlg totg vjt avtbv ytvofisvov xatd 
xoQvcpijv xal tovg yvcofiovag sv tatg fis6ovQav7]6s6i^ 

15 TtOLOvvtog daxCovg^ otav ditsxr] tfjg d^SQLvrjg tQOTtrjg 
s(p sxdtSQa td fiSQr} fioCQag o^L^^ a6ts tdg fisv Qvd' 
tavtag avtov dLaitoQsvofisvov tdg tcbv yvc3fi6vcov 
exLag ditoxXCvsLV sig td voTta, tag ds koLitdg 'ed^ slg 
Ttt ^6QSLa. xaC s6tLV svtavd-a^ olcov 6 yvafiov J, 

20 TotovTov r] fisv C6r}fiSQLvi] 6XLd d y' l^\ 7] ds d^SQivif 
xd y'y r] ds xSLfiSQLvri X^. 



1. 8id'\ $ seq. ras. 1 litt. B. 2, cccpsGTrjyisv D. 3. 

wdXo) (pr.)] TtoXoai, l in ras., A; kevtqco D. 4. SLaGT^^ficcTL] -l 
corr. ex -r\ C. 5. iv7tsQiXccfi§av6fi£V0L D. 6. S'] s ins, B, 
seq. ras. parua C. TtoXo)'] om. D, fe supra scr. D*. 8. tovzov] 
corr. ex tov D^ et mg. D, ccrpavsLg] cc- ins. D^ 10. aQOiv 

S6TLV D. d'] ins, D^ ovtos — 11. 8'] mg. B, hsl^svov 

add. B^. 11. ^OLQag] comp. ABCD, ut semper, TanQO- 

^dv7\g] Ta- supra scr. D^. 12. sctl] -l corr. ex t) C^. ovTog] 
corr, ex ovTcog C^, avTog D, dficpLGyiioav] -fi- in ras. A. 13. 
vTc'] vno D. 16. ^cp'] slg D. Td] om. D. 18. rdrta] 

vmtsia D ; similia saepius. ca] 6- renouat. A, c- e corr. B^D^ 
20. TOLOVTcov] TOLOv- iu ras. A. l§'] Z^' BC, 21. xa y'] 
xy a D. 



MA0HMATIKHS STNTAEESJS B'. 105 

y\ tQLtog ds ictiv TcaQcckXrjXog^ xad'' ov av ysvoito 
7] fisyLatrj y]^BQa hg&v l6r]^SQLVG)v a/3/.'. ovtog ds 
k%i%Bi tov L6r]^£QLvov iLoiQag fj ze xal yQcccpstai dta; 
tov AvaXCtov xolitov. s6tiv ds xal ovtog t&v d^cpL- 
6kl(dv tov r]XLOv dlg tolg vtc avtbv yivo^svov xata 5 
7C0Qvq)riv xal tovg yva^ovag sv tatg ^s6ovQav7]6s6LV 
d6xL0vg TtOLOVvtog^ orav tfjg d^SQLvrjg tQOTtrjg ditsxr} 
Sfp^ sxdtSQa td ^SQrj ^OLQag l-O*, S6ts tdg ^sv Qlr] 
tavtag avtov dLaTtOQSvo^svov tdg tcbv yvco^ovov 
6XLdg djtoxUvSLV TtQog ^s^rj^^QLav,, tdg ds XoLitdg 6x^ 10 
TtQog ccQxtovg. xaC s6tLV svtavd^a^ olcov 6 yvco^cov |, 
tOLOvtcov rj ^sv L6r]fiSQLvii 6XLd fjC y\ r] ds ^SQLvij 
TgC y\ r] ds xsL^SQLvr] AJ/.' y' ls. 

d\ tstaQtog ds s6tLV utaQaXXrjXog ^ xad'^ ov dv 
ysvoLto r] ^syC6tr] r]^SQa gjq&v L6r]^SQLvcbv l^L' 8'. Ib 
ovtog d' ditsxsL tov L6r]^SQLvov ^oCQag l^C ^^^ yQa- 
(pstaL dLd tov ^AdovkLtLXOv x62.7tov. s6tL ds xal ov- 
tog t&v d^(pL6xCcov tov r]XCov itdkLv 8lg totg 'bno 
avtov yLVO^svov xatd xoQvcpi]v xal tovg yvm^ovag sv 
tatg ^s6ovQav7]6s6LV d6xCovg Ttoiovvtog^ otav djtsxi] 20 
tfjg d^SQLvfjg tQ07tf]g scp' sxdtSQa td ^sQr] ^oCQag v^ 



1. 8i ECTiv] E6XI D. 2. ds] d' D. 3. ccTtExsi] corr. ex 
anixv C^. 4. Supra Avoclixov ras. B. ovxoq'] corr. ex 

ovxmg C^, avxog D. 5. xoLg'] corr. ex xcclis D^. 6. iisoov- 

Qavri6E6i D. 8. qXri] -73 e corr. D. 11. tiqo?] Ttgbg xdg D. 
12. fii' y] TiU y' A; similiter saepe. 13. ls'] A, t' s' §' B, 
Ts p^ C, i§ D. 14. di] d' B, om. D. fW D, comp. B. av] 
STipra scr. A. 15. L6r]^tQLv&v] om. D. d'] in ras. D, seq. 
ras. 1 litt. 16. S'] da\ A, in ras. D. 17. 'JSovXlxlkov] 

alt. L corr. ex D. i'6xlv D, comp. B. ovxog] post pr. o 
ras. 1 litt. A, corr. ex ovtcog C^, avxog D. 18, V7t' D. 19. 
yivo^ivoLg D. 20. TtoLovvxog] -og corr. ex -cog C. 21. xa] 

om. BC. 



106 KAATAIOT nXOAEMAIOT 

r§, S6tE tag ^sv ^ y' tavtag avtov dcajtOQSvo^svov 
tag tcbv yvco^dvcjv 0XLag aTtOTtXCvnv TCQog ^s6rj^PQiav^ 
tag ds loiTCag 6^d rg TtQog tag aQxtovg. xaC iativ 
svtav^a^ oX(QV 6 yva^ov |, tOLOvtov ri ^sv LerjfiSQcvri 
6 0XLa Ty y\ r] ^s d^SQLvrj 6/3, ri ds xsl^sqlv^ ^d g\ 

s\ Tts^TCtog s0tlv jtaQdXkrjXog^ xad'' ov av ysvoLto 
ri ^syCatri rj^SQa caQ&v L0r}^SQLvS)v Ty, ditsxsL d^ 
ovtog tov C6r]^sQLV0v ^oCQag Tg x^ xal yQdcpstaL dLa 
MsQorjg tfjg vr]6ov. s6tL ds xal avtbg tcbv d^(pL6KCG)v 

10 tov rjXCov dlg totg vit avtov yLvo^svov xatd xoQvq)r]v 
xal tovg yva^ovag sv tatg ^s6ovQavr]6s6LV d6xCovg 
TtOLOvvtog^ otav dTtsxjj tfjg d^SQLvrjg tQOTtrlg s(p^ sxdtSQa 
td ^SQrj ^oCQag /Zf, &6ts tdg ^sv c, tavtag avtov dLa- 
7tOQSvo[isvov tdg tcov yvca^ovcjv 6xLdg dnoxXCvsLv JtQog 

16 ^s^rj^^QCav^ tdg ds loLitdg ^ JtQog tdg ccQXtovg. xaC 
sCtLV ivtavd^a^ olcov 6 yvcb^c3v |, tOLOvtcov rj ^sv 
C6r]^SQLvrj 6xLd l^C ^\ V ^^ ^SQLvi] t, L' 8\ r] ds ^sl- 

[ISQLVY] Vd. 

g'. sxtog i6tlv 7taQdXXr]kog^ xad'' ov dv ysvoLto 

20 i] ^syC6tr] r]^SQa cdq&v i6r]^sQLV&v Ty d\ djts%SL ^ 

ovtog tov L6r]^SQLvov ^oCQag x Ld xal yQacpstai dtd 

Najtdtcjv. s6tL ds xal avtbg t&v d^(pL6xCcjv tov 



1. r^] (hoc est %) fo A, i§ C, tp BD, corr. in tqCtov B^ 
y']^ut. in Fo B\ 3. r^] fo A, cp C, 7§ BD, mut. in i^ B\ 
5. (iS] post ras. B, (iX D. 6. ioxL D, comp. B. 7. r]fi8Q D. 
OQoav C. d'] di D. 8. ypaqpftat] yQ- renouat. B^ 9. 

MeQor^g xfjg] -g x- renouat. D^. v^aov] vrj- renouat. B^. ^azLV D, 

comp. B. 10. dig] Slo BC. Post yLvoiiivov 1 litt. del. D^. 
13. rdg] rcctg C. 15. >tat sgtlv] bis D, corr. D^. 18. vcc] 

r ra D, iv akXco ^l^Xlco nQoayiSLxaL tOLg vcc xal t6 y mg. D^ 
19. iaxL BD. ' 20. OQoav C. Lf] -y ins. D^ S'] di D. 
21. Sid] ^ D, ut saepius. Slcc Nandtcov] corr. ex Sl' ccvoc- 

ndxoav B^, dLauvccndxoov C. 22. eazLV D. 



MA0HMATIKHS 2TNTASE^S B'. 107 

rjlLov rotg xat^ ccvtbv dlg ycvo^svov Tcatcc xoQV(piiv 
Tcal tovg yvih^ovag iv talg ^s^Tj^^QLaLg a6Ktovg 
TCOLOvvtog^ otav ccTtsxr] tflg d^sQivflg tQOTCijg S(p sxd- 
tsga ta ^sqt] ^oiQag Aa, S6ts tdg ^sv |^ tavtag 
avtov diaTtoQSVo^svov tdg tcbv yvco^ovov (Sxidg dito- 5 
xkCvsLV TtQog ^sdri^^QLav^ tdg dh XocTtdg e^ JtQog tdg 
ccQXtovg. xaC s6tiv svtavd^a^ oXcov 6 yvco^cov |, tOLov- 
tcov ^i fihv i^rj^SQivii 0XLd xp g', ij ds d^SQLvii y C ^\ ^ 
ds xsL^SQLVYj vri g\ 

t,\ spdo^og s6tL TtaQdXXrjXog^ xad"^ bv dv ysvoLto 10 
r] ^syCijtr] rj^SQa Sq&v C6r]^SQLvav Tyi^. ditsxsL d' 
ovtog tov L6ri\iSQLVov ^oCQag xy vd xal yQacpstaL d^d 
Z!o7]vrjg. %Qcbtog ds s6tLV ovtog TtaQallrjXog tcav 
xalov^svcov stSQ06xCcov' ovdsTtots yaQ totg vTtb avtbv 
oIxov6lv sv tatg ^s^rj^^QCaLg at tcbv yvco^ovcov 6xLal 15 
TtQbg ns^rj^^QCav djtoxXCvov^LV^ dXX^ sv \jisv avtfj \i6vtj 
tfi d-SQLvfj tQOTtfj xatd xoQVfpfjv avtotg 6 ijXLog yCvstaL, 
xal OL yvco^iovsg d6xL0L dscoQovvtaL' to6ovtov ydQ 
dnsxov^Lv tov L6rj\isQLvov ^ o6ov xal ro d^SQLvbv tQO- 
TtLxbv 6rj\istov' tbv ds dXXov Ttdvta %q6vov aC t&v 20 
yvco\i6vG)v 6xLaL TtQbg tdg aQXtovg djtoxXCvov^Lv. xal 
ivtavd^d idtLv^ olcov 6 yvco^icov J, tOLOvtcov ij \isv 
i6rj\isQLvi} 6XLd xgL\ V ^^ xsL^iSQLvi] ^sL! y\ rj ds ds- 



1. roLg] om. D. ccvxov] avr&v A. 2. (UfffTjfi^ptatg] (isoov- 
QocvrjGEGiv D. 7. ol'(ov] o- corr. ex i. A. 6 yvcbfwoj/] corr. ex 
xav yvcofiovcov D^ xoGovxoov D. 9. vjj <s'] corr. ex rL ^ ^^' 

10. iGxiv C, comp. B. naqaXkiiXoii] n- corr. ex v A. ys- 
voiro] ysvoL C. 11. d'] Ss D. 12. ovxog] corr. ex ovx(og C. 

13. Z(oCv7]g D. ovxog] ovxmg C, ovxog 6 D. 14. vno] 

vn CD. 15. av.iaL] -v,- in ras. A, pr. t e corr. D. 16. 

iis6ri\L^QLav] -6- e corr. D. ccnoy,uLVOv6LV C. 19. ansxov6L D. 

22. S6XLV svxavd-a D. 23. 17 (alt.) — p. 108, 1. S6ri] om. D. 



108 KAATAIOT nXOAEMAIOT 

QLvrj cc6m6g £6X1. xal itdvreg de ot rovtov ^oqsioxeqoo 
xaQccXXrjXoL inexQi xov xijv rj^sxaQav OLXOv^evrjv cccpoQL- 
t,ovxos exeQodKLOL xvyxdvov0LV ovxeg' ovdeicoxe yccQ 
Ttax avxovg ol yvco^oveg ev xatg ^e^rj^PQLaLg ovxs 
5 a0XLOL yCvovxaL ovxe xccg ^KLccg %olov6lv TtQog ^e6rj^- 
PQLav^ dkkcc Ttdvxoxe TCQog aQKXovg^ dLa xb ^r^de xbv 
7]Xl6v Ttoxe xaxd xoQvcpijv avxotg yCyve^d^aL. 

r]'. '6ydo6g iexLv TCaQdXlrjXog^ xad'^ bv dv yevoLxa 
r] ^eyL^xrj rj^eQa Sqcov L6r]^eQLVG)v Tyi! ^- diteyeL d' 

10 ovxog xov C^rj^eQLVov ^oC^ag scj fc/3 xal yQdcpexaL dta 
nxoXe^atdog xrjg iv ©r^PaLdL^ xaXov^evr^g de 'EQ^eCov, 
xaC i6xLV ivxav&a^ oXcov 6 yv6^cov |, xolovxov '^ ^ev 
d^eQLvij 6xLd yi\ r] 8e i^rj^eQLV^ 2,g L' y\ "h <^^ %fif*f- 
QLvri od g'. 

15 '9''. evax6g i6XL TtaQdXXrjXog^ xa-O-' bv dv yevoLXO 
ri neyC6xri ^rj^eQa Sqcov L6ri^eQLvcbv l8. d%e%eL d* 
ovxog xov L6r]^eQLV0v fioCQag A x/3 xal yQdcpexaL dta 
trjg xdxcj x^Qag xijg Aiyvnxov. xaC i6XLV ivxavd^a^ 
OLcov 6 yvd)^c3v |, xolovxcjv r} ^ev d^eQLvi] 6xLd g/.' y\ 

20 r] de L6r}^eQLvri ke l^\ rj Se xeL^eQLvrj jty t/3'. 

l\ dexax6g i6XLV TtaQdXXr^Xogy xad"^ bv dv yevoLXcy 
rj fieyC6xrj rjfLeQa aQcbv C6r]^eQLv&v lS d\ ditexeL d^ 



1. a<Jxtog] &- supra scr. Al 5. ■noiovGi B. 6. ndvtors] 
seq. ras. 1 litt. D. ccQyizovg] -%- supra scr. A^, raff ccQv.tovg J). 

(iTidsl fii] D. 7. avtoig nots v,ccta ■aoQvtprjv D. yCvscd-cci 
CD. 8. iatL D, comp. B. 9. 8"\ di D. 10. fiotQccg^ 

om. D. 11. iv] sv tjj D. ©rj^aiSri C. @r}§ca8i —_Ss] 

mg. A\ 'EqiisCov] 'Eq- in ras. 4 litt. A^ 13. X?i'] Xi D. 

14. od] e corr. D^. 15. svvcctog C. iativ C. 16. d'] 
Ss D. 17. X] in ras. A. 810] dh 8id C. 19. /.'] its D. 

20. i^' (pr.)] z fi' BC. ny] corr. ex Ey D^. i^' (alt.)] Z |3' 
BC. 21. icti D, comp. B. 22. 8'] 8s D. 



MA0HMATIKHS STNTASESiS B'. 109 

ovrog xov i^rj^sQLvov ^OLQag Xy Trj xal yQdcpsxai dia 
0OLVLxr]g ^E6rjg. xaL s6vlv ivtavd-a^ olcov 6 yva^cov 
I, toLOvtcDv rj ^sv d^SQLvij 0xLa r, r} dl L^rj^SQLvri kd^C^ 
rj ds xsL^SQLvij ^ t/3'. 

La\ svdsxatog sCtL naQallrilog^ xad'' bv av ysvoLto 5 
17 [isyL^trj ij^SQa G)Qcbv L6r]^SQLvav LdL', aitsiSL d^ 
ovtog tov L^rj^SQLvov ^oLQag Ag xal yQcccpstai Slcc 
^Podov. xaC s6tLV svtavd-a^ olcov 6 yvcD^cov |, tOLOvtoav 
rj ^sv d-SQLvrj 6xLa L^i' y' l^\ r\ ds L6rj^SQLvri JiLyi' y\ 
r] ds %SL^SQLvri 'oy y\ 10 

t/3'. dcjdsxatog s6tLV TCaQaXXriXog ^ xa%^ bv ccv 
ysvoLto rj ^syL0trj ri^SQa Sq&v L6rj^sQLVC)v Ldi' d\ 
ccjtsxsL d' ovtog tov L6r]^sQLvov ^OLQag Xrj Xs xul yQa- 
<pstaL dLcc U^VQvrjg. xaC s6tLv svtavd^a^ olcov 6 yvd)- 
ftov I, tOLOvtcov rj ^sv dsQLvij 6KLa Ts r^^ rj ds L6rj- 15 
^SQLvri iit,L! y\ rj ds xsL^SQLvij QLdi' y' l^'. 

Ly'. tQSL6KaLdsxat6g i6tL JcaQccXXrjXog, xad'^ bv av 
ysvoLto r] ^syL6tr] rj^SQa Sq&v i6i^^SQLVK>v Ts. aTCsxSL 
d' ovt og rot) L6r}^sQLvov ^OLQag ji vg xal yQcccpstaL 
Sl^ ^EXXrj67c6vtov, xai i6tLv ivtavd^a^ oXcov 6 yvch^cov 20 
5, tOLOvtcov rj ^isv d^SQLvi} 6xLa Trji^ rj ds L6ri^SQLvii 
^^ g', i] 8s xsL^SQLvii Qx^i' y'. 



2. fisGiqg] -6- e corr. A. 3. 7] ins. D^. /_'] om. D. 4. 

t^'] t' ^' AB^, l §' BC; similiter saepius. 5. ta'] ca B. 

EGTiv C. 6. S'] ds D. 9. 97 ^^ — i' y'] bis A, sed 

corr. fly] ^ y D, /x add. D^. y'] om. C. 11. i^'] §1 B. 
icTL D, comp. B. 14. SyLVQvrig'] -g e corr. D. iGtiv] 

^Gxai D. 15. r^] to A, T^ B, Fo B3, r^ C, i8" C^ U ^ D. 
16. fi^ — ;u£t/x£9tvj7] supra scr. D^ 17, ty'] yt B. xQiG- 
'AaidBv.uxo£ B. 19. 8'] 8b D. i^] X tg D. 22. 5'] in 

ras. A. Qv.^] corr. ex ^x B^, px C. 



110 KAATAIOT nTOAEMAIOT 

td'. r£60aQe6xaLdexar6g i6rt, JtaQdlXrjXog, xad'^ bv 
ctv yivoLro yj ^syL^rrj rjfisQa Sq&v l67]^sqlvg)V Ts d\ 
a%s%SL d* ovrog rov i^rj^SQLvov [lOLQag fiy d xal yQa- 
^raL dLO. Ma66aUag, xaC s6rLV svravd^a^ olcov 6 
5 yvcb^cjv I, roLovrcov 7] ^sv d^SQLvri 6xLa x/.' /, rj dl 
CerjfisQLV^ vsL! y' t,^\ ri 8s xsL^iSQLvii Q^id. 

Ls\ TtsvrsxaLdsxarog i6riv TtaQaXXrjlog^ xa%^ bv av 
yivoLro r] ^syL^rrj ij^iQa Sq&v t0r}fiSQLVcov lsL!. a%- 
i%SL d* oiirog rov l6r\yiSQLVov fiOLQag JTs d xat yQcccpsraL 

10 dLcc [lieov Udvrov. s6rLV ds ivravd^a^ oXcov 6 yvch- 
^cjv I, roLovrcov r] ^sv d^SQLvrj 6xLa xy d\ rj ds L6ri- 
[iSQLvr} rcov avrcbv \^ r] 8\ xsl^sqlvtj qvs l^\ 

Lg\ sxxaLdixardg i6rLV TtaQccXXrjXog^ xad^' bv ccv 
yivoLro 17 ^syL6rr] rj^iQa d}Qcbv L6r]^SQLv&v ls L! ^» 

15 a7ti%SL ds ovrog rov i6rjfisQLVov ^OLQag jilg va xal 
yQacpsraL dt^ r&v nrjy&v rov "l6rQ0v Jtora^ov. s6rLv 
ds ivravd-a^ oXcov 6 yvco^cov |, roLOvrcov rj ^sv d-SQLvr] 
6xLa xsi\ rj ds L^rj^SQLvrj ^yi! y' t/3', r] 6s %SL^SQLvi] 
Qoa g'. 

20 L^'. STtraxaLdixardg i6rLV jtaQaXXrjXog^ xad'' bv av 
yivoLro r] ^syC^rr] rj^iQa &)Qcbv C6r]^SQLva)V Tg. a7ci%si 
df ovrog rov C6r]^SQLVov ^oCQag ]ir] A/3 xal yQacpsraL 



1. i,d'~\ 81 B. x£66aqi6v.ui8BY,axoQ CD. 3. iioiQug] om, 
AC. S'] corr. ex l B'C^ 4. Mci66ccXCa(s] pr. 6 in ras. A, 
8iu §v^avxLOV mg. A*, Ma6aXCag BC, pr. a corr. ex ta D^ 5. 

x] X C, xp D. 6. ^] ^ (J' BC. 7. tf'] Ei B. 86X1 D, 

comp. B. 9. a] X C. 10. ftfffov] -v supra scr. C^, (iseov 

xov D. hxL A, comp. B. 12. tp'] corr. ex l8 Cl 

13. ig'] gt B. sti-iiaLdiyiaxog] AB, e^yiaLdsKaxog B^CD. 

iexLv] comp. B, 8s s6xl D. 14. t^rifiSQLvcov] om. D. 15. 
8s] d' C. yial yQcccpsxaL] bis D. 16. xov "l6XQ0v] "I6xqov 

xov D. 18. ly] l^ D. 19. Qoa] mut. in ^B^. s'] mut. 

in Ss" C*. 20. L^'] ^L B. t6XL D, comp. B. 22. di] 6' BC. 



MA0HMATIKH2 STNTASESiS B'. 111 

dia tav ixPoXav BoQved^svovg. a6XLV de ivtavd^a, 

OLCOV 6 yVCO^CDV ^, tOLOVtCOV 7] H£V d-EQLV^ ^KLO. X^L\ 

7] de L6r]^£QLvrj J^/,' y\ 7] de %£Lii£QLvii qtitjL' ^/3'. 

Lr}\ dxtooxaLdixatog £6tLV TtaQccXXi^Xog^ xad'^ bv av 
yivoLto ri n£yL6tr] rj^iQa coQav L6r}ii£QLVG)v Tg d\ 5 
a%i%£L d' ovtog tov t6rj^£QLvov ^OLQag v d xal yQcc- 
<p£taL dLoc ^i6rjg trjg MaLcatLdog XL^vrjg. £6tLV ds iv- 
tavd^a^ OLCov 6 yvw^cov |, tOLOvtcov r] ^uv d^^Qiv^ 
6XLa xd^C y' t'^\ V ^^ L6riiii£QLvri oa rS, 17 <^^ x^l^^qlv^ 
6rj y\ 10 

Ld''. ivv£axaLdixat6g i6tLV TCaQaXXrjXog^ xad"^ bv ccv 
yivoLto rj ii£yL6ti] rj^iQa coqcov i6rj^£QLVcbv Tg/,'. djc- 
iX£L dh ovt og Tot) L6rjii£QLV0v fiOLQag vaC g' xal yQa- 
q)£taL Sid t&v votLcotdtcov trjg BQ£ttavLag. £6tLV d\ 
ivtav&a^ olcov 6 yva^cov |, toLOvtcov r] ^£v ^£qlv^ 15 
6XLd Xa y' L^\ r] ds i6ri^£QLvri oi y' l^^ 17 dh %£LiL£QLvii 
6x0" y\ 

X . £lxo6t6g i6tL TtaQallrikog^ xa^ bv dv yivoLto 
rj ^£yL6tr] rj^iQa coqcov L6r]^£QLVcov TgL' ^* dTti%£L d' 
ovtog tov l6r\yb£QLVov [lOLQag v^ v xal yQd(p£taL did 20 
tG}v tov ^Pt^vov ix^oXcbv. £6tLV Ss ivtavd^a^ olcov 6 
yvco^cov I, toLOvtcov r] [uv ^£QLvr] 6xLd Xy y\ r] ds 
L6r]^£QLvr] od' t/3', r] ds %£L^£QLvr] 6vy g'. 

1. ds] S' D. ivtav^Dc] -cc e corr. C^ 3. ;ffi/*f()ti;r]t A. 
Qnri] QTt D.' Mg. yQ. y B^. 4. lt}'] rjt B. iGn D, comp. B. 
nagdXl D. 6. 8'] di D. v d] C, ^ ABD. 7. McaotiSog C. 

_Si] S' D 9. r*] h in ras. A, r BC, Fo D. 10. ^ y'] 

6riy D, -T? e corr. C^, supra y' add. o B^ euan. (mg. 25 B^) et 
co C^. 11. t-O-'] "S-t B. ivvsccnaiSi-iiaxog] pr. -a- supra 

scr. D3. iaxi D, comp. B. 13. Ss] S' C. g' xat'] g D 

(h. e. xat). 17. ayid-] 6yi§ post eras. ayid' y D. Supra y' 

add. io B^ 18. icxLv C, comp. B. 19. S'] Si D. 21. 

scTL A, comp. B. 22. Supra y' add. S B^ 



112 KAATAIOT nXOAEMAIOT 

'na . eixo^rbg TtQCJtog s6tLv TcaQcclXrjXog ^ xad'' bv 
av yivoLXO r] ^EyCcrri rj^SQa Sq&v i6rj^SQLVCov t^. 
aTtexsi ^£ ovxog xov i6rj^sQivov ^oiQag vd k xat yQa- 
tpsxai 8ia xcbv xov Tavdidog ixPoX&v. s6xiv d^h sv- 
6 xavd^a^ oi(ov 6 yvco^cjv ^, xoiovxcjv r] ^ev d-eQivii 
6Xia Id C y t/5 5 r] de iarj^SQivii %^C ^/3', r] ds xsi^SQivij 
6orjL' 8' 

xp\ SiKoaxbg dsvxsQog s6xi TtaQallrilog^ xa%-' ov 
av yevoixo rj ^eyiOxrj ri^eQa g)q&v i6ri^eQivcbv i^ d'. 

10 ditiyei d' ovxog xov i0r]fiSQiVOv fioiQag vs xal yQa- 

(psxai did BQiyavxiov xr]g ^sydXrjg BQSxxavCag. s0Xi 

ds svxavd^a^ otov 6 yvco^cjv ^, xoiovxcov rj ^sv d^SQivrj 

exid Xg d\ rj ds C6rj^sQivri jte r§, rj ds xsi^sQivi] xdi\ 

xy\ slxo6xbg XQCxog s6xlv TtaQdXXrjXog^ xa&^ bv dv 

15 yivoixo rj ^syCaxrj rj^iQa ciQcbv C^rj^SQiV&v i^L'- ^^- 
i%si d' ovxog xov C^rj^sQivov ^oCQag vg xal yQdipsxat 
did fiidrjg xfjg ^sydXrjg BQSXxavCag. sdxiv ds ivxav^a^ 
Oicov 6 yvcb^cov J, xoiovxcov r] ^sv d^SQivi] 6Xid kt, rS, 
r] ds i6r]^SQivr] ytrjL' y\ r] ds xsi^iSQivi] xks d\ 

20 x8'. sixo6xbg xixaQxog i6xiv TtaQdXXrjKog^ xa%^ bv 



1. BhoGroq nQ&x6g iariv] nQcbxog xat sUoaxog D. 3. ds] 

d' C. 1] A, cc BCD. 6. y'] corr. ex t D.^ «^'(alt.)] om. C. 

8. sUoaxbs dsvxsQOs] dsvxsQog xal sUoaxog D. 10. d'] 

8i D. 11. BQLxavlccg D, t corr. in s D^. ^axLV D. 13. 

d'] ins, A^ ante ras. 1 litt. Tts] corr. ex jry D. r^] ij A, 

i^ C, r" BD, corr. B^ /_'] g D, 14. xQLxog xat sUoaxog D. 

saxL p, comp. B. 15. cctisxsl] Slsxbl C, 16, d'] Ss D, 

17, BQSxxavLocg] xfjg BQSxxavlag A, xfig del, A^; BQSxavviag D, 

Ss] d' D. _ 18. U] -^ e corr. D^. r^] Fo ins. A\ y BC, 

corr, B^; ijo D, o del, 19. y'] om. D. %ftfi£ B extr, co- 

lumna, xXs] xX^ D. 20, xsxaQxog v.al sUoaxog D. iaxL D, 

comp, BC. 



MA0HMATIKHS STNTASESiS B'. 113 

€cv yevotto rj iisyC^xri i]^iQa Sqcjv i^rj^SQLV&v tj/.' d\ 
aitiiu 8\ ovtog tov Ldr^^SQcvov ^OLQag v^ %al yQacpetaL 
Slcc KatovQaxtovLOv trjg BQSttavCag. s6tL da ivtavd-a^ 
OLcov 6 yva^cov |, tOLOvtcov ii ^sv d^SQLvrj 6xLa AO' y\ 
4] ds Ldrj^sQLvrj c,^ y' l^\ rj ds xsl^sqlvyj to/3 t/3'. 5 

xe\ SLK06tbg TtifiTCtog i6tlv TtaQdXXrjlog, xad'' bv av 
yivoLto rj ^syL6trj rj^iQa d)Q&v icfrj^sQLV&v Trj. dTtiyjsi 
d\ ovtog tov L6rj^SQLvov ^otQag vrj xal yQdcpstaL dLd^ 
tcbv votLcov tfjg iiLXQag BQSttavCag. s6tLV 8s ivtavd^a^ 
OLCov 6 yv6^cov |, tOLOvtcov rj fisv d^SQLvrj 6XLa Ji rS, 10 
ri ds L6r]^SQLvri 9g, ^ df xsL^SQLvrj vlO" l^\ 

xg\ SLX06tbg sxtog i6tlv TtaQdlXrjXog, xad''' bv av 
yivoLto ri ^syC6trj rj^iQa coq&v L6r}iisQLV&v Trji'. dit- 
ixsL ds ovtog tov L6rj^sQLvov ^oCQag vd^L' xal yQdcpstai 
Slcc tcbv fii6cov tfjg ^LXQccg BQSttavCag. 15 

ovx ixQri6diis%^a ds ivtavd^a tfj tov tstdQtov tcbv 
SqS)v 7taQav^7j6SL dLa ts tb 6vvsxsLg rjdrj yCyvs^d^at 
tovg TCaQakkrikovg xal trjv tcbv i^aQ^dtcov dLacpOQav 
firjxitL ^rjds^tag oXrjg ^oCQag 6vvdys6d-aL xal dta t6 
^fj o^oCcog rj^tv ijtl t&v itL ^OQSLOtiQcov TtQo^rjxsLV 20 
i7ts%SQydt,s6%^aL. Slo xal tovg tcbv 6xLcbv TtQbg tovg 
yva^ovag X6yovg cog inl dcpcoQL6^ivcov tOTtcov 7tSQL66bv 
^yrj^d^sd^a TtaQatLd^ivaL. 

2. dil S' C, 3. KarovQayitovCov] xov G(xv,xovlov D. Bqex- 
raviccg] -xa- in ras. A, BQetravvLag D. ^gxlv J). 4. y'] s D, 

supra y' scr. s B^ 5. to^] to§ D. i§'] L.- j. D, Fo supra 

scr. B^ 6. 7ci(i7cros ■nal sUocrog D. 86rL D, comp, B. 

TtaQaXXrjXog] pr. X e corr. C. 9. BQEravvCag D. 10. ]L] 

/t fl D. r"-*] i5 AD, in ras. B^, p C, supra scr. quaedam 

«uan. Cl 12. %v.rog val sUo6x6g D. hrC D, comp. B. 

14. di] d' C. 15. (layiQ&g C. BQsravviag D. 16. iv- 

rsv&sv D. Tsr\rdQrov D. 17. rs] corr. ex di D. yCvsod-aL C. 

21. i^SQyd^s6d-aL D. 22. acpoQL6[Liv(ov CD, corr. D^ 

Ftolemaeua, ed. Heiberg. 8 



114 KAATAIOT nTOAEMAIOT 

xj'. oial Zitov ^sv xoivvv rj ^syc^trj 'fj^ega coq&v 
i^tiv L6rj^£Qivav id'^ iKStvog 6 TtaQciXXrjlog aitixsL tov 
i6r]fi£Qtvov iioiQag ^a Tial yQd(p£tai dicc tmv ^oq^Cov 
tfjg ^iXQdg BQSttaviag. 
6 xrj\ OTtov ds rj ^£yi0trj rj^iQa coQcbv i6tiv L6rj- 
liEQivcbv id^C^ £K£iVog 6 naQakXrikog aiti%£i tov iOt]- 
fi£Qivov fiOiQag |j3 xal yQdcp£tai did^ t&v xaXov^ivtov 
^E^ovdcov v^fi^ov. 

^%'\ onov d£ i} ^£yi6trj rj^iQa coqcov i6tLV i6r]- 
10 ii£Qivcbv Xy ix£Lvog 6 7taQdXXr]Xog ditiiEi tov l6Y]\i£QLVo'v' 
^OLQag ^y xal yQd(p£tac Sid OoMrjg trjg vr]6ov. 

X' . OTtov dl r] ^£yi6tr] r]^iQa Sqg^v i6tiv i6r]^£Qiv^v 
xd^ iK£ivog 6 7taQdXXr]Xog aTtiyEi tov i6r]^£Qivov ^oiQag 
^dC ^c^l yQd(p£tai did Uxvd^ijc&v id-v&v dyv(o6t(OV, 
15 Xa. OTtov dh r] [i£yi6tr] r]^iQa Sq&v i6tiv L6r]- 
fi£QLVcov xp^ £X£LVog 6 7taQdXXr]Xog aTtii^i rov l6r]- 
^£QiVOV inoiQag ^£i\ 

A/3'. OTtov 61 r] fi£yi6tr] r]^£Qa coQcav £6tiv i6r]H£Qivcbtr 
Ity^ ix£ivog 6 7taQdXXr]Xog d7t£%£i rof) L6r]^£QLV0V 
20 iLOLQag %<s. 

Xy\ OTtov dh r] ^£yL6tr] r]^iQa gjq&v i6tLv L6Y]^£QLvcbv 

3cd, ix£Lvog 6 7taQdXXr]Xog d7t£%£i roi) i6r]^£Qivov 

[lOLQag |g r] ]i. 7tQcbtog di i6tiv o{>tog tcbv 7t£Qi6Kicov' 

xatd yaQ [lovrjv tr]v ^£Qivr]v tQ07tr]v [li] dvvovtog 

25 ix£i: tov r]Xiov at 6xial t&v yvcofiovov i7tl 7tdvta td 

4. BqExccvviccg D. 7. ^f\ -§ e corr. B^ 10. lcri^Bqivov] 

corr. ex tar^iisQLV&v Cl H- ^y] ^^^L- D. @ovlr]? tfjg 

vi]6ov\ corr. ex cnvoLy.cov sovoov ayvmaroiv D, cfr. lin. 14, 12. 
ioTiv tarjiisQLv&vl om, D, 14. ZHvd-LKcbv'] Ztiv&riyimv C, corr. 
ex av.voiv.oiv D^. bQ^v&v'] corr. ex eovo3v D^ ayvcoGxcov'] 

corr. ex Dcyvaiax(06 Dl 16. v,f\ tt%06i8vo D. 19, xy] etnoci- 
XQi&v D. 23. ^^] I D. ds] d' D. 25. ra] om, B, add. C^,- 



MA0HMATIKHS STNTASESi2 B'. 115 

Tov dQi^ovtog (leQrj rag nQO6vsv0sig TtOLOvvrccc, xac 
s6riv svravd^a 6 ^sv ^SQivbg rQOJtixbg TtaQccXXrjlog asl 
(pavsQdgy 6 ds xsL^SQtvbg rQOJCLxbg dsl dq^avTJg^ d^d rb 
dfitporsQOvg ivaXXd^ scpaTCrsad^aL rov bQL^ovrog. yCvs- 
raL 8s Kol 6 lo^bg xal dLa ^s0(dv r&v ^G>dLOv xvxXog 5 
6 avrbg rm bQL^ovriy orav avrov rb iaQivbv i^rj^SQLvbv 
0rj^SLOv dvarsXXrj. 

m si ds rLg akkog d^scjQLag svsxsv xal tcsqI rwv srt, 

fioQSLorsQcov syxU^scov sjtL^rjroir] rLvd rcov oIoGisqs^- 

Xd' rsQcjv 6v^7trco^dra)v^ svqol dv^ OTtov rb s^aQ^a rov lO 
fioQSLOv TtbXov [lOLQcbv s6rLV IJ syyLOra^ sxst fiij 
dvvov6ag oXcjg rdg s(p sxdrsQa rf^g d^SQLvrjg rQOTtfjg 
rov dfca insCcov rcbv ^GtdCcov xvxXov ^oCQag Ts' co6rs 
T?)v ^syC6rr]v rj^sQav xal ri^v rcbv 6xLcbv STtl Ttdvra 
rd iiSQri rov bQC^ovrog TtSQLaycoyfiv 6%sdbv ^rjVLaCav 15 
yCvs^d^aL. s6raL ydQ xal ravra si)xarav6rira dta tov 
sxrsd^SL^svov xavovCov rfjg Xo^m^scog' o6ag yaQ dv 
svQco^sv rov i6rj^sQLvov ^oC^ag rbv jtaQaXXrjXov dits- 
%ovra rbv dTtoXa^pdvovra X6yov svsxsv scp sxdrsQa 
rov rQOTtLxov 6rj^sCov ^oC^ag ls^ yLvb^svov ds r6rs ijroL 20 
dsl cpavsQbv -») dsl dq^avfj^ ^srd Tot) ditoXa^^avoinsvov 
r^fj^arog Toi5 dLa ^s6c3v rcbv ^cjdCcov xvxXov^ ratg 
ro6avraLg ^oC^aLg drjXovorL Xsl^sl rcbv rov rsraQrrj- 
IhoqCov r^rj^drcov 9 t6 s^aQ^a rov poQsCov TtbXov. 

1. fi^^r]] fii- in ras. A. 3, ro] om. D. 4. ivccXa^ D. 

6. l6r}(i8Qvv6v] om. C, supra scr. B^. 7. avccriXXrj] B, ava- 
tiXX^ D, ScvatiXr] A, &xiXX7i C. 8. Xd mg. D^. 9. iy%XL- 
Gsojv] corr. ex ov kXlgso) D^ 10. Xd'] B, om. ACD. 12. 
dvvovaag] -0- in ras. A\ 14. fqv (pr.)] ^ijV rs D. 16. yLyvs- 
6^ai D. 17. av] D, sdv ABC. 19. scp'] t&v icp' A, corr. A\ 

20. yiyvoiisvov D. tors'] om. D. 21. r/'] ins. C^, st D. 

23. XsLipSL] X- e corr. C^ 24. ty,r}}idt(av] -tj- in ras. A, 

-V supra scr. D^ ^oqslov] -i- ins. D^. 

8* 



116 KAATAIOT nTOAEMAIOT 

Af'. xal oTtov fi6v roivvv ro ^%aQfia tov 7c6kov 

ILOiQGiv £6tiv l-O"/.', ixet av tig evqol ^ij dvvov6ag 

oXcog tag icp EKdteQa trjg d^EQivrjg tQOTtrjg fioLQag X' 

Sets 6xedov inl ^fjvag Eyyieta dvo ti^v te iieyCdtriv 

5 r]^eQav xal tovg yvafiovag 7ceQ(,6xLovg yCve^d-ai. 

Ag'. 03tov de tb e^aQfia tov Ttolov iiolq&v i6tiv 

oy y\ ixst av ttg evQOt /iti) dvvov6ag tag iq) exdteQcc 

tfjg d^eQtvrjg tQOTtijg ^oCQag jTe' &6te t7]v te ^eyC6trjv 

rj^eQav xal tovg yvco^ovag 7ceQi6xCovg ijtl tQi^rjvov 

10 eyyL6ta TtaQateCvetv. 

Xt,\ oTtov de tb e%aQ^a tov 7c6Xov fioiQ&v i6tiv 

ori y\ ixet dv ttg evQOi firi dvvov6ag tdg icp* exdteQa 

trjg avtrig tQOTtfjg fioCQag |* cj6te tetQafirivtaCav ^xedbv 

tijv te [ieyC6trjv rnieQav xal tfiv tmv 6xiG)v TteQiaycoy^v 

15 aTtoteXet^d^aL. 

Xri , OTtov de tb e^aQfia tov 7t6kov fiOLQcbv i6tLV 

jrd, ixet dv ttg evQOL iifj dvvov6ag tdg icp ixdteQa 

tf]g d-eQLvfjg tQOTtfjg fioCQag oi* cS6te 7tevtafir}VLaCav 

7tdXLv 6%e8bv tfjv fieyC6tr]v r]fieQav yCve6^aL xal toi)g 

20 yvGifLovag tbv l'6ov %q6vov 7teQi6xCovg. 

A-O"'. OTtov de tdg olov tov tet aQtrjfioQCov fioCQag 

9 6 p6QeLog 7t6kog aTtb tov oQC^ovtog i^fJQtat, ixet tb 

fiev PoQeL6teQov tov i6rjfieQivov fjfmxvxXiov tov did 

fi£6cov tcbv t^codCav olov o\)8i7tote VTtb yfjv yCvetat^ 

25 t6 d\ votiCJteQov okov ovdi^tote v7teQ yfjv &6te fiCav 



1. Is'] add. D^ 2. iatL D. 5. yCyvsad^cci, D. 6. Xg'] 
add. D^ 11. X^'] add. D^ 12. o^] -tj renouat. C*. 

y' SKsi] corr. ex ysxft D. 13. mars] mg D. 16. Xrj'] 

add, D^. 19. a%s8bv icdXiv D. 21. rag] ravxccg D. oXov\ 
corr. ex oXi] D^, deinde ins. rdg D^. rsrccqrTnioQCov] tert. r 
supra scr. A^. 24. yivsrai] ylyv^^uL D. 25. yfiv] yijv 

yCvsrccL D. 



MA0HMATIKHS STNTASESiS B'. 117 

p,lv '^^eQttv ixcc6tov hovg yCyvE^Q^ai^ ^Cav de vuxra, 
ixatsQav syyieta i^a^rjvtaCav, tovg de yv6^ovag itdv- 
tots 7t£Qc6xCovg tvyxdvBLV. Idca ds ietiv xal tfjg 
tOLavtrjg eyxXC6SG)g to ts tbv ^oqeiov tcoXov xata 
xoQv^pijv yCyvs^d^aL xal tbv Cerj^sQLvbv tnjv ts tov 5 
dsl cpavsQov xal triv tov dsl dcpavovg xal stL triv tov 
bQC^ovtog d^s^Lv dTtola^pdvsLv {jtcIq yfjg fisv noLovvta 
Tcdvtots tb ^OQSLOtsQOV iavtov jcdv r]fiL6(paCQL0V ^ VTcb 
yfjv ds tb votL(otSQOv. 

g'. IIsqI t&v ijcl tf^g syxsxXLfidvrjg 6(paCQag tov lO 
dLa ^s6(x)v tcov ^GjdCcov xvxXov xal tov l6ri- 
liSQLVOv 0vvava(poQG)v. 

'Extsd^SL^svcov dfj tav xa&oXov jcsqI tdg syxXCesLg 
d^scDQOv^svcov i^fjg dv stri dst^aL^ TCcbg dv Xa^pdvoLVto 
xad'' ixd6trjv syxlL0LV xal ot avvavacpSQO^svoL tov 15 
i6rj^SQLVoij XQOVOL tatg tov dta ^e6cov tcbv t^cpdCov 
xvxXov TCSQLcpEQsCaLg ^ d(p G}v xal td dkka jcdvta twv 
xatd ^EQog dxoXovd^csg i^itv fisd-odsvd^TJdstaL. xata- 
XQrjCo^sd^a ^EvtOL tatg tG)v t^codCcov 6vo^a6CaLg xal 
sic avrwi/ tcbv tov Xo\ov xvxXov dcodsxatrj^OQCcov xal 20 
ojg t&v dQ%cbv avtcbv dicb tcbv tQOTCLxav xal L6rj^sQL- 
vcbv arj^sCcov Xa^^avo^svcov^ t6 ^ev d%b tfjg iaQLvf]g 



1. ytvtad^ai CD. 2. ^yytcra] Bixicra D, ^'rot D^. s^a- 
^LTiviaiav] alt. v ins. D^. 3. bgxi D, comp. B. 4. 7t67.ov^ 

om. D. 5. yLyvsad-aC] A, yCvEGd-ai BCD. 6. acpavovis] &- 
ins. D^ 9. voxsLcoxBQOv C, corr. C^; voxsioxsqov D, voxloxs- 

Qov D^ 10. ^'] ^ BC, om. AD. iyxtxXtftfVrjs B. cgjat- 
qag] GtpaC- e corr. D. 12. cvvavacpOQaiv] -o- e corr. C. 13. 
\ mg. A. 14. av lafipdvoivxo] avaXafi§dvoLVxo D. 17. xcc 
aXXa] A, xaXXa BCD. 18. 7]fiLV aKoXovd-ag D. 20. x&vj 

xovxoov D. xai] om. D. 



118 



KAATAIOT nTOAEMAIOT 



i6r]^SQias dyg stg ta sjio^svu tfjg tcov oXcov q)OQag 

TiQcbtov dcodsxatrj^oQLOV Kqlov xakovvtsg^ tb ds dsv- 

tspov TavQOv^ %al iTtl tcbv «l^? h&avtcag xata tijv 

jtaQa$sdo^sv7}v rj^tv td^tv t&v l^ ^GydtcDv. 
5 dsL^o^sv ds TtQcbtov^ otL at l6ov aitsjipvaaL tov 

avrov L6r]^sQLVov 6rj^SL0v TCSQnpsQSLaL tov dLa ^s0a>v 

t&v ^G)dLC3v xvxXov tatg t6aLg dsl tov tarj^SQLVOv 

xvxXov TCSQnpsQsCaig 6vvavag)SQ0vtaL. 

s6tC3 yaQ ^s6r]^pQLvbg ^sv xvxkog 6 ABF^^ 6ql- 
10 ^ovtog d^ r]^LXvxXLOv tb BE/d^ tov ds i0r]^SQLvov t6 

AEF xal tov Ao|oi> xvxXov 

dvo tfir^^ata to ts ZH xal 

tb @K^ cj0ts sxdtsQov ^sv 

t&v Z xal ® 6r]^SLGiv tb xatd 
15 f^v iaQLv^v i6r]fiSQLav vtco- 

xsL6%'aL^ l'0ag dl stp' sxdtSQa 

avtov 7tSQL(psQSiag aTCoXr^cpd^SL- 

6ag tag ZH xal ®K dLa tcbv 

K xal H 6r]^SLCov dvag^SQS^d^aL. 
20 Xsyo^ otL xal al sxatSQa avt&v 6vvava(psQ6^svai tov 

L6r]fiSQLvov TCSQLtpsQSLaL^ tovts6tLV aC ZE xal ®Ey 

i'6aL sl6Lv. 

s6tG} yccQ dvtl t&v tov L6r]^SQLVov TCoXcov td A 




2. KqlovIi comp. B, ut semper in signis. 4. if] A, dm- 
dsiicc BCD. 6. Xri(i(ia a mg. B, a Xijfifia mg. C. dsL^o[iev 
3e'] om. B. Si^ di^ D. ScTtixovaaL] -ai in ras. A. 6. 

avTov taT][i£QLvov] tG7](iSQLV0v Tov avTov D. 7. TaLg] oTL Tatg D. 

8. nsQLcpFQSLaL C. 12. ZH] corr. ex ZE D. 14. yiai] 

om. D. 18. xat] om. D. 19. xat] om. D. avatpEQS- 

ad^aL] -va- supra scr. C*. 20. at] supra scr. D^. avvavava- 
cpsQo^isvaL D. 21. xal @E] E0 D. 23. ^gtco] mut. in 

sGTcocav A*. icvTL] del. A*. t&v] om. B, supra scr. C. 

Tov] om. D. TtoXov B. 



I 



MA0HMATIKHS STNTASESiS B'. 119 

otal M 6rj^stcc^ xal yeyQccg^d^odav dt' ccvtcbv iLByC6xG)v 
xvxXcjv r^TJiiata to te AEM xal A0 zal eti, t6 te 
AK xal ZM xal MH. eicel ovv l'6rj e6tlv ri ZH 
rfj @K^ xal 01 dia t&v K xal H yQaq)6^evoi TCaQ- 
dXXrilov l'6ov d7tsxov6Lv aqp' exdteQa tov C6rjiieQLVov^ 5 
w6te xal tijv filv AK tfj MH ytve^d^aL t6riv^ f^v 8\ 
EK tfi EH^ L667tlsvQa ccQa yCvstaL th ^sv AK& 
rc5 MHZ^ t6 ds AEK tip MEH xal rj ^ev vTtb 
KAE ocQa ycovCa l'6r] e6tlv tfj vjtb HME^ rj de vTtb 
KA0 okri tri vnb HMZ oXrj' &6te xal XoLJtri r] vjtb 10 
EA0 XoLTtfi tfi vTtb EMZ t6ri e6taL. xal ^d6Lg ccQa 
ri E@ pd6eL tfj EZ l'6ri e6tCv' OTteQ edeL det^aL. 

TtdXvv 8e deC^o^ev^ otL aC 6vvava(peQ6fievaL tov 
C^rj^eQLVOv TteQLCpeQeLaL tatg L6aLg xal l'6ov aTtexov^atg 
tov avtov tQOJtLXOv 6r]^eCov roi) dLcc ^e6ov tcbv t,(p- 15 
dCcav xvxXov 6vva^cp6teQaL 6vva^cpotSQaLg avtcbv tatg 
ijt' OQd^rlg trjg 6(paCQag dvacpoQatg L6aL sC6Cv. 

exxeC^d^co yccQ 6 ABFA ^e^rj^^QLvbg xal tcav rj^c- 
xvxXCcjv t6 te BE^ rov OQC^ovtog xal tb AEF tov 
l6ri^eQLvov y xal yeyQdcpd^co^av dvo l'6aL te xal l'6ov 20 
d7texov6aL roi) ^jjftiL^f^fcVoi) 6rj^eCov tov Xo^ov xvxXov 



1. xat(pr.)] om. D. di* avt&v\ corr. ex 810. r&v D. 2. 
t6 t£ (pr.)] om. D. xat (pr.)] AK e corr. D^ xat hi — 
3. ZM ■AccL^ MZ D. 4. dia ta>v] corr. ex dt' avt&v D. 

Ha£r(alt.)] om. D. 6. (liv] MENB, del. D^. 7. tao- 

jcXsvQu] corr. ex taonXsvQov D^ AK&'] -© e corr. D^ 8. 
AEK] EAK D. MEH] -H in ras. A. 9. ycavLa aQa D. 

10. oXrj] om. D. 11. EMZ] AC^, MEZ BC, corr. ex 

HMZ I)\ 13. Xiifnia ^ mg. B, §' Xfjfina mg. C. ds] $7] D. 

16. Gvva^cpotEQaL] at owaficpotSQaL D. 6vva(i(potiQaLg avt&v 

raLs] supra scr. ^-a-y B^ 17. avacpoQaC D. taaL] lgt] D, 
supra scr. 8 B^. 18. ABFJ] ABT D. 19. tov (pr.) — 

AET] mg. B^C^ to (alt.)] om. D. 20. taaL] supra scr. D. 




120 KAATAIOT nXOAEMAIOT 

itEQKpiQSLau i] te ZH tov Z vjtoxeL^isvov ^stOTtcoQivov 
arnLsCov Kul rj @H tov ® vTtoKSi^evov saQivov ^rnisCov^ 
&6ts xal tb ^sv H 6r]^stov xolvov tfjg dvatoXrjg avT(5i/ 
slvaL xal tov 6QClovtog dia tb vnb tov avtov TCaQ- 
6 aXXrjXov xvxXov rc3 C6r}^SQLV^ 
7tSQLXa^pdvs0d-aL tdg ZH xal 
®H TtSQLCpSQsCag^ 6vvavacpsQS- 
(Sd^aL ds drjXovotL trjv ^sv ®E 
tri &H, triv ds EZ ti] ZH 

10 (pavsQbv ovv yCvstaL avtod^sv^ 
otL xal oXr] r] ®EZ L6r] S6tlv 
tatg STt^ OQd-rjg tijg 6cpaCQag 

t&v ZH xal @H dvafpOQatg. sdv ydQ vjtod^siisvoL tbv 
votLOV tov £0r]^sQLvov TtbXov tb K 6r]^stov yQdi{j(X}fisv 

15 ^L^ avtov xal rov H ^syCatov xvxXov tstaQtrj^oQLOv 
tb KHA ieodvva^ovv ta sii OQ^r]g tfjg 6cpaCQag 6qC- 
^ovtL^ yCvstau TtdUv r] ^hv ®A r] 6vvavaq)SQ0^svri 
tf] SH STt^ 6Q^f]g tfjg 6(paCQag^ r] ds AZ r] avvava- 
(psQo^svr] tf] ZH 6^oC(Dg' &6ts xal 6vva^(potsQag 

20 tdg ®AZ 6vva^(potsQaLg tatg ®EZ l'6ag ts slvaL xal 
'bitb liidg xal rijg avtfjg 7CSQLsxs6d^aL tfjg SZ' otcsq 
sdsL dst^aL. 

xal ysyovsv ij^ty q^avsQbv dLa tovtcov, ort, xdv scp' 
ivbg ^6vov tstaQtr]^OQCov xad'' sxd6tr]v syxXL6Lv tdg 

25 xatd fiSQog 6vvavacpOQdg STtLloyL^ca^sd^a^ 7tQo6a7tods- 



4. vnb tov] vn B: 6. xat] om. D. 8. @E] E6)D. 9. 

@H] @- e corr. D. 13. xat] om. D. @H] corr. ex @N A. 
vnod^sfisvoL] V- e corr. D. 16. tGodvvafiovv] -v add. B^C. 
xfig] om. D. 17. i] (alt.)] ins. D^ 18. t^] corr. ex x6 D^ 
19. ZH] HZ D. &6xi] corr. ex xe B^, t£ C. 20. Ante 

xdg ras. 1 litt. C. @EZ] @- q corr. D^ 21. onsq ^Sbl 

8Eih,ai] T D. 23. ^gj'] titi D. 



MAOHMATIKHS STNTASE5iS B'. 121 

deiyiiBvag £%o^£v zal tag tcov XoiTt&v tQcav t£taQtrj- 

^OQICJV. 

tovtcov ovv ovtcog ix6vtG>v 'bno7i£i6%'G} TtdlLV 6 dici 
'Podov JcaQaXXrj^og^ OTtov ^i fi£v ii£yC0tri ri^£Qa wqcov 
iativ l6riii£Qivcbv td L\ 6 dh p6Q£tog 7t6log i^fJQtat tov 5 
OQt^ovtog iiotQag Ag, xal £6tcD ii^arni^Qtvog ocvxXog 6 
ABFjd Ttal OQtiovtog ^hv b^otcog rj^txvxhov tb BE^^ 
i6rj^£Qtvov dh tb AEF, tov 81 
dta ^£6ov tcjv ^codtcov tb ZH® 
ovtcog £XOVj &0t£ tb H vjto- 10 
X£t6d-at tb iaQtvbv 6rj^£tov. xal 
Xricpd^ivtog tov §OQ£tov 7c6Xov 
tov l6rj^£Qtvov xata tb K 6r}~ 
^£tov y^yQdcpd^o) dt avtov xal 
tfig xatd tb A to^rjg tov t£ 15 
dtd ^i6cov tcbv ^codtcov xvkXov xal tov bQt^ovtog 
lisyt6tov xvxXov t£taQtriy,6Qtov tb KAM. TtQOX^tCd^co 
d£ trjg HA 7t£Qtq)£Q£tag dod^^tGrjg tr^v 6vvavacp£Q0^ivrjv 
avtf] rot) t6r]^£Qtvov^ tovtiattv trjv EH^ £i)Q£tv' xal 
jt£Qt£%itG) TtQcbtov rj HA tb tov KQtov dcod£Katri^6Qtov, 20 

i7t£l totvvv TtdXiv iv TcatayQaq)^ ii£yt6tcov xvxXcov 
£tg dvo tdg EF xal FK y^yQa^jiivat £t6tv i] t£ EA 
xal ri KM tiavov6at dXXf^Xag xatd tb A^ 6 trjg vnb 
rrjv dtJt Xfjv trjg KA JtQbg tfiv V7tb tf^v dtTtXfjv trjg 
AF X6yog 6vvfi7ttat ix t£ roO tf]g V7tb tf^v dtTtXfjv 25 




4. jLifV] om D. r}ii£Qa] r}- corr. ex v A. 5. ^OQLog A. 

i^fjQtai] D, B^fiQxrjraL ABC. 6. X?] -s e corr. C^ 7. [liv'] 
om. D. 9. (licoav] -co- e corr. A. 14. di,* avTov] corr. ex 

dia tov D^. 15. tf\ te di D. 16. v.v-nXav D. 19, ccvtj]] 

bis D, corr. D^ 22. xat] om. D. ij ts — 23. rj] cct EJ D. 

25. jr] rz/ D. 



122 KAATAIOT nTOAEMAIOT 

rfjg KA JCQog trjv vxb tijv dLTcXfjv tijg AM xal tov 
tijg VTto tijv dLTtXijv tijg ME TtQog triv vtco triv diJtXijv 
tijg EF [p. 74, 9]. aXX 7] ^sv tijg KJ dLTtXri ^oiq&v 
i6tiv 0/5 nal tj VTt avtijv svd^sta t^rjy.dt(ov o X^ d, 
& rj ds tijg Iz/ ^olq&v Qrj xal rj vno avti^v svd^sta t^rj- 
fidtcav Cf? S vg^ xal JtdUv rj ^sv dntXri tijg KA ^ol- 
Qcov Qvg ]id xal ri vjtb avtijv svd^sta t^rj^dtcov ql^ ka ii, 
r] ds dLTtXij tijg AM ^olqcjv xy tO- vd" xal rj vjtb avtijv 
svd-sta t^rj^dtcov otd ls v^' sdv ccQa djcb tov tcbv 

10 o A/3 8 TtQog td <^^ d vz koyov dg^sXo^sv tbv tcov 
QL^ Xa LS TtQbg td xd Ts v^, xataXsL(p%"^6staL 6 tijg 
VTtb tijv dLTtXijv tijg ME JtQbg tijv vitb tijv dLTtX^v 
tijg Er Xdyog 6 tcav Trj o s TtQbg td qtc. KaC s6tLV 
ri VTtb tijv dLTtXijv tijg EF t^rj^dtcov qti' r] ccQa VTtb 

15 tijv dLTtXijv tijg ME tcbv avtcbv s6tLV Irj o s. C36ts 
xal rj ^sv dLTtXij tijg ME TtSQLCpSQsCag ^olqcjv siStav 
t^ ^ syyL0ta^ avti] ds rj ME tcov avtcav rj Xrj. dXX' 
STtsl oXrj rj HM jtsQLCpsQSLa tfi HA STt' dQd-ijg tijg (Sq^aC- 
Qag 6vvava(psQStaL^ tcov TtQoajtodsdscy^svov [j^. 84, 11] 

20 s0tl iiOLQav x^ V' xal XoLjtii ccQa rj EH ^olqov sOttv 

4. 6] mut. in y" B^. _ 6. dilds SLnlfj D. vno] vn D. 

6. rg] V?" £ D. 7. ^] ^i^' D et, Q in ras., B^ vno] 

vn D et corr. ex vno C*. 8. vno\ vn D et e corr. C*. 9. 
t^riiidTco^ A. 10 6 (pr,)] y" in ras. B^ 11. Xa] la' D, 

corr. D^ yid Ts v^] renouat. B^ Ts (alt.)] trj' D, corr. D^ 

6 tfjg vno] renouat B^ 12. ME] ME Xoyog D. 13. 

EF] E- renouat. B^, ut in seqq. complura. Tri o 1] corr. ex 
ij fl fi-O" trj 1« D^ 15. o b] corr. ex Ts D^ 16. sctai] htiv D; 
deinde del. T^ vg ii§. 17. ts] add. B^, om. C. Xrf] rjX B. 

18. 0^,73] e corr. D^ HM] corr. ex M C*. 19. avvava- 
vacpSQStai D. nQoanodsdstyfisvcov] post -a- ras. 2 litt. A. 

20. iotiv D. 21. i^] i- in ras. B^, x|3 C, i^ supra scr. C. 



MA0HMATIKH2 STNTASESiS B'. 123 

xal avvaTtodedsLKtaL^ otc xal tb ^sv tav 'Ix^vcov 
dodexatrjfioQcov totg avt otg XQOvoig 6vvava(psQStaL 
irO" t^, STcdtSQOV ds rd ts tfig IlaQd-svov xal t&v Xrjk&v 
xoig ksLTtovOvv slg trjv dcnXilv tfjg ii^ dQdijg f^g 
6cpaLQag avatpoQav XQOvoLg Xg ktj' otcsq sSsl dsl^aL. 5 

TtdXLv 7] HA TtsQLfpsQSLa TtSQLSxstGj tcjv dvo do)- 
dsxatrj^oQLCOv tov ts Kqlov nal tov TavQov ^OLQag f * 
dLa dij va 'bjtoxsL^sva tCbv akkov ^svdvtcov t&v ai>tG)v 
^ ^sv dLTtkfj ri}g KA ^olqcjv yCvstaL Qkrj vd' ft/3 xal 
i] VTto avtijv svd^sta tfirj^dtcav ql^ xy vg, ^ ^\ dLJtkf} 10 
tfjg AM ^OLQcbv ]ia d" i^ xal ri 'bn avtijv svd^sta 
t^rj^cctcov /Lt/3 a Jltj. s^v ccQa Ttdktv ccno tov tav 
o kp d TtQbg td ^i d v^ koyov dcpsko^sv tbv t&v 
QLp xy v^ TtQog td /Lt/3 a ft^, xataksLcpd^rjestaL 6 tfjg 
"bnh trjv dLTtkfiv tijg ME TtQbg tr^v vitb tijv dLitkfjv 15 
rfjg EF kdyog 6 tcbv A/3 Ag d TtQbg td qx. xaC s€tiv 
•^ bTtb tfiv dLTtkfiv tfig EF tfirj^dtcav qx' 17 ccQa vitb 
tijv dLTtkfjv tfjg ME tav avt&v s6tLV A/3 Ag d. mets 
3£al rj ^sv dLTtkf} tfjg ME TtSQLCpSQsCag ^olq&v i6tLv 
ka A/3 syyL6ta^ avtii 8s rj ME tav avtoiv ls Ji^. 20 
akkd f] ME okrj xatd td avtd TtQoajtsdsCx^rj [p. 84, 13] 
fioLQ&v vt, fid' xal koLTtij ccQa f] HE ilolqCov i6tLV 
fta vf]. 6 aQa KQLbg xal 6 TavQog dvacpsQOvtaL 6vv- 
aficpotsQOL sv XQOvoLg Jid vrj^ g)v 6 KQLbg idsCx^rj 6vv- 



1. avvavanodsdsLiitDa D. 2. <jvvavuq)^Q£Tai] post pr. a 

ras. 1 litt. A. 3. xat] xal to D, t6 ins. B^ 4. r^s(alt.)] 
om. D. 5. onsQ sSsl dst^ai] om. D. 6. t&v] om. D. 9. 
yivstai (lOLQ&v D. qXti] qvti D, 10. vno] vn D. 11. jS^] 
-a renouat. C^ ^] ABD, o A^B^ et in ras. Cl 21. i^ 

Hal 17 D. 22. HE iioiQ&v satLv] EH J). 23. awaficpotsQOL 
iv] avvaficpotSQOLs D. 24. avvavacpsQOfisvog] D, corr. ex avv- 
avacpsQO^ivoLS AC, avvavatpSQOfisvoLg B. 



124 KAATAIOT nTOAEMAIOT 

avaipeQo^Evog xQOvoLg Ld" i^' Tcal fidvov aQa to tov 
TavQOv dadexatrjfioQLOv 6vvava(pBQStai, ;u(>(5i/otff x/3 jit?. 
dca Ta avta ds TcdXiv xal tb iihv tov ^TdQrjxdov 
dcodsxatri^dQLOv 0vvavev£xd"i]0stat totg l'0oig xqovolq 
5 kP ]i^^ ixdtSQOV ds t6 ts tov Asovtog xal tb tov Zxoq- 
3CL0V totg Xsi7tov6iv slg trjv diTtlfiv trjg sti' OQd^rjg trjg 
6€patQag dvacpoQav XQOVotg Xt, ^. 

STCsl ds Tcal rj ^sv ^syi^trj rj^SQa cjq&v s6tiv L6r}- 
fiSQLVcov td L\ rj ds sXaxt6tri Q' L\ drjXov^ otv xal tb 
10 fisv djtb KaQXiVov liSXQi tov To^otov r}^LXvxXLOv 6vv- 
avsvsx^rJ6staL tov L6rj^sQLV0v ^pdvotg ^tj A, tb dh 
djcb AiyoKSQG} iis%ql ALdv^cov xQovoLg q^^ X. cj6t£ xal 
sxdtSQOv fisv tc5v sxatSQcod^sv tov saQLvov 6rjnsL0v 
tstagtrj^OQLCOv ^vvavsvsx^^^^staL xQ^voLg od Ts^ sxdts^ 

15 QOV ds t&V SXatSQCOd^SV tOV [IStOTCCOQLVOV 6ripbSL0v XQ^- 

voLg 'qtj jTs. xal XoLTcbv ^sv ccQa to ts tmv AlSv^cov 
xal TO Toi> Aiy^xsQco dcodsxatrj^oQtov sxdtsQOV 6vv- 
avsvsx^r]6staL xQOVOLg xd" l^ totg Xsl7Cov6lv sig tovg 
tov tstaQtripLOQLOv xQ^^^ovg oa tf, XoLJtbv ds to t£ tov 
20 KaQXLVOv xal t6 tov To^otov £xdt£QOv XQOvoLg X£ ls 
totg X£L7C0v6l TcdXcv £ig tovg xal tovtov Tof) TfTa^^T-»;- 
pUOQLOV XQOvovg qtj Jl£. 

xal (pavsQov^ otL tbv avtbv dv tQOTCOv tovtocg 



3. SbI dr^ D. 'TdQTjxoov'] A, comp. B, vdQLxodv C, vdQO- 

Xoov D. 4. GvvciVBx^riGBTCii B, 6vvocvcc%Q"riGttciv D, corr. D^ 

Ante toLS del. o D. 5. gxaTfpov] -o- in ras. 2 litt. A. 6. 

r^s(pr.)] CD, rotff AB. 8. di'] corr. ex 8ri D^. 9. ^f'] 8' D, 

10. tov\ om. D. 14. Gvvavavtx^riGttccL A, supra scr. vs A^ 

Tb\ corr, ex ti^ D. 15. -qov 6s t&v E-nati-'] mg. A^. 17. avv- 

avavBx^riGttuL AC, corr. C*, vb supra scr. A^ 19. roi) (pr.)] 

om. BD. 20. ro rov] BD, ro-O to A, roi; C. 21. Xbltiovglv 

CD. ro-O] om. D. 23. avtov'] bis D, corr. D^. tovtoLg 

tQOTtOV D. 



MA0HMATIKHS 2TNTAHESJ2 B'. 125 

Xa^^avoLiiev Tcal tag tcbv ikattovov tfirj^atcjv tov dva 
lie6(ov tcjv Jcjdtcoi/ tcvkXov 0vvavatoXdg. 

iti d' av svxQrj6t6tEQOv xal ^sd-odLxatSQOv avtccg 
ETCLloyL^OL^sd-a xal ovtcjg. 

S0tc3 yaQ TiQcbtov fis0riii^QLVog xvxlog 6 ABT^ 5 
xal OQi^ovtog ^sv ri^LxvxXLOv tb BE^^ L6r]^SQLvov 
ds tb AEF^ tov ds dicc fisdcjv tcbv ^csdLCJv tb ZEH 

trjg E tofirjg xata tb suql- 
vbv arjfistov VTtoxsLfisvrjg. xal 
d7toXr]g)d^SL6rjg sii avtov tr\g 10 
ES TtSQL^SQsCag tv%ov6rig ys- 
yQd^pd-cD tfifjfia tov dLa tov 
@ jtaQaXlrjlov ta L6rjfiSQLV^ 
xvxXg) t6 ©jK", xal krjcpd-sv- 
tog tov A TtoXov tov l6riyis- 15 
QLVOv ysyQdtp^Gi dt' avtov tstaQtrjfioQLa fisyL6tG)v 
xvxXav tb ASM xal tb AKN xal stL tb AE. 
<pavsQbv tOLvvv avtod^sv s6tLV, otL tb E® tfirjfia 
tov dta fis6cjv tcbv ^adLCDV sjtl fisv oQd-rjg trjg 6(paLQag 
tfi EM itSQLCpSQSLCc tov L6rjfiSQLVov OvvavacpsQStaL^ 20 
S7tl ds trjg syxsxXLfisvrjg tfj t6ri tfi NM^ ijtSLdr^JTtSQ 
r] fisv K0 Toi) TtaQaXXriXov itSQLcpsQSLa^ ^ <?wava- 
tpsQStaL tb E® tfirjfia^ bfioia i6tl tfj NM tov £6rj- 
fiSQLVOv^ aC d' ofioLaL TtsQLcpSQSLaL tmv jtaQaXXrjXciv 
iv t60Lg Ttavtaxfj XQ^^otg dvacpSQOVtaL. xal tfi EN 25 




2. GvvavcicpoQdg D. 3. xat fte-O-o^nKorfpov] mg. A^. 5. 
IfiiilLu mg. BC. 1. AEF^ corr. ex. AErJ)^. 10. ano- 

Xsicpd-riarig C. 14:.'nvv.Xov D. 17. to (pr.)] r6 rs D. 20. 
EM] ENM D. nsQLcpsQsiag D. 21. syyiUfievrig A, corr. A^ 
NM] MN D. 22. KG] OKB, @K D^. 6vvavava- 

ipsQSTai D. 23. iGTLV D, comp. B. 24. d'] d^ D. naQ- 
aXXT]Xcov] corr, ex TcaQaXXi^loLg D^ 



126 KAATAIOT nTOAEMAIOT 

aga iteQttpEQSia iXd66cov i6xlv -t] STtl trig iyKsxXi^Evirjg 
0(patQag tov E& t^TJfiatog ava(poQa trjg ijt' 6Qd"f}g tTJg 
6fpaCQag^ didsLXtai Tf, ott xal xa-O-dAov, iav yQa^pobcC 
tivsg ovt(og TtBQKpiQEiai ^syC6t(ov xvxXcov ag i} AKN^ 
5 ro EN t^fjna TtSQi^si f^v VTtsQoxrjV tmv iitC ts tr\g 
dQ^fjg xal tfig iyxsKXtfiivrjg 6(paCQag ava^poQ&v t&v 
aTtoXa^pavo^ivcjv tov dta }ii6(ov tG>v ^mdCcov xx>xXov 
7tSQi(psQSLG)v 'iJTtd ts tov E xal tov yQa(po^ivov dta 
tov K jtaQaXXrjXov oTtSQ sdsc dst^aL. 

10 tovtov TtQod^scjQTjd-ivtog ixxsC^d^co r] xatayQa(pii 
^dvcjv tov ts ^s^rjfi^QLVov xal tcjv tov bQCtpvtog xal 
tov C6rifiSQLV0v rjiiLxvxXCcjv^ xal 
dta tov Z votCov 7t6Xov tov 
L6rj^SQLV0v ysyQ^x^pd^co di^o ts- 

15 taQtriiLOQLa ^syC6ta)v xvxXcov 
To ts ZH® xal t6 ZKJ, 
'b7toxsC6%'Gi ds t6 ^lv H 6rj- 
flSLOV t6 xoLvbv TOV dLa tov 

XSL^SQLVOV tQOTtLXOV ^rjflsCoV 

20 yQacpoiiivov JtaQaXXtjXov xal tov oQC^ovtog^ t6 ds K 
tb xoLvbv tov yQa(po^ivov dt^ trjg aQxfjg X6yov svsxsv 




1. iXdttmv D. 2, 6(pocCqai] 6(paiqa$ ccvatpoqu D. ava- 
fpoqa] om. D. ^tt'] ^tcl D. 3. oti v,al v.a%^6lov] ■Kal v.aQ-- 
oXov otL D. idvl corr. ex &va D^. 4. TtSQLtpiQSLai ovtcog D, 

cbs 1^] AC, A@M supra scr. A^, j) ASM v,aL post ag ins. 
mg. C*, cbff 7] A@M in ras. 7 litt. B^, dtg t) A@M nal 7] D. 

AKN, to\ %a\ 7} AKN to mg. Bl 6. xai] xai inL D. 8. 
E xat] corr. ex EK C^. 9. onsQ ^Ssl Ssl^ul] om. D. Deinde 
s^fig 7) v.atayQa(pri D (fig. in eadem pag. est). 11. ybsejiyir- 

§QLVov] D*, ;J D, ^ D^ t&v] om. D. 12. tov\ t&v tov D. 

l6rtitSQLvov~\ D*, ft D, ft D^ 14. terjiisQLvov] D*, M D. 16. 
to ts] td D. Tial rd] om. D. 17. ds] drj D. 18. did'] oql- 
^ovtog g did D. 20. xal tov OQi^ovtog] om. D. to Ss K] mg. A\ 



MAGHMATIKHS STNTASESiS B'. 127 

rav 'Ixd-vov tj xccl ccXXov rcvbg tav tov reraQtrj^OQLOv 
t^rj^dtcov dsdonevov. eig dvo dri Tcdhv ^syi^tcov xvxXcov 
7t6QL(p€Q£Lag tag Z® xal ES ysyQafi^evaL sCdlv ij ts 
ZKA xal 7} EKH ts^vov6ac dXXijlag xatd tb K^ xai 
s(Stiv 6 tr^g vTcb tijv dnckfiv trjg ®H TtQbg f^v vnb tijv 5 
diTikfiv tfig ZH koyog 6 avvrj^^svog sx ts tov tfjg vitb 
rrjv SiTtXfiv tfjg 0E TtQbg trjv vnb tijv diTtXrjv tfjg EA 
xal sx roi) tfjg VTtb tijv diTtXrjv tfjg KA TtQbg trjv x)7tb 
trjv dinXfiv trjg KZ [p. 74, 9]. «AA' iv nd^atg tatg 
iyxXL6s0tv 7] ts dLTtXfj trjg ®H TtSQLfpSQsCag ^ avtrj 10 
dsdotat' s6tLv yaQ 'fj ^ista^v tcov tQOTtLxcbv xal d^d 
tovto xal koLTtri i^ $LnXfi tfjg HZ. xal b^oCog ijtl 
tcbv avtcbv tov d^d ^s6c3V twv ^mdCcjv t^rj^dtcov rj ts 
trjg AK nsQLcpsQsCag dLTtXfj xatd jtdeag rdg iyxXtastg 
ierlv rj avrfi xal dCdoraL dLcc rov rrjg Xo^cb6scjg xavo- 15 
vCoVy xal XoLTtr} dtd rovto TtdXtv rj dtTtXfj zrjg KZ' 
cj6ts xal tbv tfjg vnb trjv dtTtXfjv tfjg SE itQbg tijv 
ffbnb tfiv dfjtXfiv tfjg EA xataXsCjtsed^at Xoyov tbv 
ax)tbv iv 7td6atg talg iyxXC6s6tv iitl tcbv avtav tov 
tstaQtrj^OQCov t^rj^dtcsv. 20 

idv drj tovtcov ovtcog i%6vtGiv tfjv tfjg KA TtSQt- 
cpSQsCag dtacpoQav dtd dsxa t^rj^idtcov tov ditb trjg 
iaQtvrjg L6rj^SQCag og JtQbg tb ^SL^SQLvbv tQOTtLxbv 
6rj^SL0v tstaQtriiLOQCov JtaQav^TJ^cjiisv trjg ^isxQt tcbv 
trjXtxovtcDv JtSQLcpSQSLcbv dLaLQs6scog avtdQXOvg xatd 25 
triv XQV^^'^ i6o^svrjg^ tfjv ^sv trjg 0H TtSQLCpSQsCag 



1. rov] om. D. 3. xat] om. D, ^ xb] at D. 4. xat 

7]] om. D. iiXXriXaiq C. 6. ZH] HZ D. 6] om. CD. 

8. KA] AK D. 15. Sidotai] -o- corr. ex -i- in scr. C. 

17. -nXfjv — 18. dL7iXr]v] mg. C^ (alt. -nXfjv etiam in textu C). 

19. iv] £> D. 26. SH] corr. ex 0E D. 



128 KAATAIOT nTOAEMAIOT 

dLJtXfiv €%0^£V TtKVtOte ^OIQCOV /i^ ft)3 ft Xal tijV VTtO 

avtijv svd^stav t^r}^dt(DV ]irj Xa vh^ triv 8\ tfjg HZ 
dLTtXfjv ^oiQcav gXp l^ % 'naX tY\v vith avtrjv svdstav 
t^rj^dtcov Qd" ftd vy. w^avtcjg ds xal STtl ^sv tfjg 
5 dsxa^OLQLav d7tsxov6rjg tov saQLVov 6r]^SL0v cjg TtQog 
tb xsL^SQLvbv tQOTtLxbv TtSQLtpSQsCag triv iisv tfjg KA 
dLTtXfjv ^oLQwv rj y T^ %al tfjv vjtb avtfjv svd^stav 
t^rj^dtcav rj tis Id'^ tfjv ds tfjg KZ dLTtXfjv ^olqcov 
Qod v^ [id xal tfjv vjtb avtfjv svd^stav ty^rj^dtcav 

10 QLd- fi./3 lS. sjtl ds tfjg 7c ^OLQag co^avtcog d7tsxov6rjg 
TtSQLcpsQSLag tfjv ^sv tfjg KA dLTtkfjv ^olq&v Ts vd ^ 
xal tfjv VTtb avtfjv svd^stav t^rj^dtcav I^ ks vg, tfjv 
8s tfjg KZ dLTtXfjv ^OLQmv Q^d s vd Tcal tfjv VTtb 
avtfjv svd^stav t^rj^dtcov qltj v /liJ. sjtl ds tfig X 

15 fiOLQag d7ts%ov6rig TtSQLcpSQsCag tfjv ^sv tfjg AK dLTiXfjv 
^LOLQ&v Tcy id" vfj xal tfiv 'bTtb avxfiv svd^stav t^rj^d- 
tcov xd Ls i^, tfjv ds tfjg KZ dLTtkfjv ^olq&v qv? Ji /3 
Tcal tfjv vjtb avtfiv svd^stav t^rj^dtcDV ql^ Xa ls. sitl 
ds tf]g fl iiOLQag d%s%ov6Yig jtSQLCpSQsCag tfjv ^sv tfjg 

20 AK dLTtXfjv [iLOLQcbv X r] fj xal tfjv vTtb avtfjv svd^stav 



1. iLoiQ&v] sic ACD, vno] vn D. 3. vno] vn D. 5. 

dsv.aiLOiQlav] tag I ^ D, cbg] corr. ex coato D^ 6, tfiv] 

corr. ex tt?? D^. KA] AK D. 7. ^y] rjy AD, corr.^D^. 

t-^v] tr}(i, B, V7c6] vn D. 9. vno] vn D. 10. Bni] 

corr. ex in C, x pLOLQccg] hhoatfi^^ \l D, sf^noGt ^ D^. 11, 

tfjv] -V ins. D^ KA] AKJ). 12. xat] ins. Cl vno] 

vn D. tg] corr. ex Xg D^ 13. vno] vn' D. 14. t^iiq- 

(iccta D. 15. AK] KA D. 16. vt]] rj BC. vfi xat] 

m %\jy. ^no] 81 vn D. 17. Ze] t^' D. _ qv^ qti? D. 

Ji ^] (i^ J), (la ABC. 18. vno] vn D. Xa] A, o supra 
scr. A^, X8 C. Ts] l§ D. 20. AK] KA D. SLnXfjv] -v 

ins. D^ r^] Xr\ D. ^ (alt.)] om. C. vno] vn D. 



MA0HMATIKHS STNTASE<iS B'. 129 

r^rj^dtcov lcc Tcc Jiy^ rriv de rfig KZ dLTtlijv ^ocq&v 
Q^d- va vp xal rrjv 'bTth avrriv evd-stav r^iri^drcov qlb 
vfi tO-. 67tl ds rfjg v fioiQag aTCSxov^rjg TtSQicpsQSiag 
rrjv ^6v rfjg AK diTtXfjv iioiQcbv Ag i jic^ xal rr^v vTtb 
MVtrjv svd^etav r^rj^dtcov Af T AO-, triv ds trjg KZ 5 
diJtXrjv ^oiQcov Qiiy vd id xal trjv V7tb avtr^v svd^etav 
r^rj^dtov Qid i ^d. iTtl ds trjg f ^ioiQag d7t6xov6r]g 
TtSQiCpSQSiag trjv ^sv trjg AK diTtXrjv ^oiQ&v Jid o Trj 
xal tijv VTtb avtijv evxtetav t^rj^dtcov ^p d ]Trj^ tr^v 
d% trjg KZ diTtlrjv fiOiQa>v Qkri vd' fi/3 xal triv 'bitb 10 
ccvtrjv svd^stav t^rj^dtav Qi^ xy vt,. STtl 8s trjg o 
liOiQag d7t6xov0r}g TteQicpeQeCag tijv ^ev trjg AK diitXrlv 
liOiQcov ftd ji x^ xal tijv vnb avti^v evd^etav t^rj- 
fidtcjv JTs Xg Trj^ tijv ds tfjg KZ diTtXrjv ^OiQcov Q^e 
id^ kri xal tijv vjtb avtijv evd-etav t^rjiidtcov ^ vd^ ftj. 15 
67tl de tfjg 7t ^oiQag d7t6xov6rjg 7t6Qi(p6Q6iag tijv ^ihv 
xfig AK diTtlfjv pLOiQmv JTg vS l^ xal trjv VTtb avtijv 
svd^etav t^rj^dtcov ^^ fij jT^ tijv dh tfjg KZ di^tkfjv 
(lOiQcbv QXy y mj xal tijv V7tb avtiiv ei^d^etav t^rj^d- 
rcov qI d Tg. 20 

xal did rd 7tQOX6i^6va^ idv aTcb toij rfjg xjTtb rijv 
di7tkr]v rfjg 0H 7tQbg rijv 'bTtb rijv di7tXrjv trjg HZ 
Xoyov^ tovt66tiv tov tcov ]Trj Xa ve 7tQbg td Qd' ^d vy^ 
cccpiXco^ev sxa6tov tcbv xatd dexa^oiQtav ixxeifiivcov 



2. V7c6] vTt' D. qTb'] qiQ- D. 4. zriv (pr.)] -v renouat. 

B\ corr. ex -a J)\ AK] KA D. U^ -? renouat.D^. -^Ttd] 
vn D. 6. vTio\ V7i' D. 7. F] e corr. D. 9. vno] vn D. 

10. ri)s] T7]V D. qXri\ Xt] C. vito] vn D. 11. tfirjtid- 
tcov] -T]- corr. ex v in scr, A. 13. vito] vtc' D. 15. vno] 
vn' D._ v^] corr. ex v~s D. 17. AK] KA D. vno] vn' D. 

18. jLt^ (alt.)] fl seq. ras. 1 litt. C, om. D. 19. vno] vn D. 

20. Qi8]~qT8 ABCD, similiter saepius. 22. HZ] ZH D. 

Ptolemaeua, ed. Heiberg. 9 



130 KAATAIOT nTOAEMAIOT 

tilg VTcb triv diTtXriv rtjg AK TtQog trjv VTtb f^v dtjtXfiv 
trig KZ Xoycjv^ JiataXstcpd^TJaatai, rj^tv xal 6 tfjg VTto 
triv diTtXfjv trjg ®E itqbg tijv vitb tijv dLTtXrjv trjg EA 
Xoyog xata 7td6ag tag syxXL0£Lg 6 avtbg t(p tcbv | i^Jtl 
5 iiev trjg dsxa ^oigag, Sg scpa^isv^ d7ts%ov6rig TtsQicpSQsCag 
TtQbg td d" Xy^ inl ds trjg % Tt^bg td Trj v^, STtl d^ 
trjg X Jtgbg td xrj d^ STtl ds trjg jl TtQbg td Xg Ay, STtl 
ds trjg V itQbg td fid t/3, snl ds trjg | TtQbg td v ^dy 
STtl ds tfjg b TtQbg td vs fTe, sjtl ds tfjg n jtQbg td 

10 vrj vs* 

cpavsQbv ds avtodsv^ ot^ ycal %a^ S7cd6trjv tCbv 
syxXC(SsG}v dsdo(X£vrjv s^ovtsg tfjv diTtXfjv tfjg ®E nsQC- 
(pSQsCag^ STtSLdrJTtSQ to0ovtcov s6tlv ^olq&v^ o^oig VTtSQ- 
sisi XQOVotg tf^v sXaxC^trjv rj^sQav fj i6rj^SQLvrj^ xal 

15 tfjv vjtb avtfjv svd^slav rdv ts Xoyov tavtrjg tbv TtQbg 
tfiv VTtb tfiv dLTtXfjv tfjg EA^ s%o^sv xal avtf^v dsdo- 
^svrjv Tial tfiv dLJtXfjv tfjg EA TtSQLCpSQsCag^ '^g tf^v 
fj^C^SLav^ tovts6tLV avtfjv tfjv EA^ 7tsQLSXov6av tf^v 
TtQOSLQrj^svrjv [p. 126, 5] vTtSQOxriv dcpsXovtsg ditb tav 

20 in OQd^fjg tfjg 0(paCQag tf^g sxTcsL^svrjg tofj dtd fis6(ov 
TtSQLCpSQsCag dvacpoQcbv tf^v xatd tb vjtoxsC^svov xlt^a 
tf]g avtfjg jtSQLCpsQsCag dvacpoQav sx^Qrj^o^sv. 



1. ri)s (pr.)] zbv rris D. 3. TiQog — EA'} om. D. 4. ra] 

Tcot corr. ex tot C. 5. dsyia (lOLQag] dE%cc[iOLQLag B. icpafisv] 

t- e corr. C^ 6. d-] corr. ex o D^. Xy] corr. ex Xrj D*. 

TCQog rd] om. C, TtQog D. ^f (alt.)] q ins. D^, (j D^ 10. 

ve VT]' D. 13. iarC D, comp. B. 15. vno] vn' D. 16. vTto] 

-6 e con-. D. vnb tfjv] om. C. 17. TtsQLCpSQsCa D. fig] 

corr. ex stg C^D^ 22. Hic des. fol. 42^ col. 1 in A uacante 
plus quam dimidia parte, in qua av(o r] xaray^aqp^; fig. initio 
columnae 2 est. 



MA0HMATIKHS STNTASESiS B'. 131 

ixxsL0d^co yaQ vTCodeiy^arog svsxsv Tcdhv r} xUeLg 
rov dca 'Podov TiaQaklrikov^ xa-O'' ov ri ^sv diTtXij tfjg 
E® 7CSQC(psQ£iag ^olqcov s0xlv Xt, A, i^ d' vit avtrjv 
svd^sta r^7]^drcov kri kd syyL6ra. stcsI ovv 6 avrbg 
Xoyog s6rlv rav | TtQog rd kri Xd xal rav [isv O" Ay 5 
TCQog rd ?; rj^ rav ds T^ v^ ^Qog rd t/3 ta, r&v dsxrjd 
TCQog rd Ttj Oy rcbv 8s Ag Xy TCQog rd xy xd^^ rcbv ds 
fid t/3 TCQog rd xrj jci, r&v ds v ^id TCQog rd A/3 AJ, rav 
ds vs jis XQog rd Xs v/3, rcov ds vrj vs TCQog rd Xt, v/3, 
yCvsrai, xal i^ M^ "^^b rrjv diTclrjv rrjg EA TCSQLCps- lo 
QSLag xad"^ sxd6rrjv rcbv dsxa ^olq&v v7Ceqo%g)v rcbv 
sxxsL^svcov OLXSLCog r^rj^drcov^ rj ds rj^c^SLa rrjg vtc 
avrijv JCSQLfpSQsCag^ rovrs6rLV avrri ij EA^ ^olq&v stcI 
fisv rfjg TCQarrjg dsxa^oLQCag /3 vs^, stcI ds rrjg dsvrsQag 
€ V, STcl ds rrjg rQCrrjg rj Xrj^ ijcl ds rrjg rsraQrrjg Td l^^ 15 
inl ds rfjg TCs^TCrrjg Ty ^/3, ijcl ds ryjg sxrrjg ls ^ts', ijcl 
dh rfjg s^dofjLrjg tf xd^ inl ds rfjg oyddrjg Trj xd, xal ijcl 
rfjg ivdrrjg ds drjXovorc avrcbv rcbv Trj JTs. C36rs 
ijcsLdrj [p. 84, 15] xal ijc oQd-fjg rfjg 6(paCQag rj ^sv 
^sxQL rfjg TCQarrjg dsxa^OLQCag jcsQLCpSQSLa 6vvava- 20 
(pSQsrac XQOvoLg -9' t , rj ds ^sxql rfjg dsvrsQag Tr] xs^ 
rj ds ^sxQL rfjg rQCrrjg x^v^ rj ds ^sxql rfjg rsrdQrrjg 



1. %vBY.£v TtccXiv] xdqiv D. 3. E0] 9E D. X] seq. 

ras. 1 litt. D. ^'] 8b D. 5. -9^] corr. ex D^. 7. 0] 

in ras. A^; b B, ut semper fere. xy] -y in ras. C^, v.d B. 

it^] x^ D. 9. ^ — Xi] bis D. vf] v- e corr. C. 11. 
/xotpcov] post Q ins. ^ D^ vTtsQOx&v^ vnsQox B, -t]v add. B^ 

15. Jv^svD. fi] corr. ex 17 D^ Xr}] X- euan. B. 16. 
«XTTjg] 5 AC. 17. xd (pr.)] v,T]^ A; x^ D, 7] supra scr. D^; xrj 
BC. 18. Se] om. D. 20. d syia fioLQiaiG D. TceQLq^SQsCaa D. 
_ 21. Z, 7}] corr^ex Z^ ADl SsvxiQag] § D, § Dl 22. 

Vy ri] corr. ex vri C. 

9* 



132 KAATAIOT nTOAEMAIOT 

sxtrig v^ fid, i^ ^^ i^^Q^ '^'^S ipdd^rjg ^rj Trj^ r] de 
HTB%QL tfjg dydorjg od' f, rj ds ^^%Ql trjg ivdtrjg 
totg oXov tov tstaQtrj^oQLOv %Q6voi,g 9, (pavsQ&v^ 
5 ort, Kctv dq}sX(D^sv dcp szd^trjg tcbv stcxsl^svcov sti 
OQ^f[g tfjg 6(paLQag dvacpOQcbv trjv olKsCav 7tr]XLx6- 
trjta tfjg Tcatd trjv EA jtSQLcpsQSLav v7tSQ0%r}g^ s%o^sv 
xal tdg sv ta VTtoxsL^svG) xlL^atL t&v avtcbv dva- 
cpOQag. ocal 6vvavsvs%d^7]6staL r} ^sv ^s%ql trjg itQ^trjg 

10 dsxa^oLQLag TtSQLCpSQSLa totg koLitotg %Q6voLg ^ Ld^ rj 
ds iis%QL tfig dsvtSQag l^ Xs^ rj ds ^s%ql trjg tQLtrjg 
td' t/3, ri ds ^s%QL tfjg tstaQtrjg ic^ ly^ -fi dh ^s%ql tfjg 
Tts^Tttrjg ly Ji?^ r] 8s ^s%ql tfjg sxtrjg Jid vrj^ i^ ^^ 
iis%QL tfjg ipd^^rjg v vd^ rj ds ^s%ql trjg 6yd6r]g | jiZa, 

15 i^ ^^ ^^%Q'' "^^? svdtrjg^ tovts6tLV rj oXov tov tstaQtrj- 
piOQLOv^ totg ix. tfig '^^LCfSLag tov ^isysd^ovg tfjg ri^sQag 
6vvayo^svoLg %Q6voLg od Ts. xal avtav ccQa tcbv dsxa- 
liOLQL&v rj ^sv TtQcotrj ^vvavsvs^d^TJ^staL %Q6voLg ^ td, 
r] ds dsvtSQa ^ xd^ rj ds tQLtrj ? X^^ rj ds tstdQzrj t, «;, 

20 17 ds Tts^Jttri ^ ly^ rj ds sxtrj rj t/3, ri ds i^d6^ri rj vg, 
rj ds 6yd6rj d" ftj, ij dh svdtrj T Ad. 



1. PostJ, del. 7j D^_ 2. fxrr]?] 7cey!itrig D. fid] -S 
euan. A. |r]] corr. ex ^r} D^. 3. g] ins. D. 5. cccp'] anb 
zfig i(p' D. £yy.SL(isvcov D. sn'] sni D. 7. vnsqoxfig] 

corr. ex vnsqo%riv D^ 9. Gvvavccvsvsx^riGszcci D. i] [liv] 

corr. ex riiilv D^ 11. 8svtiQuq\ ^' AC. 13. flg] jLiy D. 

16. p Ifi^^a mg. C. 17. avvccvacpSQOfisvoig D. XQOVOig] 
corr. ex XQ^^og A^. %at] tial tav D. dsyiafioLQ&v D. 18. 
cvvavavsx^^^GsraL, supra scr. s, D. 19. ^ a] a^ D, ^ V D^ 

20. EKtr}] r B. 



MA0HMATIKHI: STNTASEiiS B'. 133 

(bv anodadeiyiiivcov avx6%^ev £6ovrai TtdUv 8ia xk 
TtQoxed^ecoQrj^eva avvaTCodedeiy^evaL xal ai x&v XoLTtcbv 
xexaQxr^iioQCcov xaxa xb dxoXovd-ov dvacpOQaL xbv 
avxbv drj xqotcov eitiXoyi^d^evoi Kal xdg xcbv dXXcov 
TtaQakXrilcov ecp exdaxrjv dexa^OiQiav dvacpoQag^ ecp' 5 
o^ovg ye xr^v jtaQ^ exa6xa xQfl6iv ev8e%exai cpd^dveiv^ 
eTcd-rj^o^ed^a ravra? xavoviK&g TtQbg xrjv eitl xd loiTtd 
lied^odov dQxo^evoi ^ev djtb xov v% avxbv xbv t0r]- 
lieQivov^ (pd^dvovxeg de ^exQi xov jtoiovvxog dyQcbv it, 
xr]v ^eyiexrjv rnieQav^ xal xr^v TtaQav^rj^iV avxcbv 10 
rj^icoQiC) Ttoiov^evoi did xb ^rj d^iokoyov yive6%-ai 
xr^v xcbv iiexa^v xov rj^icoQiOv JtaQa xd b^aXd dta- 
(pOQdv. TtQoxd^avxeg ovv xdg xov kvxXov Ag dexa- 
^oiQiag 7taQad'r]6o^ev exd^xrj Tcaxd xb e^rjg xovg xe xfjg 
Oixeiag dvacpOQccg xov xXi^axog xQOvovg xal xrjv eTti- 15 
6vvaycoyrjv avxcbv xbv XQOTtov xovxov. 



2. avvccnoSsSsLyfiEvca'] -ca corr. ex a) D^. 5. icp' i-ad- 

GTTiv'] supra scr. D^. Ante civa(poqd.g del. xcc-O-' s-ndGrriv D^. 

6. ooovg] ovg D. 8. vTr'] corr. ex in' D^ tarj^SQLVov] 
^ D. 11. iiyiicoQLGi noLOv^svoi] r](iLa)Qic(67tOLovfisvoL D, cc mut. 
in co D^ ysviod^aL C. 13. TtQoatd^avTsg D, corr. D^. 

In extr. col. del. '/.avovLov t&v yiatd 8sY,a[ioLQLav dvacpo- 
Q&V D'. 



134 



KAATAIOT nXOAEMAIOT 







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MA0HMATIKHS 2TNTASESiS B' 



135 






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136 



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t 

o ^ 

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«o ^ ca. 




ti2 


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MA0HMATIKHS STNTASESiS B'. 



137 



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te to g 










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IP IP IP 






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co. . t^ i> ip 



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138 



KAATAIOT nTOAEMAIOT 



5^ 4 

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MA0HMATIKHS STNTAHESiS B'. 



Qr te 


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S ^ ^ >-S 

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r^ O 2 * -i 

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? O 



140 



KAATAIOT nTOAEMAIOT 



t 














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MA0HMATIKHS 2TNTASESJ2 B'. 



141 





«J <>a) ^, 


;La. 

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<>^ lr> >. 


t^ (^ ^ 






tfO CQ-U» 

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og . I — 1 . 



142 KAATAIOT nTOAEMAIOT 

d^\ IIsqI rCbv xata ^sgog tatg avacpoQatg 
jcaQaTcoXovd^ovvtcov. 

"OtL ds tG)V avafpOQLXCbV XQOVCOV tbv JtQOXSi^SVOV 

tQOTCOv rjiitv ixted-SL^svov svXrjTCta ra XoLJta ndvta 
6 y£vrJ06taL t&v sig tovto tb ^SQog 6vvtSLv6vt(X)v^ xal 
ovts yQa^^LX&v dsL^scov TtQbg sxa0ta avz&v dsrj^d^sd^a 
ovts xavovoyQa(pLag 7CSQL(f07Jg j dt' avr^i/ tcbv 'bico- 
ta%%"ri0o^svov scpodcov (pavsQbv s0taL. 

TCQotov iisv yccQ tfig dod'SL6rjg rj^sQag 7] vvKtbg 

10 laii^dvstaL tb ^sysd^og aQLd^^rj^svtcjv tov iqovcov tov 
OLKSLOV xXL^atog^ stcI iisv trjg 'fj]isQag tov ccTcb tfjg 
'^XLaxflg ^OLQag ^s%ql trjg dLa^stQ0v6r}g og slg tcc 
STCo^sva tcbv dcodsxatrj^OQLCOv^ stcI ds tfjg vvxtbg tCbv 
dicb trig dLa^stQ0v6rjg tbv tjXlov stc avtijv tijv rilLayiriv 

15 ^otQav tcbv yaQ ^vvaxd^svtcjv %q6vg)v t6 ^sv TCsvts- 
TcaLdsxatov Xa^6vtsg s%o^sv^ o6ov i6tlv d)Qov L6r}- 
^SQLVcbv tb {^TCOKSL^svov dLd^trj^a^ tb ds dcodsxatov 
Xafiovt sg s^o^sv^ 66cov %q6vcov s0tlv rj xaLQLKrj coQa 
tov avtov dLa6t7]^atog. 

20 svQL0KStaL ds Kal 7CQO%SLQ6tSQOv To coQLatov ^sysd^og 
Xa^^avo^svrjg sk tov tcqoksl^svov tov dvacpOQov jtavo- 
VLOv tfig v7CSQ0%fig tcbv jcaQaKSL^svcov STCL^vvaycoycbv^ 
rj^sQag ^sv tfi rjXLax^ iioLQa^ vvKtbg ds tfi dLa^stQov0rj 
sv ts to vjcb tbv i6ri^SQLvbv TCaQaXlfiXco xal sv to 



1. d"'] om. AD, mg. BC. 2. aaoXovd^ovvTcov D. 3, avcc- 
(poQLyibv xQOvov D, sed corr. 7. vnodBixQ^riGoiiivcov D. 9. r/] 
g D. 10. ccqid^^riQ^sv D, tcov supra scr. D^ 12. yboCqas] 

ABC, ^oiQ (q D. 15. fiotgav] ft ABC, om. D. 16. Xa[i- 

§dvov'j D. 17. Si] om. C. 18. la^ovtsg] om. D. 20. Post 
oiQLaiov add. v,aiqiv.6v B^ 21. TcqoXa^^avo^ivrjg D. 22. 

v7ieQ%fis A, corr. A*. 23. iioCqa] AD, comp. B, ^v^at C. 

24. tov] -6- in ras. maiore A^. to5 (alt.)] bis D. 



MA0HMATIKHS STNTAgESiZ! B'. 143 

tov 'b7toxei}i8vov xXi^cctog' rfjg yag svQt6xo^svrjg vjtsQ- 
OXVS "fo g' Xaii^ccvovtsg xal snl ^sv tov ^oqsCov yj^l- 
xvxUov trig si6svrjvsy^svrig ^oiQag ov6rjg nQO^tid^svtsg 
avtb totg tijg larjiisQivfjg ^iag coQag ls XQ^voig^ snl 
ds tov votCov dcpacQOvvtsg djcb t&v avtCbv Ts XQOVCJV 5 
7toi,r]6o^sv t6 TcXrjd^og tcbv xqovcov tfig VTtoxsi^svrig 
xaiQLxfjg G)Qag. 

scps^fjg ds tdg ^sv dsdo^svag xaiQixag coQag dva- 
Xv6o^sv sCg L6rj^SQLvdg 7tolXa7tla(SLd€avtsg tdg {isv 
ri^SQLvdg sitl tovg tfjg rifiSQag ixsCvrjg tov olxsCov xXC- 10 
[latog wQLaCovg xQOvovg^ tdg ds vvxtSQLvdg STtl tovg tfjg 
vvxtog' tG)v ydQ 6vvax^svtcov tb ls' la^ovtsg s%o^sv 
TtXfjd^og G}QG)v L^rj^sQivav. dvdjtaXLV ds tdg dLdo^svag 
L6rj^SQLvdg aQag dvaXv6o^sv sCg xaLQLxdg 7toXka7tXa6Ld- 
6avt sg avtdg S7tl tbv ls xal ^SQC^ovtsg slg tovg vTto- 15 
xSL^svovg Tov OLXsCov dLa6tr]^atog coQLaCovg xQovo.vg. 

7tdXiv dod^svtog rj^tv xQOvov xal aQag 67tOLa6drJ7tot6 
xaLQLxfjg 7tQG)tov ^LSV tfjv dvatslXov6av tots ^otQav 
Toi) dLd ils6g)v tav fcodtcov xvxXov Xrjil^o^sd^a TtoXka- 
%ka6Ld(5avtsg tb ^tXfjd^og tcbv coq&v r]^SQag ^sv tcbv 20 
d7tb dvatoXfjg 'fjXCov^ vvxtbg 8s tcbv d^tb dv6SG)g i7tl 
tovg olxsCovg coQtaCovg XQOVOvg' tbv yaQ 6vvax^£vta 



2. g'] enzov D. Xafi^dvTsg A, corr. A^; Xcc(i^ccvov'i D, 3. 
sv7]V£y[i£V7}g C; sCGsv7]yfisvrig D, post st6- ras. 2 litt. 6. Ts] 
dsyiansvzs D. ^u^oi^cov] -cov e corr. D^. 8. didofisvccg D. 

avaXvofisv C. 9. 7coXXanXa6Lccaav'j D, Post (isv del. 

ovv D^ 11. mQiaCovg] -i- ins. A\ seq. ras. 5 litt, D. 12. 
1«'] Ts ABC, TtsvTsyiaidsTiatov D. 13. avccTtaXiv'] corr. ex 

avccTcav D^. Ssdooiisvag D, dsSo^ivag D^ 14. noXXajcXa- 



aid^ovTsg D. 15. xbv Ts] r&v 8EV,anivts D. 16. oiQaCovg C. 
17. oiaGdriTiots D. 18. yiOLQav] corr. ex coQav D. 20. nXfi- 
^og] -og renouat. B^. t&v (pr.)] t&v Ssdco^^voov D. 



144 KAATAIOT nTOAEMAIOT 

aQLd-^bv diSKpaXov^sv ri^eQag ^sv ccTtb rrjg rjXiaKfig 
^OLQag^ vvKtbg de ccTtb trjg dLa^srQ0v6rjg cjg slg ra 
STto^sva r&v t^codCov xara rag rov vtcoxsl^bvov ocXl- 
^arog avacpOQag^ nal sig riv d' ctv xaravrtj^r} ^oiQav 
6 6 aQid^^og^ SKSLvrjv g)7]6o^sv rors rrjv ^otQav avarslXsiv. 
sav 8s rr^v ^s0ovQavov6av vtcsq yr]g d^sXco^sv ka^stv^ 
rag xaiQLxag wQag Ttdvrors rag UTtb rrjg ^s^rj^^QLag 
rrjg TtaQsXd^ov^rjg ^s^ql rrjg dod^SLdrjg 7toXXa7tXa6id0av- 
rsg sjtl rovg OLXSLOvg G)QLaLOvg xQOvovg rbv ysvo^svov 

10 ccQLd^^bv SK^aXov^sv ccjtb rrjg r]XLaKfig ^OLQag slg ra 
STto^sva xard rdg sit OQd-yjg rfjg ^cpaLQag dvacpoQdg^ 
ocal stg 7]v dv SK7ts6rj yiotQav 6 dQLd^^og, SKSLvrj rj ^otQa 
rors vjtSQ yfjg ^s6ovQav7]asL. 

o^OLcog ds ditb {isv rfjg dvarskXov6rjg ^OLQag rr]v 

15 fis6ovQavov6av vTtsQ yfjg Xrjjljo^s^a 6KS2l^d^svoL rbv rfj 
dvarsXXov6r] JtaQaKSL^svov rfjg s7tL6vvayc!)yf]g dQLd^^bv 
sv rip rov olkslov KlL^arog KavovCcp' d(psX6vrsg yaQ 
aTt avrov 7tdvrors rovg rov rsraQrrj^oQLOv xQovovg c, 
rf]v TtaQaKSL^svrjv rm dQL^fta ^otQav sk rfjg S7tL6vv- 

20 aycDyf]g rov S7t^ OQd^fjg rf]g 6(paLQag asXLdCov rors v7tsQ 
yfjg ^s6ovQavov6av svQr]6o^sv. dvd^talLv 8s d7tb rfjg 
VTtsQ yf]V iis6ovQavov6r]g rf]v dvarsXKov6av 7tdhv Xr]- 
ifjo^sd^a 6Ks^diisvoL rbv r^ fis6ovQavov6r] ^OLQCf 7taQa- 
KSL^svov rfjg S7tL6vvayc3yf]g dQLd^^bv sv ra rfjg OQd^rjg 

25 6cpaLQag 6sXl8lg)' 7tQ06%^svrsg yaQ avr» 7tdvrore TtdUv 

1. r]Xiv.fiq A. 3. rov] supra scr. B^ 4. %at] om. D, 

6. Ante yfis ras. 1 litt, A, 8, doQ^SLGriq] do&SLorjg aQug D. 
9. wQLULovg'] corr. ex %(oqiaLOvg C^ 11. mg] tfig B. ava- 

cpoqdg'] mg, A^, 12. dv] D, sdv ABC, 16. avarsXovGTj C, 
17. oUsLov'] pr. i e corr. C, y.avovL D. 18. ccTt'] seq. 

ras. 1 litt. A, ano D. 22. ndXLv] om, D. 23. ftot^a] (loiQai 

ACD^, ^' B, ^OLQL D. 24. iv] om, C, 



MAOHMATIKHS STNTASESiS B'. 145 

rovg avTovg 9 XQdvovg iTCLexsfo^sd^a ix rfjg i7Ci6vv- 
ccycoyfjg tov vTtoxeL^svov ocXc[iatog^ TtoCa fiotQa jcaQcc- 
xELxai Td5 «^tO^ftco, JcazELvrjv xota avaxiXkov6av svqtj- 
Co^av. 

(pavaQhv da xav^ oxl xolg fiav vtco tov avtov ^a6- 5 
Ti^^Qivhv otKOv6iv 6 7]lLog xag l'6ag i6rj^aQLvag cogag 
a7ci%ai xijg ^a^rj^PQoag r) xov fia6ovvzxLOv^ xotg da firi 
V7C0 xov avxov ^a^rj^^QLvhv xo6ovxoLg t6rj^aQLvotg xq6' 
voLg dL0L6aL^ o6aLg av ^OLQaLg 6 ^a^rj^^QLvhg xov ^a6- 
fj^pQLvov TCaQ axaxiQOLg dLag^iQrj. 10 

i'. IlaQl xcbv 'bjch xov dto: ^i6cov xcbv lcadCcov 

icvTckov xal xov ^a6rj^pQLV0v ycvo^ivcjv 

ycavLGiv. 

AoLTCov d\ ^vxog alg xriv vTCOTcaL^iivrjv d^acoQCav xov 
xhv TCaQl x&v ycovLav TCocri^a^^^aL koyov^ Xiyco da x&v 15 
-TCQhg xhv dt« ^a6cov x&v ^cydCcov ocvxkov yLvo^iivov^ 
^QoXrjTCxiov^ OXL OQd^rjv ycavCav vTch ^ayC6xcov xvkXcov 
liyo^iav %aQLi%a6^aL^ orav 7c6kco xfj KOLvy xo^y xav 
tcvkXcov xal dLa6xr]^axL xv^^vxl yQacpivxog kvtcIov rj 
ccTCola^Pavo^ivrj avxov 7CaQL(piQaLa V7ch xcbv xrjv ycovCav 20 
^aQLaxovxcov x^rj^dxcov xaxaQxr]^6QL0v xov yQacpivxog 



2. v7tov.SLiiivov'\ corr. ex iTtiyieLfiivov D^. fiOiQcc'] B; 

II ACD, ut solent. 5. cpoivsqov — ftfV] supra scr. D^. 7. 

xoig\ coiT. ex rovg D^, 8. [lsgthi^qivov'] ft D. 9. oWtg] 

cdq corr. ex olg D^. iioiQaig'] om. D. 10. Tca^'] (lOLQcag 

nccQ' D. diacptsQBL B. 11. t'] om. AD, mg. BC. tcov (pr.)] 
corr. ex tov B, corr, ex tov D^ 12. yivyiXov] om. D. ^sorifi- 

^QLVOv] li D. 14. ovxcog C. 15. x&v (alt.)] xov B. 16. 

ytyvoiievcov D. 18. Xiyoiisv] -v supra scr. A^. 19. yQa- 

4psvxog] corr. ex yQcktpovxeg D^. 

Ptolemaeus, ed. Heiberg. 10 



146 KAATAIOT nXOAEMAIOT 

KvxXov TtOLfi, Kad^62,ov te^ ort, bv ctv £%!] Xoyov rj dico- 
XaiL^avoiiBVYi TteQLcpsQSta TCQog tbv yQacpivta kvkXov^ 
xad'' bv £tQ7]Ka^sv tQoitov^ tovtov s%SL tbv Xoyov 7} 
7tSQLS%o^£vrj ycDVLa VTtb trjg xXL0scog t&v iitLTtsdcov 
5 TtQbg tag ts66aQag oQ^ccg. a6t£^ £7t£Ldri triv 7t£QL^£tQ0v 
VTtottd^i^^d^a t^rj^dtcov t|, o6cjv dv £VQL6xrjtaL t^rj- 
^dtcjv rj aTtoXa^^avoiisvri %SQL(psQSLa^ to6ovtcov s0tac 
xal rj {)7totSLVOv0a avtrjv ycovLa^ olov ri ^Ca OQd^rj 9. 
tG)V dij 7tQbg tbv Xo^bv tcvjcXov yLvo^svcjv ycavLcbv 

10 at ^dXL0ta xq7]6l^ol 7tQbg trjv V7tOKSL^svrjv ^scoQLav 
SKStvaC sl6lv a% ts VTtb tr\g to^rjg avtov xal tov 
^£6rj^pQLV0v 7t£QL£%6^£vaL KOL at vTtb trjg to^fjg avtov 
xal tov OQC^ovtog xad'' indotrjv d^ddLv Tcal b^oCcog aC 
VTtb tfjg toiifjg avtov xal tov dLcc t&v 7t6Xcov tov 

15 bQC^ovtog yQacpo^iivov ^£yC0tov kvkXov dvva7tod£Lxvv- 
^svcjv tatg tOLavtaLg ycjvCaLg xal tcbv aTtoXa^^avo- 
^svcov tovtov tov TcvxXov 7CSQLCpSQSLcbv V7t6 ts trjg 
to^rjg xal tov 7t6lov tov OQCtftvtog^ tovtsatLV tov 
Tcatd xoQvcprjv 6rj^sCov. SKa6ta yaQ tav sxksl^svcov 

20 aTtodsLX^svta 7tQ6g ts trjv ^scoQCav avtrjv Cxavcotdtrjv 
s%SL %(xiQav xal 7tQbg td 7tsQl tdg 7taQaXXd^SLg tfjg 
OsX^^vrjg S7tLt,ritov^£va ^dXt^ta 6v^pdXX£taL tb 7tX£L6tov 
lirjda^cbg tfjg tOLavtrjg xataXtjTp^cog 7tQO%coQ£tv dvva- 
^svrjg dvsv trjg sxsCvcov ^tQodLaXrj^scog. 

25 STtsl ds Xal tS66dQC0V 0V6cbV yC3VLG)V t&V 7tSQL- 



1. noiEL B. 6V] corr. ex D^. ScTtoXa^^avo^svrf] pr. o 
corr. ex s A^ 3. txsC] corr. ex sx^i-v D^. 4, V7t6] om. D. 
5. oaoz' D. iTCEiSij] corr. ex iniSij A^. 6. EVQLGTirjTaL] 

corr. ex EVQi]6%r]Tca A. 9. 81]] di supra scr. D. 11. tov 

— 13. yiai (pr.)] supra scr. D^ 12. at] om. C. 17. vTto] 

V in extr. lin. A, no add. A*. 18. xat] avTOv yiaC corr. ex 

avTdiV yiaC D. 22. 6vii§dXETai C. 



MA0HMATIKH2 ZTNTASESiS B'. 147 

sxo^svG)v VTtb tfjg tcjv dvo kvkXcov to^fjg^ tovts6tiv 
tov dia ^s6(x)v tcbv ^adtav xal ivbg tav 6v^7cXsko- 
fisvcsv avtipy tisqI ^cdg tijg %ata triv d^sdiv o^ocag tbv 
X6yov 7t0Lsl6^aL ^sXXo^sv^ TtQodiOQL^tsov^ otL Kad-oXov 
tG)V dvo ycovL&v tCbv tcsqI tr^v STto^svrjv tfj xoLvfi to^f] 5 

tG)V KVkIoV 7tSQL(pSQSLaV tOV dia ^S0G)V tCOV ^CjdLCOV 

tijv ajt^ ccQXtcov V7taxov6tsov^ C36ts ta 0v^paLvovta 
xal tag TtrjXLKOtrjtag tag aTtodsLxd^rj^o^svag slvaL tG)V 
ovtcog sxov6g)v yovLcbv. a7tXov6tsQag ds trjg dsL^scjg 
ov0rjg tG)v TtQbg tbv ^serj^^QLvbv kvkIov d^SG^Qov^svov lo 
rov Xo^ov ycovLcov d7tb tovtcov aQ^oiisd^a xal dsL^o^sv 
TtQcbtov^ otL To: l6ov ccTtsxovta tov avtov L6rj^sQLvov 
6r]^SL0v tov dLcc ^s6cov tcbv icpdicov xvxkov 6rj^SLa tag 
SKXSL^svag ycovCag l'6ag dXktjXaLg 7tOLSL. 

s6tco yaQ t6r]^SQLVov ^sv 15 
7tSQL(psQSLa rj ABF^ tov ds 
dLcc ^s6g)v tG)v ^goSlcov rj 
^BE^ 7t6Xog 8s tov L6r}- 
liSQLVOv tb Z 6rj^stov^ xal 

d^toXrjtfxtSL^&V L6G)V TtSQLCpS- 20 

QSLcbv tijg ts BH xal B® 
s(p SKatSQa rov B l6rj^sQL- 
vov 6r]^SL0v ysyQacpd^co^av dLa tov Z 7t6lov Kal 

tCbV if, 6r]^SLG)V ^S6r]^PQLVCbV KVkXgJV 7tSQL(pSQSLaL 




3. Post iLL&g ins. C^ 5. yavi&v tav] supra scr. D^- 

6. TCSQKpsQSLav^l mut. in TtSQiq^SQSicc C^; nsQicpSQSia xat D, 

corr. D^ 7. ra] ta iiiv D. 8. tdq (alt.)] om. D- 

9. anXovatSQag] -ov- e corr. D. 11. a Xfjfifia mg. C, paragr- 

mg. B. 12. l6r]fisQi.vov] comp. D, ut saepius. 20. ano- 

XsLcp^siG&v A. 21. B&] tfjg B& D. 22. E] supra scr. D^ 

24. Ante nv-nXcov del. rcov D^. nsQLcpSQSiai] -i in ras. C. 

10* 



148 KAATAIOT nTOAEMAIOT 

fi re ZKH xal rj Z@A. leyco, otc l'0r} idtlv yj vtco 
KHB ycovia rfj vith Z@E. %aC e6tLV avtod-ev (pave- 
QOV L^oy^vLOV yaQ yCvetai tb BHK tQCTtkevQov ta 
B@A^ eTteLdtJTCeQ Kal tas tQetg jcXevQag tatg tQL0LV 
5 TtlevQatg i'6ag e%eL exd6trjv eKaatr]^ tijv ^ev HB tfi J5@, 
f^v de HK tfi ®A [I, 15], triv deBKtfi BA [p. 118, 5]' 
dedeLXtaL yaQ Ttdvta ravra ev rotg e^TtQoe&ev xal 
ycjvCa aQa rj vno KHB ycjvCa tfj vjtb B&A^ tovt- 
e6tLV tfi vTtb Z&E^ e6tLV L6ri' oiteQ edeL det^aL. 

10 TtdXLV deLxteov^ otL tav tb l'6ov aTtexovtcov 6ri^eCcov 
tov dLcc ^e6c3v tcbv ^mdCcjv ocvxXov tov avtov tQO- 
%Lxov 0rj^eCov al TtQog tbv 
^e^rj^^QLvbv yLvo^evaL ycj- 
vCaL 6vvaii(p6teQaL dv6lv 6q- 

15 ^atg i'6aL el^Cv. 

e6tC3 yaQ tov dLoc ^e6cjv 
x&v ^tpdCcjv xvxkov TteQL- 
(peQeLa r] ABF tov B VTto- 
xec^evov tQOJtLXOv 6r]^eCov^ 

20 ;cal ditoXrjipd^eL^&v eq)' exdteQa avtov 7CeQL(peQeLG)v i'6cov 
tfjg te BA xal tfjg BE yeyQdtpd-co^av dcd r&v /d 
xal E 6rj^eCc3v xal rov Z TtoXov tov C6rj^eQLV0v ne6- 
rj^^QLV&v Kvxlcov TteQLCpeQeLac rj te Zz/ xal rj ZE. 




1. 7] Tf] cii D. xal 17] om. D. l'6r}] V- in ras. A. 2. 
Supra Z@E scr. BSA D^ 3. iGoyoviov A, corr. AV yCyvt- 
xai D. 5. £Y.(x.6trf\ om. C. tjf\ corr. ex T7/g D^ 6. t^ 

(utrumque)] corr. ex ttJs D^. &A\ A@ I). 7. Ta-uTa ndvtu D. 

8. KHB\ corr. ex KBH D^. E©^] corr. ex B@A B^Cl 

9. Ze)E] -0E e corr. D^. ZnsQ idn dEi^ai] om. D. 10. 
Ififificc § mg. B, (3 Ifniiia mg. C. Post t6ov ras. 8 litt. B. 

13. iiiE6riiL^Qiv6v\ comp. D, ut saepius. 14. 6vva(i(p6tstEQai A, 
corr. A^. 18. 1^] corr. ex v A. 21. tt)? ts — tfjg] t&v 

BJ D. 22. xat(pr.)] om. D.. 23. ij ts — 7]] ZA D. 



MA0HMATIKHS 2TNTASESi2 B'. 149 

Xeycj^ ott 7] X8 vtco ZzIB ycovia xal i] v%o ZEF 
(fvva^g)6t£Qat dvelv oQd-atg l'6ac £l6lv. £6ti d£ Tcal 
tovto dijXov avtod-^v. £7C£l yccQ ra z/ xal E 6ri^£La 
l'6ov aitii^i tov avtov tQOTtLXov 6rj^£L0v^ l'6i^ £6tl ;cat 
Yj ^ Z 7C£QL(p£Q£La tfi ZE' xal ycjVLa aga r] vTtb ZzlB 5 
yc3VLa tf] vTcb ZEB L6rj £6tCv. alXa rj vicb ZEB xal 
ZEF dv6lv OQ&atg L6av £i6LV' xal rj vTcb ZAB aQa 
^£ta tfjg 'bjcb ZEF dv6lv dQd^atg l6ai £l6lv' otc^q fdf^ 
d£t^aL. 

tOVtCJV 7CQOt£^£G3Qri^£VG)V £6tG) ll^^rj^^QLvbg fl£V 10 

xvxXog 6 ABFzt.^ tov d£ dva ^£6C3V tcbv ^adLCOv rnic- 
xvkXlov tb AEF tov A 6rj- 

^£LOV V7C0K£L^£V0V TOV %ftftf- 
QLVOV tQOTCLXOV^ Xul %6kC0 tW A^ 

8La6triiiatL d£ tfj tov t£tQa- 15 
ycDVOV 7ck£VQa y^yQacpd-cj t6 

BEzf rj^LKVxXLOV. £7C£L tOLVVV 

6 ABFzl ii£6riii^QLvbg dtd t£ 
tcbv tov AEF 7c6Xc3v xal 
dLO. tcbv tov BEA yiyQa^ctaL^ 20 
t£taQtr]^OQLOv £6tlv rj Ezl 7C£QL(p£Q£La [Theodos. I, 9] • 
hQd^ri aQa £6tlv rj vTcb zlAE ycovCa. OQ^ri d£ dta ta 
7CQod£d£Ly^£va [p. 147, 11] xal rj V7tb toi) d^^QLvov tQO- 

7CLK0V 6rj^£C0V yLVO^dvrj' 07C£Q £d£L d£t^aL. 




1. Zz/B] corr. ex JZB J)\ i) (alt.)] om. D. 2. slaiv 
tGCii D. 3. xat] om. D. 4. f(TTtV D. xat] om. C. 5. 
JZ\ ZAJ). ZJB] JZBB. 6. Lor] — xat] mg. D^ xat] 
«ai 7] vno D^ 7. dv6Lv] -C- in ras. C. doLV tacct D. 

ZJB] -d- e corr. C^, Z^E B. 8. 8v6iv] 8- in ras. C. 

OTTf^ f^ft ^ft|at] om. D. 10. ft£v v.v%Ioq\ om. D. 13. 

To^] om. D. 14. Tc5] corr. ex to C^ A] corr. ex TtQoaTcp D^ 

19. TtoXcov] -V ins. D^ 23. TtQoaTtodBdELy^svu D. r}] add. D^ 

24. ori^ELOv] om. D. oTtSQ sdsi Ssl^kl] supra scr. Dl 




150 KAATAIOT nTOAEMAIOT 

TCccXiv 86X0} fi£6rj^PQLvbg ^ev xvxlog 6 ABF^^ 
i0rjiiSQLVov ds rj^LxvxXLOV tb AEF^ xal ysyQcccpd^co tov 
dia lii^ov tG)v ^adLGyv tb AZF ri^LXvxhov ovtcjg^ 
&6ts tb A 6ri^siov SivuL ro iistOTCcoQLvbv tarj^sQLVOv^ 
6 jcoIg) ts ro5 A xal dLaatri^atL 
tfi tov tsxQayavov TtXsvQa ys- 
yQacpd-co ro BZEzf rj^LTiVKliov. 
dLcc ta avr^ drj, stcsl b ABFzi 
did xs tG)v tov AEF xal dia 

10 tG)V tov BEA TCoXcov ysyQaTCxac^ 
xsxaQxrj^oQLOV s6x\v rjxs AZ xal 
rj Ezl' G)6xs xal xb ^sv Z arj^stov 

s0xai xb %SLy.SQivbv XQ07Ci7c6v^ r] 8s ZE TCSQicpsQSia xav 
aTCodsdsiy^svcov [p. 81, 50] ^oiQcov xy va syyL6xa. xal 

15 oXrj ^sv ccQa rj ZE/1 jcsQLCpSQSLa ^olqcjv s6xiv Qiy va, 
r] ds VTcb AAZ ycovCa xoiovxcov QTy va^ oicov s6xlv 
'fj ^Ca OQ^tri 9. dLcc 8s xa TCQodsdsLy^sva [p. 148, 10] 
tcccXlv ocal rj vjcb xov saQLVov i6rjpiSQivov 6rj^Siov yivo- 
^isvri ycovCa xcov loiTCav slg xag 8vo oQd-ccg s6xaL 

20 [LOLQCbV |g %-. 

tcccXlv s6xg) pLs6ri^^QLvbg ^sv zvxXog 6 ABFzl ocal 
i6ripiSQiV0v ^sv rj^ixvTchov xb AEF^ xov ds dia ^s6g)v 
XG)v t,codicov xb BZA^ co6xs xb ^sv Z 6rj^Siov vtco- 
xsL^d^ai xb ^sxo7CcoQiv6v^ xijv ds BZ TCSQicpSQSiav tcqco- 



1. ^ffTco] corr. ex iGziv in scr. C. 4. wffrf] corr. ex 

OTS C^ 6T](iSL0v] corr. ex Gr][isicov C^. 5. to5] corr. ex 

To C^ A] corr. ex nQmxcp D^. •xat] om. D. ' 6. Tf;] ds 
Tji D. 9. dLci (alt.)] dLoc ts D. 11. sgzlv] ccqu sgtlv B. ' 13. 
tqoniv.ov'] -ixo- in ras. A. 14. syyiGTa] alt. y corr. ex l in 

scr. C. 16. 7] — im] om. D. 20. ^rf (h add. D. 21. 

fi^v] om. D. 22. 8s] comp. ins. Dl 23. BZz^] corr. ex 

Ez/Z D^. &6Ts] «s D. 




MAOHMATIKHS STNTASESiS B'. 151 

rov ivbg dcjdsKatrj^oQLOv tov trjg UaQd^Evov xal tb B 
6rj^stov aQx^v drjXovotL tijg IlaQd-avov' tcoIg) de TtdXiv 

ta 5, diadtT^^atL dh tr] tov 
— ~^ tetgayavov JtXsvQa ysyQaq^d^c} 

tb H@EK ri^LTivnXLOV ^ Tcal 5 
jtQoxsL^d^co triv vTtb KBS yco- 
vCav svQslv. 

STtsl tOLvvv 6 ABF^ n>s6- 
rj^PQLvbg dLa ts tcbv tov 
AEF xal Slcc tcbv tov HEK 10 
TtdXcov yiyQaTttaL^ tstaQtr^io- 
Qiov fisv sxd0tr} yCvstat t&v BH xal B® xal EH 
TtSQLtpSQSLGyv. ^La ds tr^v xatayQaiprjv 6 trjg vitb trjv 
SLTtXfiv trjg BA TtQbg trjv vTtb trjv dL7tkf}v trjg AH 
2.6yog evvrjTttaL sx ts tov tijg VTtb f^v dLTtkrjv trjg BZ 16 
^Qbg trjv vTtb tijv dLJtlrjv trjg @Z Tcal tov trjg 'bTtb 
triv dLTtXrjv tfjg ®E TtQbg tijv vjtb trjv dLJtXrjv tfjg EH 
[p. 74^ 9]. dkX' rj fisv dLTtXfj tfjg BA dLa td TtQO- 
dsdsLy^sva ^olq&v s6tLV 7cy x xal ri {}7tb avtijv sv^sta 
t^rj^dtcov zd Zg, ri ds dLTtXfj tfjg AH [iolqS)v qv? ji 20 
ocal ri vTtb avtijv svd^sta t^ri^dtcov QLt, Aa, Kal TtdXtv 
rj ^sv dLTtXf} tfjg ZB fiOLQ&v 5 ^cal r} vitb avtr}v 



1. IIccQd^svov^ nuQVOv C. xat rdj tb ds D. 2. TJccq- 

^hov] nccQvov D. 5. H0EK] corr. ex @HEK D^. 9. tov 
AEF %at] supra scr. D^ 10. dio. %&v'\ om. D. HEK'^ 

mut. in HGEK Dl 12. >ial B@ yiccC] B@ B. 13. di] corr. 
ex XE D^ 14. Ante ttjs (pr.) eras. Tf]g vitb r^i/ diiiXfiv A. 

15. GwfiTiTcci] b Gvvrjfifiivog D. 16. &Z] Z6> D. 19. jc] 
om. BC. vTto] vit' D. 20. tg] corr. ex X^' D^ ^?g] -v- 
corr. ex rj in scr. D. 21. vno] vn D. ivQ^Eia] sv- e corr. A. 

Uc] Ucis D. 22. Tfig] T- in ras. A. ZB] BZ D. |] 

• icTiv ^ D. vno] vn D. 



152 KAATAIOT nTOAEMAIOT 

s^dd^sta t^rj^drcov ^, ^ da diTtXfj rfjg Z® ^olq&v qtc 
xal rj vTcb aifri^v evQ^ata r^rj^drcov "oy vs xy. iav aga 
TtdXiv djcb rov r&v xd 7g Tt^bg ra ql^ Xa Ad}^ov d(pEk(o- 
^6v rbv r&v | TtQbg rd Qy vs xy^ xaraXsicpd"i]0erat, 6 
5 f^g "bjtb rijv diTtXfjv rijg 0E TtQbg rriv 'bnb rijv dLTtlijv 
trjg EH Xoyog 6 rcbv ft/3 vrj eyyi^ra Ttgbg rd qtc. xat 
e6rLV rj vjtb rijv diTtXrjv rfjg EH r^rj^drcov qx' xal 
rj vTtb rijv diTtXfjv dga rfjg ®E rcbv avr cov e^nv /it/? vrj. 
a6re xal rj ^iev dcTtXfj rfjg @E fioiQ&v e^riv ^ifi eyyi6ray 

10 avrii de rj @E rcbv avrcbv 7cd. xal oXrj ^ev aQa rj 
&EK avrr] re xal rj vTtb KB& ycovCa ^olqg)v e6riv 
Qtd^ dtd de rd TtQoaTtodedecy^eva [p. 147, 11] xal rj 
^ev VTtb rfjg aQxfjg rov ExoQTtCov yivo^evrj ycovCa tmv 
l'6cov e6raL ^olqcov Qid^ exareQa [p. 148, 10] de i] re 

15 vTtb rfjg dQxfjg rov TavQOv xal rfjg aQxfjg t^v 'Ixd^vcov 
rcbv XoLTtcbv elg rdg dvo dQd^dg ^olqS)v ^d" oTteQ edet 
det^aL, 

TtdXtv eitl rfjg a^hrrig xarayQacpfjg rj ZB JteQL(peQeLa 
VTtoxeC^d^o) dvo dcodexarrj^OQCcov ^ &6re rb B 6r}fietov ] 

20 elvat rijv aQxijv rov Aeovrog xal rcbv avrav vTtoxet- 
y^evcov ri]v ^ev dLJtXfjv rfjg BA ^olqcov elvaL Jid xal 
rijv VTtb avrijv evd^etav r^rj^drcov ft/3 /3, rijv dh dLTtXfjv 
rfjg AH ^olq&v QXd' xa\ rijv vTtb avrijv evd^etav r^rj- 
^drcov QLp xd, xal itdXLV rijv ^ev dLJtXfjv rfjg ZB 

1. dLTtXf]'^ -i- corr. ex tj D. Z0] corr. ex £!@ A. 2. 
vTTo] vn' D. xy] om. D. 4, xy] om. D. 6. fyyKTTo;] Eyy- 
in ras. A^ e corr. Cl 7. 17] om. D. 8. iazL D. 9. 0E] 
corr. ex @M D. 10. 7} @E] e corr. C^. 11. GEK] -K 

in ras. B^C^; corr. ex 0E, KA D^ iativ'} om. B. 12. ttqo- 
dsdsiyfisva D. 15. tav] -mv in ras. A. 16. dvo] A, p^ BCD. 
SnEQ sdEL dsi^ccL'] om. D. 19. ds-natri^oQLcov D, corr. D^ 

21. diTcXfivl -v ins. C^ 22. tiqv (pr.)] corr. ex tmv D^ vno\ 
V7t' D. 23. vno] vn D. 24. ZE] BZ D. . 



,. MA0HMATIKH2 STNTASEaS B'. 163 

i _ 

' (lOLQ&v Qic xal XYiv vTto avtrjv evd^stav r^rj^dtcov 
'gy VE %y^ f^v ds dLTtXfjv tfjg Z® ^olqcov J Tial f^v 
v7to avtijv svd^stav t^rj^dtcov |. idv dga TtdXtv aTtb 
tov tmv ftj3 ^ TtQog td ql^ xd loyov dcpsXcj^sv tbv 
tcov ^ vs xy TtQbg td 5, xataXsiq)d'7]6staL 6 trjg 'bjtb 5 
tfjv dLTtXfjv tfjg ®E TtQog tfjv vTtb tf^v dLTtXfjv tfjg EH 
?,6yog 6 tcbv xs vy JtQbg td qtc' rj aQa VTtb tf^v dLTtlfjv 
tf^g ®E yCvstaL tcov avt&v tcs vy. co6ts xal rj ^sv 
dLTtlfl tfig ®E iLOLQGiv s6taL 7CS syyL^ta^ avtf^ ds ri 
@E tav avtG}v l^L!- SA^ ft£v aQa fi ®EK avtfi ts 10 
Kal f] vTtb KB @ ycovLa ^olqcov s6tLV q^ L\ ^i^d tavtd 
6s xal rj ^sv V7tb tfjg aQxfjg tov To^otov 7tsQLS%on,ivri 
ycovCa tcbv l'0cov Q^ L\ ixatiQa ds 7] ts VTtb tfjg aQxfjg 
tcbv ^Ldv^cov xal tfjg aQxfjg tov 'TdQOxoov tcov Xol- 
7tG)v sCg tdg dvo OQd^dg [lOLQcbv o^L'- ^cal didsLXtaL 15 
fjy^tv td TtQoxsC^sva tfjg ^sv avtfjg i6o^ivr]g dycoyfjg 
xal iitl tcbv stL ^LXQo^SQS6tiQCov tov Ao|ov xvxXov 
t^rj^dtcov^ d7taQxov6rjg d' cog 7tQbg avtfjv tf]v tfjg 
7tQay^atsCag %Qfi6LV xal tfjg xad'' sxa6tov tcbv dodsxa- 
trj^OQCcov ixd^i^scog. 20 



1. vTco] vn D. 2. oy vb] eras. propter fig. D, postea 

add. eadem manu. xy] om. D. 4. xov] xov Tf D, rf e 

corr. D3. 5. xy] om. D. 6. (9E] corr. ex EH D^ Deinde 
add. loyog D. nqoq — EH] supra scr. D^ 7. Xoyog] 

om. D. vy\ corr. ex ly' D^. q%- fi\ BC^D^, ^x^ ACD. 

9. S6XLV D. 10. ^'] ins. D^. ZXt]] s oXt} D. 11. ^] 

corr. ex ql^ D^ /_'] in ras. B, Hi D. xavxa] xd ccvxd B, 
xccvxa CD. 12. de] D, dt] ABC. xov] xo D, nsQLtxo- 
fisvf] ycovCa] corr. ex 7tSQi8xo}i8vr}s ycovCccg D^. 13. /_'] ins. D^, 
% ioxLV D. 14. ccQXTig] om. BC. 15. (iolqcov] om. D. /_'] 
4i S6XLV D, L «<y^tv D^ 18. d'] ds BC. 19. xcbv] supra 

scr. ADl 



154 KAATAIOT nTOAEMAIOT 

1(1 . IIsqI rcbv 'bjtb rov a-brov Xoi,ov tcvxIov xal 
rov oQL^ovrog ycvo^evov yovicbv. 

^E(ps^7jg ds dsc%oiisv^ itcbg ccv Xa^pcivoL^sv sitl rov 
dido^svov KXifiarog xal rag TCQog rbv bQit,ovra rov dia 
6 ^S0ODV r&v i,(p8Ccav xvxXov yivo^svag ycjvCag a7tXov6rs- 
Qav xal avtag s%ov(iag rijv fisd^odov rcbv Xoi%S)v. on 
fisv ovv aC TtQbg rbv ^s^rj^PQivbv yiv6(isvac «r avraC 
si6iv ratg TtQbg rbv iit^ hQ^f[g rfjg 6(paiQag bQi^ovra^ 
(pavsQov svsxsv ds rov xal rag sitl rfig iyxsxXi^svrjg 

10 6cpaiQag Xa^pccvsdd^ai dsixrsov Ttdkiv TtQcbrov^ on ra 
i6ov aitsypvra ^rj^sta rov dia ^s6cov rcbv ^aydicjv 
xvxXov rov avrov l6r}^SQivov 6r]^siov rag ytvo^svag 
TCQbg rbv avtbv OQi^ovta yco- 
vCag l'6ag dXXrjXaig Ttoist. 

15 s6rc3 yccQ ^s6rjfiPQLvbg xv- 
xXog 6 ABF^ xal i^rj^sQivov 
^sv rj^ixvxXiOV rb AEF^ oqC- 
^ovrog ds ro BEA^ xal ys- 
yQacpd^co rov ko^ov xvxkov dvo 

20 r^t^^ara rb rs ZH® xal rb 
KAM ovroig s%ovra^ co6ts sxd- 

rsQov iLSv rcbv Z xal K 6rj^sCc3v v7toxst6^ai rb ^sro- 
jtcjQivbv i6rj^SQiv6v^ rrjv ds ZH TtSQicpSQStav rfj KA 




1. Lcc'] om. D, mg. A^C^, ccl mg. B. 3. Ss] Srj D. av 
Xafi§dvoni£v] corr. ex ci.vaXcc^§dvoLfisv D^, 4. Sl8o(ievov] Sl- 
corr. ex ri- in scr. D. 7. yLVOfisvccL] -ccl supra scr. A\ corr. 
ex ysvofisvat D. at] supra scr. D^ 8. si6Lv] -v del. C*D^ 
9. xov] supra scr. D^ syv,sv.XL[iBvri A. 10. Xfifiiia a 

mg. B, d Xfi^iia mg. C. 12. criiiSLOv] supra scr. Dl yivo- 
{isvag] iy)isy,XLiisvag D. 22. v.ai] om. D. orjiiSLOV C. }isro- 
na)QLv6v] -r- corr. ex & D. 23. ZH] rr]v ZH D. KA] 

corr. ex Az^ B^Cl 



MA0HMATIKHS STNTASESiS B'. 155 

l6rjv. Aeyo, otl xal 7] vTtb EH® ycjvia l'6rj i6tlv tfi 
VTcb zlAK. TcaC s0tiv avtdd^sv dfjlov l6oy(hvLOv yag 
jtdhv yivBtai tb EZH tQLTCkevQov ta EKA^ iiCEL dLa 
td TtQodadsLy^iva xal tdg tQstg TtXsvQdg tatg tQL6l 
^XevQalg l'0ag sxsl sxd6ti]v ixd6tr}^ tY^v ^sv ZH tf} 5 
KA, tYjv ds HE tTjg to^fjg tov oQL^ovtog tfj EA^ 
trjv ds EZ trjg dvacpoQdg tfi EK [p. 118, 5]. t6ri aQa 
i6tlv ocal ii iisv vnb EHZ yovCa tfj i)7tb EAK^ 
XoLTtri ds rj vitb EH® XoLTtfj tfj vjtb AAK l'6rj i6tLV' 

OTtSQ sdsL dsL^aL. 10 

Isyo) di^ otL xal t&v 

dia^stQOvvtcov ^rj^sCcov r] tov 

stSQOv dvatoUxri ^std tfjg 

^' l^ ^l 1-^ tov stiQOv dvtLxfjg dv0lv 

OQd^atg l'6rj i6tCv. idv yaQ 15 

yQdxl^cj^sv bQCt^ovta ^sv xv- 

xXov tbv ABFA^ tbv ds 

dLd iii6cov tG)v ^(pdCcjv tbv 

AEFZ ti^vovtag dXlrjXovg xatd td A xal F 6rj- 

lista, 6vva^cp6tSQaL ^sv ij ts vitb ZAA xal 7] vnb 20 

AAE dv6lv OQd^atg L6aL yCvovtaL. i'6r} ds o^ 't>3to ZAA 




1. Igxiv\ -V del. C^D^. 3. Tc5]]corr. ex xSiv A, corr. ex 
x6 D^ 8icc\ corr. ex 8r\ in scr. D. 4. TtQOGdsdsLyfisva D, 
-0- del. D^ ratg] D, om. ABC. 5. sy.daxr}] corr. ex 

iyid6xr}v D\ 6. HE] corr. ex JVE B^Cl EA] -A e corr. C^. 

7. xji] corr. ex xfis D. 8. sgxlv] -v del. C^ EAK] corr. 
ex EKA D^ 9. EH@] EH- e corr. Cl ^AK] corr. ex 
JKA Dl tGT] — 10. dstiuL] om. D. 9. s6xl A. _ 10. s8sl] 
-8- in ras. A. 11. 8i] S' A. Xfjfifia § mg. B, § Xfi(i^a C. 

14. dvxLKfjg] -V- e corr. D. 15. l'ar] saxCv] ABC, laai 

slaiv D et supra scr. Cl yaq] AC^D^, om. BCD. ^ 17. 

xov (alt.)] renouat. C^ 18. fifdcov] -v ins. C^ 19. ti(ivov- 
tag] xi- in ras. A. xd] corr. ex x6 C^, xat] om. D. 21. 
^AE] EJJ D, -A- renouat. Dl 



156 KAATAIOT nTOAEMAIOT 

rg 'i>7tb Zrj' a)6t£ xal 6vva^q)ot£Qas tijv t£ vtco ZF/I 
xal f^v VTtb /JAE dvo OQd^ag 7tOL£iv' 07t£Q fdat d£t^ac, 

i7tl6V^^Yl6£taC t£ tOVtCOV OVtGig ixOVtCQV^ £Jt£L7t£Q 

id£cx^rj6av [p. 154, 10] ocal tcbv i6ov ccTt^xovtcov tov 
5 avtov i6rj^£Qivov 6r]^£L0v at TtQOg tbv avtbv bQL^ovta 
^£C0QOV^£vaL ycovCaL l'6aL^ tb xal t&v tb t6ov ait^x^v- 
tcov roi) avtov tQOTtLXOv 6yj^£Cov trjv tov £t£Qov dva- 
toXLxiiv xal triv tov £t£Qov dvtLxiiv 0vva^(pot£Qa$ 
dvalv OQd-atg l'6ag £lvaL. w6t£ xal dLa tovto^ iav 

10 tag ccTtb Kqlov ^ixQ'' '^^'^ XriXcbv yLVO^ivag dvatoXtxag 
ycjvCag £vqcj^£v^ (SvvaTtod^d^Ly^ivaL £6ovtaL xal at tov 
itiQOv rj^LKvxkCov dvatoXLTcal xal m au tcbv dvo rj^L- 
KvxXCcov dvtLxaC. ov dh tQOTtov d^CxvvtaL^ did ^Qa- 
xicov ix^ri^oii^d^a xQ^i^sd^^voL Ttdhv VTtod^Cynatog £V£X£v 

15 Tc3 avTcS 7taQaXXr]X(p ^ tovti6tLV xad'' bv 6 p6Q£Log 
7t6Xog i^rJQtaL tov OQC^ovtog 
fioCQag Ag. 

aC ^£v ovv vTtb tcjv C^rj- 
^£QLVG}V 6r}^£Cc3v tov dLa ^i- 

20 6(ov tcbv t,Gi8C(ov xvxXov itQbg 
tbv OQC^ovta yLv6^6vaL yco- 
vCaL TtQox^CQcog dvvavtaL la^- 
^dv£6^aL' idv yaQ yQd^coii£v 
fi£0rj^^QLvbv ^£v xvxlov tbv ABF^^ tov dl vito- 

25 X£L^ivov OQC^ovtog t6 dvatohxbv rj^LxvzXLOv t6 AE/jI 




2. 07i£Q sdsi Ssl^ccl] supra scr. D^. 3. f7CK>vfi/37](>frat] -t- 
in ras. A, hi cvfi^iqGSTaL D. tf] supra scr. D*. 6. z6 (pr.)] 
Ts D, del. D^, om. B. twv] corr. ex t6v C^ 10. tcov'] om. D. 

XrjXav] Xt]- supra scr. A^ 11. GvvanodsSsLyiiivaLl o- corr. 
ex A, GvvccTtoSsSsLfiivccL C. Deinde add. ds D, mut. in drj D^ 

12. kccl] comp. ins. D^ 15. TovtiaTLv'] -v del. C^D^. 16. 
Jlrj^rrjTort A. In fig. a polo ducta est E.ff in AC. 



MA0HMATIKHS STNTASES^S B'. 157 

xal xov iiav L6rj^£Qivov tsraQrrj^oQLOv tb EZ^ tov 
ds dia iis6(X)v tcbv Jcodtov dvo to ts EB xal EF 
ovtiDg s%ovta^ a>6ts t6 E 6r}^SL0v TCQog ^sv t6 EB 

tStaQtfj^OQLOV VOSt^d^aL flStOTtCOQLVOV^ TCQog dh t6 EF 

saQLVOv^ xal t6 ^lv B yCvsa^^aL xsl^sqlvov tQomxdv^ 5 
t6 ds r d^SQLVOV^ (SvvdystaL^ otL trig ^isv z/Z tcsql- 
cpsQsCag VTtoxsL^svrjg ^olq&v vd^ sxatsQag ds t&v BZ 
xal Zr tcbv l'6ov xy va syyL6ta^ xal rj ^sv F^ yCvstai 
liOLQav A 'O', r] ds B^ t&v avtCbv oj ^. &6t\ STtsl 
t6 E Ttdkog s6tLV tov ABF ^s6r}^PQLvov^ xal triv ^sv 10 
vjtb ^EF ycovCav tijv yLVO^svrjv V7tb tfjg dQX^yjS 'cov 
Kqlov toLOvtcov slvaL X '9' 5 oXcov s6tlv rj [iCa OQd^ri 9, 
trjv ds vjtb ^EB tijv ytvo^svrjv VTtb tflg aQxfjg t&v 
XrjXcjv tG)v avtcbv oj va. 

Lva ds xal rj t&v Xol- 15 
Ttav s(podog cpavsQa ysvrj- 
taL^ TtQOXsCcd^G) vTtodsCy^a- 
tog svsxsv svQSLV trjv 
yLVO^svrjv dvatoXLxijv yco- 
vCav vTtb tfjg dQxfjg tov 20 
TavQov xal tov OQCt^ovtog^ 
xal s6tc3 ^s0ri^pQLvbg ^sv 
xvxXog 6 ABFzf^ tov d' vTtoxsL^svov bQC^ovtog tb dva- 
tohxbv rjiiixvxlLov t6 BE^^ xal ysyQacpd^cj tov dLa 




2. ET] t6 Er D. 6. t6 Se] de xd D. F] supra scr. 
C^, E B. oTt] 'o B. 7. EZJ corr. ex EZ Cl _ 8. xai(PO] 
om. D. xal 17 \i.\v Tz/] bis C, corr. C 9. Z '&•] corr. ex l^' 
C^D^ coffTf D. 10. fW C. ^BGr\\i^qivov — 11. z/ET] 
supra scr. Dl 12. l ^] corr. ex A^ D^ 13. 8i] 8s devzE- 
qav D, T171/ add. D^ 15. 17] om. D. Xom&v'] XoLTt&v j} D. 
19. Ante y.covCav ras. 1 litt. A. 20. vtio'] vno xe D. 22. 
v.v-Alog fih D. 23. d'] ds D. t6] om. D. 



158 KAATAIOT nTOAEMAIOT 

^ECfav Tcov t^dLcov tb AEF rj^LXVKXLOv, a6tE tb E 6rj- 
^stov tijv aQ%riv slvac tov TavQov. xal STtsl sv tovtG> 
ta TcXC^ati trjg dQxfjg tov TavQov dvatslXov6r]g ^s6ov- 
Qavov0iv VTcb yijv at tov KaQTcivov ^oiQai l^ Jia^ 
5 dsdsCxa^sv [p. 144, 6] yaQ^ Ttcog ta toLavta s^ sv^SQOvg 
Xa^pdvstaL dta tCbv sxtsdsL^svcov rj^tv dvacpOQ&v 
iXd60cov yCvstau ij ^^ TCSQitpSQSia tstaQtrj^oQCov, 
ysyQacpd^co di) 7t62.(p rc3 E xal dLa6t7]^atL tfj tov tstQa- 
yavov TtXsvQa ^syC6tov xvxlov t^rjiia tb &HZ^ xal 
10 TtQo^avaTtSTtXrjQaed^co rd ts EFH tstaQtrjiioQLOv xal 
tb E^®. yCvstaL ds xal 7] ts ztFZ xal r] ZH& 
sxatsQa tstaQtrj^OQCov dLa tb tbv BE® oQC^ovta dLa 
tcbv TtoXcov slvaL tov ts ZTJ ^s6rj^PQLV0v xal tov 
ZH® iisyCatov xvxXov. Ttdhv stcsI at ^sv tov KaQ- 

15 XCVOV L^ ]ia ^OLQaL d7tS%0V6LV tOV L6rj^SQLV0V TtQbg 

tdg ccQXtovg STtl tov Slcc tcov jtoXcov avtov [isyCatov 
xvxXov ^oCQag x^ ^' sxtsdsLtat [p. 81, 32] yaQ ri^tv 
xal tavta' 6 ds C^rj^SQLvbg dits^SL tov Z itoXov rov 
hQC%ovtog STtl trjg avtrjg TtSQLCpsQsCag tfjg ZT^ ^oCQag 
20 Acr, 6vvdystaL xal rj ZT TtsQLCpSQSLa ^olqcov vrj Ji, 
tovtcov dfj dod^svtcov yCvstaL XoLitbv dLa trjv xata- 
yQaq)rjv [p. 76, 3] 6 tfjg vjtb tfjv dLTtXfjv tfjg Fz/ TtQbg 
tfjv V7tb tfjv dL7tkf]v tfjg z/Z Xoyog 6 6vvrj^^svog sx ts 



2. Ante xat ras. 6 litt. D. 4. fia] corr. ex /tA? B'. 7. 
yiyvsxai B. 9. nXsvQdc, a renouat., C^ @HZ] ZH& D. 

10. ro] roi A, sed t eras. ; corr. ex ta> D^ 11. Post EJ@ 
ras. paruam C. Ss] 8rj D. 13. (isar)(i\\(is6r}pi§Qivov C. 14. 
snsl at] corr. ex snL D^ 16. ansxov6L BCD. 16. rds] 

om. D. 17. ot^] -§ in ras. B^ syiti&siTai] -r- alt. in ras. A^ 

20. Zr] rz D. 21. Si] Sod^svtcov] AD, SrjXco&svtcov BC. 

22. tfjg (alt.)] corr. ex rrjj; C^ tfjv B, om. D. 23. ts] 

om. D. 



MA0HMAT1KH2 STNTASES^S B'. 159 

tov tfjg vTto triv dtTtXfiv trjg FE nQog tijv vno trjv 
dcTtXrjv T^g EH xal tov tfjg VTtb triv dLTtXrjv tfig 
H® TtQog trjv VTtb tr^v diTtXfjv tfjg Z&. ccXlk dccc ta, 
XQoxei^sva rj ^ev dLTtXfj tfjg JTz/ ^olqcov i6tLV |^ ^ 
y,al rj vjtb avtijv ev&Eta t^rj^dtov |/3 xd, 17 ds dcjtXfj 5 
tfjg z/Z iiOLQcbv Qjt xal rj vitb avtfjv sv&sta tiirjfid- 
tcov Qic^ xal TtdXtv 7] ^sv dLTtlf] tfjg FE ^olqcjv qvs tc^ 
xal rj V7tb avtfiv avd^sta t^rj^dtcov ql^ td, i^ ^^ ^LJtXfj 
tfjg EH ^OLQCJV QJt xal 17 vTtb avtijv svd^sta t^r]^d- 
tcov Qx. iav ccQa ditb to\> l6yov tcov |/3 xd JtQbg td 10 
Qx dcpiXco^ev tbv tcbv QLt, lS JtQbg td qtc^ xataXsLCpd"^- 
6staL rj^tv 6 tfjg vitb ti^v SLTtXfjv tfjg 0H TtQog tijv 
vTtb tijv dLTtXfjv tfjg &Z Xoyog 6 tcbv |y v^ JtQbg td 
^. xaC i6tLV 7] 'bnb ti^v dLTtXfjv tfjg &Z t^rj^dtcov 
QK' xal rj VTtb tijv dLTtXfjv aQa tfjg H& tcbv avtcbv 15 
i6tLv ^y vp. co6ts xa\ r] ^av dLjtXfj tf}g H0 ^olq&v 
i6tLV ^d 7c, rj ds H® avtij ts xal r] vnb HE& ycQvCa 
t&v avtcbv A/3 T' OTtSQ sdsL dst^aL. 

6 d' avtbg tQOJtog^ Iva \ii\ xad'^ axa6tov tavto- 
Xoyovvtag iirjxvvconav tbv V7to^vr]^atL6^bv tfjg 6vv- 20 
td^acog^ xal ijtl tcbv XoLJtcbv dcodaxatrj^oQCcov ts xal 
xhfjLdtcov rjutv vorjd^rj^staL. 



3. Z0] 0Z D. 5. vno] vn D^ Ss] Ts C. 6. iino] 
vn D. 8. vno] vn D. 9. Qn] 9^ A. vno] 'bn D. 10. 
t(bv] rov t&v D. 11. 'KataXr]cpd"iJGstaL C. 12. @H] ABC, 
H0 D et supra scr. Cl 14. &Z] Z@ C. 15. H@] corr. 
ex JI0 A^ 16. ietLv] A, om. BCD. 18. oneQ Uei SH^ai] 
om. D. 19. 8'] om. BC. iva — s%a6tov] bis D, corr. D^. 
20. vnoiivri(iatL6fi6v] -6- e corr. D. 



160 KAATAIOT nTOAEMAIOT 

t/3'. IIsqI rcbv TtQog tbv avrbv tcvxXov tov dia 
tcov 7c6X(x)v tov oQi^ovtog ytvoiisvcDV ycovi&v 

TCal 7C£QL(p£Q8LCbV. 

AeLTto^svrjg drj tijg i(p6dov^ xa^' 7]v av Xa^pccvoc^sv 
5 xal tag jtQbg tbv dLa tcbv jt6Xcov tov bQi^ovtog xaO"' 
STid^trjv syxXL^Lv xal 7ca%^ sxcc^trjv ^s^lv yLvo^svag 
tov Slcc ^s6cov t&v ^adLCJv nvTikov ycovCag 6vva7to- 
dsLKvv^svrjg^ cog scpaiisv^ sxd6tots xal trjg ditoXa^- 
^avoiisvrjg TtSQLCpSQsCag tov dLa t&v 7t6Xc3v tov 6qC- 

10 tovtog xvxkov V7t6 ts tov %atd xoQvcpriv ^rj^sCov xal 
trjg 7tQbg tbv Xo^bv xvxXov avtov tofifjg,, SKd'ri66fisd'a 
TtdlLV Ttal td sig tovto tb ^SQog 7tQola^Pav6^sva xal 
dsC^o^sv TiQcbtov^ otL tcov l'6ov d7ts%6vtGiv tov a-dtov 
tQ07tLKov 6rjfisCov tov dLa ^sacjv tcbv t^codCcov xvkXov 

15 0rjiisCcjv liSovg %Q6vovg d7toka^^av6vt(x)v scp sxdtSQa 
tov ^s6rjfiPQLVov^ tov ^sv TtQbg dvatoXdg^ tov d' 
stSQov 7tQbg dv6^dg, ul ts d7tb tov xatd nogvcpiiv It^ 
avtd 7tSQL(pSQSLaL tcbv ^syC^tcov xvxXov l'6aL dlXi]XaLg 
SL6lv Tcal at TtQbg avtd yLv6^svaL yovCaL^ Tcad'^ ov 

20 dLsetsLkd^sd^a tQ67tov^ dv6lv oQd^atg l'6aL. 

s6tcD yaQ ^sdrj^^QLvov t^fj^a tb ABF^ Kal v7to- 
KsC^d^co S7t avtov tb ^sv xatd KOQVcp^iv 6ri(istov tb 
B, 6 ds tov C6rjnsQLV0v 7t6log tb P, xal ysyQdcpd^co 
tov ^La ^s6g)v tcbv ^aydCcjv tcvkXov dvo t^r]^ata 



1. tp'] mg. C, om. AD, §l mg. B. uvtov] lo^ov BC, 

mg. Xo^ov pro scholio C. 4. djj] Ss D. 5. Tor] supra 

scr. C. 7. Post KvyiXov ras. A. 12. xccl ra] xa -hccl D. 

tovzo] corr. ex tov D^. 14. tQOTtLyiov] -l- corr. ex o in 

scr. D, supra pr. o ras. 1 litt. Ifi^ina. a mg. B. 18. tav] 
om. D. lcccl] sialv i'6ccL D. 19. sIclv] AC, comp. B, om. D, 
-V del. C^. avrov D. yLVOiiBvaC] yLvo^avaL A, mg. e. 




MA0HMATIKHS 2TNTASESJ2 B'. 161 

rd rs A^E xal t6 AZH ovTCjg sxovta^ co0t£ xa z/ 
%al Z er^^sta l6ov ts aitsisiv aTtb tov avtov tQomKov 
ocal l'0ag aTtokafi^dvsLV TisQKpSQsCag tov dv avt cbv 

TCaQallrilov s(p' sxdtSQa 
tov ABF iis6riii^QLvov. 5 
ysyQdg^&aaav ds xal 
lisyCijtcov xvxXc3v tcsql- 
cpsQSiai did tav z/, Z 
67]^SiG}v^ d%o \Csv tov r 
Tcokov tov iorj^SQivov 10 
7] ts F/J xal ri FZ, 
aTto 8s tov B tov xatd 
KOQVcprjv 6rjfiSL0v i] ts BA xal rj BZ. Xsycj, oti r] 
lisv BA %sQL(psQSia tfj BZ l'6r] f<JrtV, rj ds VTtb B/IE 
ycDvCa fistd trlg vjtb BZA dv6lv OQd-atg L^rj. 15 

STtsl ydQ td ^ xal Z 6rj^sta t6ag tov dC avtcov 
TtaQaXlrjXov itsQicpSQsCag dTts%si tov ABF fis6r]^PQi- 
vov^ L6r] s6tlv r] vitb BFA ycovCa tfj vjcb BFZ. dvo 
dr] tQCnksvQd s6tLV rd ts BFA xal tb BFZ tdg dvo 
TcXsvQdg tatg dv6l TtlsvQatg l'6ag sxovta sxatsQav sxa- 20 
tSQa^ tr]v ^sv FA tf] FZ, xoLvr]v 8s tr]v BF^ xal 
ycovCav ycovCa tr]v vnb tcjv l6cov jtlsvQcbv 7tSQLSxo^svr]v 
tr]v vTtb BFA tf] VTtb BFZ' xal pd6LV ccQa tr]v Bzf 
pd6SL tfj BZ l'6r]v £%SL xal ycjvCav tr]v vTtb BZF tf] 



1. T6(pr.) — T6(alt.)] tcc AJE D. 2. hccl] om. D. 3. 
^TtoXa^^dvsLvl corr. ex ccnoXccfi^avo^ivTjv D^. Sl'] ins. D^ 

6. Se] f' B. 10. Tov] corr. ex r6 D. 11. i] — TZ] at 
rz, rj D. 13. i7(sec.)J om. D. 14. BJ] z/B B. nsQi- 
(pEQStai D. 15. ToTj] mut. in igul D^. 16. y.aL] om. D. 18. 
7}] om. D. BFZ] -Z ins. postea D. 19. iotLv] om. D. 

BFZ] BZr D. 20. dv6Lv C. k'xsi D. 23. xy] xfi corr. 
ex xriv A. 24:. BZT] BJT D. xfi] yoovLoc D. 

Ptolemaetis, ed. Heiberg. 11 



162 KAATAIOT nTOAEMAIOT 

V7tb Bzfr, aX}J ijtel didsimai ^cxQa jtQo^&sv 

[p. 148, 10], Oti XG)V t0OV a7CB%6vtG3V XOV C^VrOV TQOItL- 

xov ^rj^SLOv aC JtQog xov dia x&v TtoXcov xov i6rj- 
liSQivov yivo^svai yavCai 6vva^(p6xsQai dvalv OQd-atg 
5 l'6ai Si6iv^ 6vva^cp6xsQai aqa i] xs VTtb FzfE xal 17 
'i)7tb rZA dvelv dQ&atg l'6ai Si6iv. idsi%d"Yi ds xal 
rj vTtb B^r xfj VTtb BZF l'6r]' xal 6vva^(p6xsQai aqa 
ri xs VTtb B^E xal r] vnb BZA Svalv OQd-atg l'6aL 
si6iv' OTtSQ sdsi dsti,ai. 

10 %dXiv dii dsixxiov^ oxi xcov avxCbv 6rj^SiG)v xov 
dia ^i^cov xcbv ^cpdCov tcvkXov l'6ovg xQ6vovg aits%6vxGiv 
icp sxdxsQa xov ^s^rj^^Qivov ai xs dnb xov xaxcc 
xoQvcprjv iit' avxd yQacp6^svai ^syi^xcov xvxXcjv TtSQi- 
(piQSiai L'6ai dkXrikciig si6iv^ nal aC itQbg avxdg yiv6- 

15 iisvai ycoviai 6vva^(p6xsQai -fj xs JtQbg dvaxoXdg xal 
rj TtQbg dv6^dg dv6l xatg vjtb xov ^s6ri^^Qivov %Qbg 
xb axjxb 6r]^stov yivo^ivatg l'6ai si6iv^ oxav icp' ixa- 
xiQag d^i^scog xd ^s6ovQavovvxa d^q)6xsQa i]XOi PoQSi6- 
xsQa Ti voxicoxsQa xov xaxd xoQvcpriv 6r]^siov xvyxdvrj, 

20 TtQcbxov d' vTtoxsi^d^co d^(p6xsQa voxicoxsQa^ xal s6xco 
^s6rj^PQivov x^rj^a xb ABFziy in avxov ds xb ^lv 
xaxd xoQvcpriv 6r}^stov xb Fj 7t6Xog ds xov i6rj^sQivov 



1. Bz^r] seq. ras. 1 litt. B, BZF D. 3. cct] euan. D. 

Tov] mut. uoluit in rcov C^, corr. ex tav D. 5. l6(xl] corr. 
ex l'6C£ig C^ 8i6Lv] ACD, comp. B, -v del. C^D^ ij te] 
(XI D. ■nul 7] vno] om. D. 6. oQQ-aC D. 7. i'6ri\ corr. ex 
L6cm, D^. 8. iq Tf] al D. vno (pr.)] supra scr. C^. %a:t 17 
v7io\ om. D. oqQ^aLg] -g ins. D^. b16lv i'6aL D. 9. onsQ 
^dsL dsL^aL'] supra scr. D^. 10. IfjyLiia ^ mg. B. 13. nsQL- 
cpEQSLaL tfeai] -L L- corr. ex N A. 14. bl6lv] comp. B, -v del. C^ 

16. 7]] om. D. 17. t6 avrb 6ri[iBL0v] mut. in xm avxco 67]- 

fiSLo) A*. yLvofitvaLg] -g e corr. D. 19. r) voTimzEQa] corr. 
ex 'rjv oxL axsQa D^ 20. 8'] Ss D. 



MA0HMATIKHS STNTASESiS B' 



163 




tb z/, xal ysyQacpd-cj dvo riLiq^axa xov dia ^e6(x)v r&v 
t,(pdC(ov xvkXov x6 xs AEZ xal xb BH& ovxco^ e^ovxa^ 
G)6xs xb E 0riii£iov xal xb H xb avxb vnoTceC^evov 
l'6rjv i(p' ixccxsQa xov dC avxov TCaQakXyjXov tisql- 

(peQ£Lav aTt£%£iv 5 
xov ABTA \)L£&' 
rj^^Qivov. xal 
y^yQ^x^pd-cj TtdXtv 
dt' avxcbv x^ij- 
liaxa ^£yC6xcjv 10 
tcvkXcjv aTtb ^lv 
xov r x6 x£ FE 
xa\ xb FH^ anb 

d£ XOV Z/ x6 X£ 

AE xal xb zJH. dta xa avxa di^ xotg i^jtQO^d^^v^ 15 
i7t£l xa E^ H 6rj^£La xbv avxbv Ttoiovvxa TtaQdXlrikov 
i'6ag avxov 7t£Qi(p£Q£Cag i(p^ £7cccx£Qa Jtoiet xov fi£6rj^- 
^Qivov^ i667tX£VQ6v x£ xal i6oy6viov yCv£xai xb FAE 
XQC7tl£VQ0v xa FAH^ a6x£ xal xrjv FE xfj FH l'6rjv 
yCv£6^ai. XeyG) dij^ oxi xal 6vva^(p6xeQai fj xe vjtb 20 
FEZ xal ri vitb FHB dv6i xatg vTtb AEZ^ AHB 
l'6ai £i6Cv. 

i7t£i yaQ rj ^£v V7tb AEZ rj avxt] i6xiv xfj {)7tb 
^HB^ rj de vTtb FE^ l'6rj i6xlv xfj V7tb AHF^ xal 

1. ^£6ov C. 2. To (pr.) — To (alt.)] tcc AEZ D. 3. ffrj- 

^itLOV^ om. D. vTtCKsi^evov tb avxo D. 4. Sl' avrov^ dia 

x&v avx&v D. 12. xt\ corr. ex xo C^, om. D. 14. xb\ om. D. 

15. 8ia\ ^'lo: ^t^ D. ^r;] om. D. 17. TrotrjCft D. (lEorjfi- 

Pqivov] -V- in ras. C. 18. yCvixai] om. D. 19. Post FJR 

supra scr. r r (^. e. xQLycovcS) B^. t^] xriv C. tariv'] -v 

supra scr. D. 20. (jwaju-qpoTFpai] -v- corr. ex ^ C^. 21. 

TEZ] corr. ex ETZ Dl zfEZ] corr. ex E^Z D^. 23. 
z/EZ] corr. ex AK D. Igxi B, ut saepius. 24. IgxI B. 

11* 



164 KAATAIOT nTOAEMAIOT 

6vva^(p6t£Qai ccqk ij te vjtb FE^ Tcal rj vtco FHB 
l'6aL £i6\v tfj VTtb ZlEZ' &6tE %a\ Gvva^cpotSQai ij te 
vjtb FEZ oXrj xa\ rj vicb rHB dv6\ tatg vjtb ^EZ, 
^HB i'6ai £l6lv' 07t£Q £§£1 d£t'^ai. 
5 icatay£yQd(pd-G) Ttdkiv td avtd t^7]^ata tcbv £K- 
K£i^£vcov xvxXcov^ &0t£ ^svtoi TO t£ A 6r}^£tov xa\ 
t6 B p0Q£i6t£Qa yCvECd^ai tov F 0r]^£iov. kiyo^ oti 
ro avtb xai ovtcjg 
6v^Pri6£tai^ tovt£<3tiv 
10 6vvau(p6t£Qai iq t£ vitb 
KEZ yovCa xa\ rj vitb 
AHB dv6\ tatg vjtb 

AEZ i'0ai £i6Cv. £7t£\ 

yaQ r] ^ihv V7tb AEZ 
ih r] avtrj £6tiv tfj vjtb 

zJHB^ l'6r} d£ rj vjtb 

AEK tfi vjtb zJHA^ 

xa\ oXrj ccQa i] vjtb AHB l'6r] £6t\v 6vva^(pot£Qaig 

tf] t£ vTtb AEZ %a\ T^ vjtb AEK' co6t£ ica\ 6vv- 
20 a^(p6t£Qai rj t£ vTtb AHB xa\ r] vnb KEZ dv6\ 

xatg vTtb /lEZ l'6ai £i6Cv. 

£KX£C6d-cj dr] TtdXiv r] b^oCa xatayQa^pt]^ a6t£ iiivtoi 

TO ^ev tov dvatokiKov t^rj^atog ^£6ovQavovv 6r]^£tov^ 

xovt£6tiv t6 A^ voti(ot£QOv £ivai tov r xatd 7C0QV(pr]v 




1. i^ th\ cii D. Y.al i] vno] om. D. 2. Gvvaii(p6x£QccC\ 

-V- corr. ex yb C. xs] om. D. 4. ^HB] corr. ex HB C^ 

0718Q MsL dsL^aC] :-X D. 5. Irififici y mg. B. Tidliv] di] 
ndXiv D. 9. xovxsGXL BD. 13. JHB mg. A*. 15. iGxiv] 
-V del. C^, ^GXi B. 18. AHB] corr. ex ^HB B^Cl IgxCBD. 

Gvvcc{iq)oxsQcas] g- e corr. D. 20. KEZ] corr. ex KEB D^ 

22. Xfj(i(ia d mg. B, cc Xfi(i(icc mg. C. i%£iGd-(o C, corr. C^. 

^rj] om. D. 24. tovxbgxiv] -v del. C*. 



MAeHMATIKHS 2TNTASES2tS B'. 165 

6ri^£L0v^ t6 ds Tov TtQog dv6^ag t^TJiiatog ^£6ovQavovVj 
tovti6tLV t6 5, ^OQSiotsQOv tov avtov. leyco^ oti, 

0vva^(p6t£Qac ij t£ vjtb 
FEZ xal ri vnb AHB 
dvo tCbv vitb AKZ, \i£i- 5 
fovfg £l6iv dvalv OQd^atg. 

£7C£l yaQ Yj ^£V VJtb 

zlHr l'6rj £6tlv ty {)7tb 
^EF^ 6vva^(p6t£Qat ds 
7] t£ 'bTtb ^HF Tial rj lo 
VTtb /IHA dvGlv OQd^atg 
l'0ai £l<3lv^ xal 6vva^cp6- 
XBQai ccQa 7] t£ VTtb ^EF xal rj V7tb ZlHA dvalv oQd^atg 
t6aL £l6lv. £0tLV d£ Tcol i^ "^Ttb ^EZ yavCa rj avt^ tfj 
•bjtb zlHB' co6t£ xal 6vva^q)ot£Qag triv t£ vTtb TEZ 15 
nal tr^v VTtb AHB 6vva^cpot£Q(x)v tG)v vjtb ^EZ Tcal 
^HB^ tovt£0tLV dlg tfjg vTtb ^EZ^ ^£L^ovag ^ivat 
6vva^(pot£QaLg tfj t£ vTtb zfEF xal tfj VTtb ^dHA^ 

aX7t£Q £i6lv dvalv OQd^atg l'6aL' 07t£Q £d£L d£L^aL. 

ixTc^L^d-co d', 07t£Q v7toX£L7t£taL^ nata trjv b^oCav 20 
KatayQacpriv t6 ^uv tov 7tQbg avatolag t^7]^atog ^£6- 

OVQaVOVV 6rifl£tOV t6 A ^0Q£L6t£Q0V yLv6^£vov tov 




2. tovxBGtiv] AC, tovtiatL BC^D. 5. zJHB mg. A^, sed 

del. 6. stcLv] -V del. C^; comp. B, ut uulgo. 8v6lv] dvo D. 

8. ictLv'] -V del. C\ 10. 17] om. D. 12. staLv] -v del. C^ 

13. 7]] om. D. 14. totiv] -v del. C\ 16. ttjv] -v ins. C^ 

y.ai] om. D. 17. tovts6tLv] AC, tovtsoti BC^D. (isi- 

^ova C. 18. 6vva^q)0tSQag D. 19. e16lv] comp. B, -v 

del. C^ dv6Lv] dvo D. oQd-dg D. otisq sdsL dsC^aL] 

om. D. 20. 7.fiinia s mg. B, y Xf^fi^ia mg. C. S'] di] D. 

21. To] mut. in tov C^. tov] om. C. tfi^qfiatog] pr. ^ 

supra scr. D^. ^s6ovQavovv] corr. ex ^s6ovQavov6Lv C^. 22. 
ToJ ov to D. Fig. e corr. A'*, litt. in ras. 



166 



KAATAIOT nTOAEMAIOT 




P, t6 ds Tov TtQog 6v6^ag r^^^iiarog ^s^ovQavovv t6 
B voticorsQov. Xsycj^ otl 0vva^g)6TEQai i] ts vtco KEZ 
xal ri vTcb FHB dvo tcov V7tb ^EZ skdTtoveg ei^iv 
dvelv oQd-atg. dia 
5 Ta avTa yaQ jtd- //^ 

hv 6vva^(p6T£Qai ^-i- 

^\v i]TS VTcbKEZ 
Tcal r} VTtb FHB 

6VVa^CpOTSQ(DV Tfjg 

10 T£ vjtb AEZ xal 
Tfjg vTtb ^HBy 

T0VTS6TLV dvO TG)V 

vTtb zlEZ^ sXaT- 

Tovsg yCvovTai 6vvan(poTSQaig Tfj ts vTtb zfEK Tcal Tf; 
15 VTtb ^HF' avTai 8s dv6lv OQd^atg L0ai dca t6 xal 

6vva^(poT£Qag ^sv rriv ts VTtb ^EK xal t^^v vitb 

^EF dvdlv OQd^alg i'6ag slvaL^ l'6rjv ds zal Trjv vjtb 

^EF rfl 'bjtb ^HF' OTtSQ sdsL dst^aL. 

OTL ds sx 7tQO%SLQov dvvavtaL Xa^pdvs^d^aL t&v 
20 yLvo^svcov vTtb tov Ao|ov tcvkXov TtQbg rbv Slcc tov 

xaTcc xoQV(prjv 6rj^£L0v ^£yL6Tov kvkXov ycovL&v ts 

Xal 7t£QLCp£Q£LCbV y Tiad-' OV £LQ7]Ka^£V TQ^TtOV^ ai T£ 

ijtl Tov ^£6rj^PQLvov Kal £7tl Tov oQL^ovtog yLv6^£vaL, 

c^vToO-ai/ dv ovTcog ydvoLTo dfjlov. idv yccQ yQdilJCDy.£v 

25 ^£6rj^PQLvbv kvkIov rbv ABFJ Kal oQL^ovTog ^£v 



1. rd (pr,)] tov BC. 2. ij] corr. ex cc in scr. C. 3. 

ildxTOVEg] -E- in ras. A^. siOiv'] -v del. D^ 4. dvaiv] dvo C. 
5. yccQ] om. D. 12. xovxiGxiv] -v del. C^, xovxbgxi D. 15. 
8id] %al dm D, corr. D^. %at] om. D. 16. cvvaiicpoxsQaigD^ 
corr. D^ 17. Tarjv] TffTj D. xr\v] r} D, 18. otisq hdsi] a 
TtQosyiSixo D. 19. at 7tr}XLV,6xr}xsg ante x&v ins. mg. A^ 20. 
yiyvo[LSV(ov D. 21. ycovycovicbv D. 




MA0HMATIKHS STNTAgESiS B'. 167 

Ti^LKvxXLOv ro BEzi^ xov ds dta ^e6cov tcov ^ipdtcov 
ocvkIov ro ZEH 67tG)0d7]7tor8 sxov^ otav ^av dta tov 
^£6ovQavovvtog avtov ^rnisCov tov Z voa^sv tbv dia 
tov A xata xoQvtpr^v 6rjfiSL0v 
yQag^d ^Evov ^syiotov xvkXov^ 5 
6 avtbg ysvtj^staL tg5 ABFzf 
^s6r]^PQtva^ xal s6tai 7] ts 
1)710 /iTjE yGivia avto^sv 
rj^tv dsdo^svrj dca tb zal tb 
Z 0rj^stov xal tijv Tt^bg tbv 10 
fis^rj^^QLvbv avtov ycvo^svrjv 
ycoviav [11, 10] dsdo^d-ai xal 
uvtrj 7] AZ 7tSQiq)SQSia dta ro s^siv rj^ag^ 7t66ag 
fioiQag S7tl tov ^s^rj^^Qivov rd ts Z 0rj^stov a7ts%si 
tov i6r]^SQivov xal 6 i6rj^sQivbg roi) A xata X0QV(priv 15 
6Yi^Siov. orav ds dia tov avatsklovtog avtov 67]^siov 
tov E voa^sv tbv dia roi) A yQacpo^svov fisyi^tov 
xvxkov G)g tbv AEF^ avtdd-sv %a\ ovtcog yCvstai 
Sijlov^ oti rj ^sv AE 7tSQi(pSQSia 7tdvtots ysvrj6stai 
tstuQtrj^OQCov^ dia ro ro A 6r]^stov 7t6kov sivai tov 20 
BEA bQC^ovtog. oQd-rjg ds ov6rjg dsl did trjv avtrjv 
altCav t7]g V7tb AEA ycjvCag xal dsdo^svrjg tfjg tov 
lo^ov xtjkXov 7tQbg tbv oQC^ovta^ tovts6tiv tfjg V7tb 
AEHj dod^7J6stai xal oXrj rj V7tb AEH ycovCa' 07tSQ 
sdsi dsi^ai. 26 



2. Kv^lov] om. D. ZEH] corr. ex ZiT D. 3. iisGcc- 

gavovvtogD. Q. ABTJ] ABT D. 8.JZE]AZED. 10. 
v.ai] v.axa. D. xiqv] corr. ex xov D^ 13. avxr^ 1^] avxr\v C, 
avxi]v xrjv D. nsQLcpsQSLav D. 15. 6] ins. D^ 16. dLo] 
mg. add. D^ 19. AE — ndvxoxs] in ras. A. 20. rd (alt.)] 
om. C, corr. ex x- D. 23. oql^ov D. 24t. JEH] JEH 

ycovtag D. onsQ ^dsL dst^aL] om. D. 



168 KAATAIOT nTOAEMAIOT 

cj6t£ (pavsQdv^ OXL Tovrcov ovtcog ixovtcjv^ iav itp' 
ixcc0t7}g iyKU6£G)g tccg jtQO tov ii£6ri^^QLvov ^ovag 
ycoviag t£ xal 7C£QL(p£Q£Lag xal ^ovcov tcov aTtb tY^g 
aQ%Yig tov KaQXLVov ii£%QL trjg dQ%7Jg tov AlyoK^QGt 
5 dcod£Katr}^oQLG}v iTtLXoyLefco^^d^a^ 0vva7tod£d£Ly^£vag 
£%o^£v [p. 162, 10; 160, 13] xal tdg t£ ^£td tbv ^£0r]^- 
^QLvbv avtcov ycovLag t£ xal 7t£QLCp£Q£Lag xal itL tav 
koL7tG)v tdg t£ 7tQb rov ^^dri^^QLvov ocal tdg ^£td tbv 
li£0r}^PQLv6v. Xva $£ Kal i7tl tovtcov rj xad'^ £Kd6trjv 

10 d^i^LV icpodog cpav£Qd yivrjtaL^ 7taQad£Ly^atog 7tdlLv 
£V£K£v iKd^rjeo^^d^a trjv i^oiiivrjv Ka&oXov d^t^LV Sl 
ivbg d-^coQrj^atog v^tod^i^^voL Katd trjv avtr^v iyKlL^LV 
tovtiatLV Kad'' r]v 6 p6Q£Log 7t6Xog tov oQL^ovtog 
i^rJQtaL iioLQag Ag, triv dQ%riv tov KaQKLVOv X6yov 

15 %dQLV ^Cav coQav L6r}^£QLvrjv d7ti%£LV TtQbg dvatoXdg 

tOV ^£6r}ll^QLV0V ^ Kad'' 7}V d^i^LV iv t& 7tQ0K£L^ivC) 

7taQaXXr}XG) ii£6ovQavov6Lv ^lv aC t&v ^lSviicov ^otQaL 

Tg tj3, dvatiXXov6Lv d£ aC trjg UaQd^ivov fiotQaL Lt, AJ. 

£6tG) di} ^£6r}ii^QLvbg KVKlog 6 ABF^ Kal 6ql- 

20 ^ovtog ^ihv r^^iLLKVKXLOv tb BEzJ^ tov d£ dta ^i^cov 

tcbv lcpdCcov tb ZH@ ovtG)g £%ov^ co6t£ tb ^lv H 



1. i(p'] inL D. 2. yiXiascog T>. tdg] e corr. D^ ngo] 
corr. ex Ttgog D^. 4. v.aQnCv D, a supra add. D^. Atyo- 

KEQO)] Tog supra co add. D^ 7. etl] corr. ex inC D^ 8. 

Post XoLTtmv add. tdg xe tiqo (huc supra est ras.) rov ^ear}^- 
§QLvbv avxibv (o supra scr. D^) ycovCag ts y.aL nsQLcpSQiCag v,al 
in\ t&v XoLnmv D, del. D^. tcig ts] supra scr. D. 10. 

&e6Lv] om. CD. 11. Sel^lv] d- corr. ex X C^ 12. ^scoQrj- 
fiatog] -'^(i- e corr. D. 13. tovtsGtL D. i^fiQtaL tov oql- 

^ovtog D. 14. i^rlQtaL] -tuL in ras. A}. Xq] tQLav-ovtas^ D. 

16. riv] riv 8i D, r^v 8ri D^ iv] corr. ex ictLV D^ 17. 
\is6ovQavov6L D. 18. avatiXXov6L D. X^] corr. ex Xh,' C. 

19. drf] D, ds ABC. 21. ovtcog] ante t ras. 2 litt. A. 




MA0HMATIKHS STNTASESiS B'. 169 

6rjuetov TYjv ccqx^W fti'^^ "^ov KaQKivov^ xo de Z iite- 
Xeiv ^Ldv^cov ^OiQag T^ t/3, ro de & IlaQd^evov ^oiQaq 
tj AJ, zal yeyQcicpd-cj dLcc re xov A xaxa xoQvcprjv 
6ri^eiov xal dia xov H xfjg 
^9XVS T^ov KaQKivov ^eyi^xov 5 
xvxXov Tft^^a xb AHEF^ tcqo- 
zei^d^cj de TtQcbxov xriv AH 
TteQicpeQetav evQetv. cpaveQOv 
drj^ oxL rj ^iev Z0 TteQnpeQeia 
ILOiQcbv e6xLv ^ xe^ rj de H0 lO 
lioiQcbv oj AJ. b^oicsg de^ enei- 
driTteQ at [lev x&v ^idv^cov 
^OiQat Tg t/3 d7toXa^pdvov6i xov ^e^rj^^Qivov dito xov 
i6rj^eQLVov TfQog ccQXxovg ^oiQag xy ^^ 6 de leri^eQivog 
xov A Tcaxcc xoQvcprjv ^rj^eiov ^OiQag Ag, e6xai xal rj 15 
^ev AZ 7teQi(peQeia [lOiQ&v t/3 vy^ rj de ZB xcbv 
XoiTtcbv eig xb xexaQxrj^oQiov aoiQcbv oj f. xovxov 
dod-evrcjv yCvexaL TtdXtv dLa xijv KaxayQacpriv [p. 76, 3] 
6 xfig vjtb xrjv dLTtXfjv xrjg ZB TtQbg xr^v vnb xrjv 
diTtXrjv xrjg BA Xoyog 6 6vvrj^^evog ex xe xov xfjg 20 
vTtb xr^v diJtXfjv xfjg Z® itQbg xfjv vnb xijv diTtXfjv 
xfjg 0H Kal xov xfjg vnb xf]v diTtXfjv xfjg HE TtQbg 
xi]v vTtb xijv SiTtXfjv xf]g EA. dXX'' r] ^ev xfjg ZB 
diTtXfj ^oiQcbv e6xiv Qvd id xal i^ ^^o avxijv evd-eta 
x^rjfidxcov Qig vd'^ r] de xfjg BA {lOiQcbv Qjt xal ri i)7tb 25 

1. arifiSLov] 67j ar](iiLOv C. 2. fioLQCcg {alt.y] om. D. 6. Tiii]iicc 
■av-aXov t>. AHEr^ A- renouat. Cl i). i]] supra scr. C^ 
7] jLtfV] in ras. 3 litt. B^ 11. iiolq&v'] om. B, (lOLQav 

S6XLV D. 13. Sc7toXa(i§dvov6LV D. 15. Xs] mut. in Xg o B^, 
corr. ex Xl D^ euan. 17. holqcov] om. D. 24. Qvd] corr. 

ex Qd B^ Qv 'Jlj D, V7t6] v7c' D. 25. BA] BA Sl^iXt] D. 

V7t6] V7t' D. 



170 KAATAIOT nTOAEMAIOT 

avtrjv svd^stcc t^rjiidrcjv qtc^ Tcal Tcdhv rj ^lv tyjg Z® 
dcTcXfj ^oLQcbv QTC^ V zal 7] VTC avtrjv svdsta t^rj^dtcov 
Qcd- vrj^ rj ds tfjg ®H ^oiQcav qvs cd xal rj vtc avtfjv 
svd-sta t^rj^dtcov ql^ cp. idv ccQa aTcb tov tcbv ^tg 
5 vd' TCQog td 0% Xoyov dq)sl(oiisv tbv t&v ql^ vfj TCQbg 
td Qi^ t/3, xataXsLg)d"^0staL fj^tv 6 tfjg vicb tf^v diTcXfiv 
tfjg EH TCQog tfjv 'bnb tfjv dL7cXf}v tfjg EA Xoyog 6 
tCbv Qid Tg syyL0ta JCQbg td ~q%. xaC s6tLV rj vicb tfjv 
dLTckfjv tfjg EA t^rj^dtcjv qx' Tcal rj vnb tf^v dLTclfjv 

10 aQa tfjg EH tav avtCbv s6tLv QLd Ts' ca6ts ocat r] ^sv 
dLTcXf] tfig EH jcsQLCpSQsCag ^olqcdv s6tLV Q^d %i sy- 
yL0ta^ avti] d\ rj HE tav avtcbv o^ Ty. xal loLTcf] 
ccQa r] AH tcbv ksLTC0v6cbv s6tLV slg tb tstaQtr^^OQLOv 
^OLQcbv Lt, ilI' 07CSQ ^dsv dstiai, 

15 icps^f^g 81 Kal tf]v VTcb A H® 
ycjvCav svq7]6o^sv ovtcog' sx- 
xsC^Q^co ydQ f] avtf] xatayQag)^].^ 
xal tcoXg) t» H xal dLa6t7]^atL 
tf] rot> tstQaycjvov TcksvQa ys- 

20 yQacpd^Gi iisyC0tov kvkXov t^f]^a 
tb KAM, G36ts, STCsl 6 AHE 
KVKlog d^d ts tcbv tov E®M 

Kal dLd t&v tov KAM tcoXgjv ysyQajctac^ sxatSQav tcbv 
EM Kal KM tstaQtrj^OQCov yCvsGd^aL. TcdXcv ovv d^d 

2. gn^ v] gn vp B. 3. &H] H@ dLnlfj D. id] corr. 
ex d' D^ 6. 'iicizaX8icpd^'^6sraL] corr. ex y.ataXr^qid^t^aetaL A^. 

7. tfjg (alt.)] om. D. 10. trjg] -?)- corr. ex o in scrib. C. 

EH] HE D. 12. HE] EH D. 14. (jlolq&v] om. D. 18. 
H] corr. ex Tfi D^. %al dLaott^^atL] dLaof^fiatL di D. 19. 

A 

TcXsvQa] TT D. 21. 6] supra scr, D^ AHE] corr, ex AE D. 
22, Tf] om, D. 23. KAM] -A- e corr. D. svMtsQav] g 
STiatSQav D. 24 %at] om. D, TeT0rpTrjiu.69i.0v D. yCvscd-aL] 
mut. in yLyvsa&aL A\ yiyvsa&aL B. ovv] d' ovv D. 




I 



MA0HMATIKHS STNTASE^iS B'. 171 

rrjv xatayQcctp^^v s6rai, [p. 74, 9] 6 tfjg vjtb tijv diTcXriv 
tfiq HE TCQog trjv vith trjv diJtXrjv tf}g EK Xoyog 
awrj^^Bvog £k ts tov tf}g vno trjv diTtXfjv tfjg H® 
TCQog tfjv VTtb tijv dLTtXfjv tfjg @A Kal tov tfjg 'bitb 
rfjv dLTtlfjv tfjg AM TtQog tijv VTtb tf^v 8i7tXf]v rfjg 5 
KM. aXX^ r\ ^sv rf\g HE diTtXfj [iolq&v s6tLV Q^d 
%^ Tcal r] vTt avtfjv svd^sta t^rjfidtcov qlS 7?, ^ ds tfjg 
EK ^OLQwv Xs Xd xal 'fj vjtb avtfjv svd^sta t^rj^dtcov 
Xg At^, Tcal TcdlLV rj ^sv tfjg @H dLTtXfj ^olq&v s6tLv 
Qvs Ld Tcal rj vjcb avtfjv svd^sta t^rj^dtcov ql^ ^/3, ri 10 
ds rfjg @A ^olq&v xd jit? zal rj vjcb avtfjv svd-sta 
tfirj^drcov its ^d' &0rs^ sdv dicb rofj Xoyov rofj rav 
Qcd 7g TCQbg rd Ag Xrj dcpsXco^sv rbv rav ql^ t/3 JCQbg 
rd ocs ftd, xataXsL(pd'7]6staL fj^tv 6 tfjg vTcb tfjv dL7tkf]v 
tfig AM TtQbg tfjv vitb tfjv dtTtXfjv tfjg MK koyog 6 15 
tav Tt^ Td syyL6ta TtQog td 'qtc. xac s6tLv f] vTtb tfjv 
dLTtlfiv rfjg MK r^rj^dtcov qtc' xal fj vnb tfjv dLTtXfjv 
ccQa tfjg AM t&v ejvrwv s6tLv Ttp Td. &6ts ocal f] 
^sv dLJtXf] tf]g AM TtsQLcpSQsCag ^olqcov s6tLV ut^ '^cf]^ 
avtf] ds f] AM tcjv avtcbv Jiy td. xal XoLTtf] aQa f] 20 
AK TtSQLcpsQSLa avtij ts xal f] vitb AHK ycovLa t^r]- 
lidtcDv s6tlv JLts^ JLtg* oj^ts Tcal f] vjtb AH0 ycjvLa tcbv 
?.0L7tcjv sig tdg dvo oQd-dg s6taL ^olqcov QXy lS' oitSQ 
sdsL dst^aL. 



6. KM] MK D. &XXd A. HE] corr. ex NE C^ 

corr. ex 0£ D^ SLitlf]] seq. ras. 1 litt. A. 7. xg] xj D. 

vn] vno B. 8. W] ly D. vn6\ vn D. 9. @H] 

H@ V). dmlfii D. BGTiv] om. D. • 10. i] (pr.)] ins. A*. 

vno] vn D. 11. vno] vn' D. 12. xi] -s e corr. D. 

zov (alt.)] om. D. 13. l§] ins. D*. 16. n§] n- in ras. B. 

f}] om. D. 17. 17] om. D. 18. x&v — ld. AM] r<^ D. 21. 
AK] KA D. AHK] -HK e corr. A^ 23. tds] td C. 



172 KAATAIOT nTOAEMAIOT 

6 ^SV OVV TQOTtOg trjg t&V 7tQOX£i^eVC0V SVQ£6£(0g 

xal £7il t&v XoL%G)v 6 avtog 6vvdy£tai^ ri^^tg df, iva 
xal tag aXXag ycovLag ts xal 7t£QL(p£Q£Lag, o6<x>v ys 
SLKog XQsCav sv talg xata ^SQog £7tL6x£f£6Lv £(?£(?^a^, 
5 7tQO%SLQCog sxcousv sxtsd-SL^svag^ £7tsloyL6d^sxta xal 
tavtag yQaii^LKcog aQ^d^svoL ^sv aTtb tov dt« MsQorig 
7taQaXXYikov ^ jtaO*' ov tj ^syL6tr] rj^SQa cjqo^v s6tLV 
L6r]^SQLva)v Tyj (pd-d^avtsg ds iii£%QL tov yQacpoiiivov 
V7t£Q tbv Tlovtov dLcc tav ixfioX&v BoQvad-ivovg, OTtov 

10 17 ^£yL6tr] rjpL£Qa cjq&v i6tLV L0r]ii£QLVcbv 7?. i%Qri6d- 
li£^a ds tfj xad'' sxa6tov 7taQav^r]0SL iTtl ^sv tav 
xkLiidtcov tfi xad'' rj^LcoQLOV 7tdXLVy co67tSQ xal iTtl tG)v 
dva(poQcbv^ iTtl ds tcov tov dLCc ^i^cov tcov t^codCcov 
xvxXov t^rj^dtcov tf] Sl svbg dcodsxatrj^oQCov, i^tl ds 

15 tcov TtQbg dvatokdg r) xal TtQbg dv6^dg tov ^s6r]^- 
pQLVov d-i6scov tfi dLa ^Ldg 6)Qag L6r]^sQLvfjg. 7tOLr]66- 
lis^a ds xal trjv tovtcov sxd-s6LV xavovLXcog xad^' sxa- 
6tov xXt^a ts xal dcodsxatrj^oQLOv ^taQattd^ivtsg iv 
^sv totg 7tQ(htOLg ^iQs6LV tijv 7to66tr]ta tcbv tfjg icp' 

20 sxdtSQa tov ^s6rj^pQLV0v dLa6td6scog ^std tr^v ;car' 
avtbv d-i^LV i6r]^sQLVG)v g)qg)v^ iv ds totg dsvtiQOLg 
tdg 7trjlLx6trjtag t&v d7tb tov xatd xoQvcpfiv 6r]asCov 
lii%QL tfjg aQ^fjg roi) ixxsL^ivov dcodsxatrj^oQCov yLvo- 
liivcov^ cog scpa^sv^ 7tSQL(pSQSLcbv^ iv Ss totg tQCtOLg xal 

25 tstdQtOLg tdg 7triXLx6trjtag tcov V7tb tfjg 7tQ0XSL^ivrjg 



1. t&v'] om. D. 7tQoyiELiiivr]s D. 4. iisQog] A, supra 

scr. '97 A^ 6. did] om. D. MsQorjg] Msqoc A. 7. t6tt D. 

11. eKccGtriV D. 13. ^egov D. 14. dcoSsnatr]^ D. 19. 

(liQsaiv] -V del. D^ 21. ccvtov] corr. ex avt&v C^. 23. do)- 

SsKatri^OQLOv] crjfiELOv dcodsiiutrjli D. 



MA0HMATIKHS LTNTAS;ESi2 B'. 173 

to^fjg xara tbv dL(OQi6^Bvov i]^iv tQoitov 7CEQL8%oiiivG}v 
ycovLav, iv ^£V toig tQLtOLg tccg tcbv TtQog avatoXag 
tov ^sarj^^QLvov O-fVfcov, iv ds totg tstccQtOLg tag 
tcbv TtQog dv6^dg. mg xal iv aQxfj ^svtoL dLSdtSLXd- 
^sd^a, ^s^vfi0d-aL dst, otL tav dvo tcbv vTtb tov S7to- 5 
^svov t^TJ^atog tov dLO. ^s6(ov t&v ^oydLOV tcvkXov 
7tSQLS%o^sv(ov ycovL&v triv dit^ aQKTcov tov avtov t^t^- 
liatog dsl 7taQSLl7](pa^sv to0ovt(X}v icp' SKdetrjg avtcjv 
tfjv 7trjhx6tr]ta TtaQatt&svtsgj oXcov iatlv rj liCa OQd-rj 
9. KaL i6tLV r] tcov xavovLOV SKd-s^Lg tOLavtrj. 10 



1. TOfi^ff] -0- corr. ex q in scrib. C. 2. r&v] supra 

scr. D. 3. ^^J post d ras. A. 4. (livtoi] corr. ex fiEvtOLg Cl 



a 



6. Tftryfiaroff] corr. ex tfiri^dtcov D. 8. to6ovtcov~\ mut. in 

toiovtcov D. 10. v.civovCGiv'] ~vo- add. A^. In extr. pag. 

(fol. iS'^) add. fxO-ffftg ta>v v.uta naqdlXr]kov ycovLoov v.ccl tcsql- 
q)8Q£Lav (iSQorig dtQmv ly (lOLQoiv l^ l^ D, mg. (iSQor^g. 



174 KAATAIOT nTOAEMAIOT 

















Tov 8ia 


MsQorig 


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yojviat 
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1. ly'] om. AB C D. Ordinatio est codicum AB C, in D tres columnae sunt 

o ' o o 

cum quatemis signis. 6. /S(pr.)] AB, IV C, om. D. /* (alt.)] om. D. r(pr.)] 

om.D. r (alt.)] JV in ras. A, om. D. ^8. ()o] seq. ras.A. rcJ^^/d D. 9. r(pr.)] 
post a B, suo loco B'^. 2>;] vt D. r] post qoyi B (qui omnino numeros huius 
columnae uno loco altius coUocat), corr. B*; om. D. of (alt.)] l D. 10. cy(sec.)] 
/l B C. ;.d] -8 e corr. D. „11. e (pr.)] e corr. C. /?] xa D. 12. 7fy] tT? A. 
<^] corr. ex ty D. 15. /?(utr.)]^om. D. J (utr.)] om. D. 16. xq\ corr, ex 
^g- B*. Qori\ Q- in ras. D. vl\ r^ D. 17. r] om. D. 18. e] corr. ex t D. 

_ 19. r?] fi:; B C. 20. x/?] corr. ex xX C. /1] om. D. 21. r] om. D. o (tert.)] 

A D. 22. xe\ om. C. 24. (»ta] DB», ^<c^ A, ^\ B C. r] om. D, mut. in /1 B'. 

o ^ o] om. D. Ac] ;.£ D. r (tert. et quart.)] om. D. 25. /§] om. D. o (sec.)] 
corr. ex. y D. 26. o (pr.)] corr. ex y D. 27. ^t] /c D. fn]\ fia D. 28. //*] 
«>j BC. 29. ;ic] X- B. c] A^- D. Qoa\ Qod D. 30. Ae] corr. ex fxe C. 2] 
om. C. 31. dj A B C. 



MA0HMATIKHS STNTASE-^iS B' 
ycovL&v xccl TtSQKpeQeicbv. 



175 



wqmv ly ^olqcov ^? x^. 



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Qfta D. 10. e (pr.)] in ras. B. ^ij] A, vr] B C, fi& D. 13. 

om. D. fiC] ftS B. h om. D. 14. X&] -& e corr. D. 
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24. Qts] tsB. v&] D, v^ ABC. v] om. BCD. 25. ^^s] Q^a BO 
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A. 19. 

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176 



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Xs Xa 
Xtj xs 


Qia 
Q Xy ts 

QV ItJ 


TttJ flS 

oa fi(i 


s 


^a ;U(y 
rc id 


^o^ y 

QoQ itj 
Qoy fi 


xs 

ri 


v!; 
fili 

X 


s 


rc X 
hrj Xa 
Tta x(i 


QOS X 


1 i9 

v[i vs 
fi^ X 


20 ?, 


?ta r^ 

9 o 


qhj r? 
q^:; vy 


Xtj 


6 

c 


s l^ 


9 


Qo; fia 


fis td- 




JTa^-^-f y V 






Tolorov 


fisatjfi 
a 

25 (i 


t/9 <a 


Qia o 

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Qoy fi6 


fltj 


X 


fisatjfi 
a 

/* 


jU(F xa 
fig fi 
vy 6 


Qfi X 

Qxa X 
qX^ t^ 


ity X 

t; fid 


s 


fj; a 
oa fiy 


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flfi 


o 

flS 


s 


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Tts xy 


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Qi;d fig 


vs Xs 
fl to 


30 s xa 


TtS X 

9 o 


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Qo; fia 


fcd 

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xa 


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9 o 


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hj c 



5. o (quart. et quint.)] om. D. 6. Qfi6] Qfia A, Qfia D. rty] ;r- D. 9. 

vS] va D. 17. Q0&] Qos BC. X] Xf A. (Xtj?). 18. q^&] I^ A. 24. fig] 

e corr. D. 25. vy] rg- D. 28. Qo&] qoe BC. fi/i] post fi raa. 1 litt. A. 
Q^d] D, Q^a ABC. SO. fia] o BC. 



MAOHMATIKHS STNTASEiiS B'. 



177 



wQoav ly /_' (lOiQav xy vcc. 



(bQ&V 


ymviai 


yojviat 
ovttxai 


dlQ&V 


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a 


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ve ■v/? 


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o 


e 


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c ts 


9 o 


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iC? 


tS 


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9 o 


qX^ tri 


o o 




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T a V Q V 


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a 


fid xa i oC ^ 
fi^ (*\ <^g X 
vy 6 1 Qi^ ig 


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c 


fid x/S 
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a vC 
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s xp 


C, 


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ty 


C 


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a 


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k9 o 
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QiS' fia 

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xd- 


flS 


5 
fisatjfi 
a 


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td ttj 

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oC X 
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« 


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Tta x/i 


'V 
t 
s 


vs 
X 


s 


fia fiS 
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^ri fiy 


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10 



15 



25 



30 



1. va] s va D 
Borib. D. 6. oi;] ^r B. ' y] ABCT oaj in ras'. D, vrj BC. v^] XBC 
Supra xrt " 



va] V D. 1?] corr. ex |t in 



5^ o] i B C, seq. ras. D. 

~ oa] i 

7. Xa] ig BC. vg] in ras. D, fi(i BC. 
Qid] Q D. 8. 2C(alt.)] xjE BC. fi6] 



99"] 9 D. Supra xrj raa. D. 

x&] ft6 BC. ^ls-] ;i- in ras. A 
in ras. D, ;. B C. xy] Xs B C. fi&^ -^ e corr. C. qx6] o D. y (tert.)] 
Halma, ;i AB C, om. D. 9. vC] vrj B C. Xs] in ras. D, x^ B C. y (pr.)] /? B C. 

^x^] ^ D. i^] ed. Basil., C ABCD. 10. o (pr.)] fig BC. xrj] ts BC. 

o(sec.)] i6 BC. 11. Qvy] Qfia B C. jus'] vy BC. x?] ty BC. iS] 

C BC. 23. y] seq. ras. 1 Utt. C. 25. fiS] fts D. 26. vg] fig BC. qv6] 
Qvtt D. 28. fi] Halma, fig ABCD. 

Ptolemaeus, ed. Heiberg. 12 



178 



KAATAIOT nTOAEMAIOT 



Tov dia. tfjg KCCTca x^9"S tfjg Aiyvnxov 



thqGrv 



I ymviat , 

TteQi^e-^ &ra- /«'»'^'«', 
C*"»»' I toXixal ovtixal 



JQOIV 



JteQttpe- 
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ytaviat , 

&va- Ytoviai 
toXixai ovttxtti 



30 



Ktx.q%ivov 



Z V y o V 



5 fieatjfi 
a 



g Xa 
tS vg 
xf xy 



fi i^ 

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X o 
X x^ 



fiearjfi 
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xa 9 
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Xy X^ 



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1 
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c, o 


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Aiovxog 



Zv.OQTiCov 



fieatjfi 
15 tt 

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S v^ 
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y 

8 


fia Xa 

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Q^S xg 

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20 g 
g va 


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c, 


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S 
fitatjfi 
tt 

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Xe XS 
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fia td 
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X^ 



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To|6tov 



fiear^fi 
tt 

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ttj fi^ 
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30 g xrj 


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C 


Qoa e 

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og fi^ 
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fiearjfjt 
a 



V V^ Q^ X 

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1. *^s(alt.)] om. D. 6, Xy Xe] Xe X& D. 12. ^] g va BC. 14. Qia] 
taA. 15. ^e] fig D. 16. vtj] scripsi, fitj ABCD. QfiS] qvS BC. 18. q^S} 
corr. ex q^S in scr. D. v^ ] corr. ex vS in acr. D. 19. q^^ (pr.) ] corr. ex 

Q^g in scr. D. e (alt.)] e X{i B. 20. Q^y] Q^g D. 21. va] v D. 26. a] 
in ras. B. 27. X^] in ras. B. 28. Qvtj] Qvy C. fiy] in ras. B. 



MA0HMATIKH2 STNTASESJS B'. 



179 



p^coi; lS iiOLQmv X x|3. 


^ 7r 


Yoaviai 

hva- 

toXixal 


\ yeaviai 
dvtixal 


tiiQSiV 


1 Y^^fft 
! 9^"^ toXixai 


ytoviat 
ovttxai 


AtyoKSQO) 








K Q 1 V 






ftMOtJH 


v6 CY 


9 o 
qe Xd 

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od 

t 

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x^ 


fisarjfi 
a 
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xrj 
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« 


on vS- 
9 o 


qXS k 
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fis 

Xy 


i6 
X 


Y 
6 
s 


v8 xs 
IS xr, 


Qtg xrj 

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ts 
t 


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la 


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a 


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1. * x/i] X^ xD. 6. /y] ts jy. Z x;^] in ras. C, 10. e(pr.)] e 5 A. 

11. givT.)] ? 5 A. g Xa] om. D. 18. "rdQoxoov] ix&iiorv D. 14. $&] 

^s D. 15. X&] BCiipsi, Ae ABCD. xa] -a e corr. C, x D. 16. fi^] -C e 

corr. D. 18. vtj] corr. ex. firj D. v] x D. 26. 1] C C. 27. oa] od D. 

28. Qfi^] Qv[i D. 29. t] e corr. D. 

12* 



180 



KAATAIOT nTOAEMAIOT 



Tov Slcc "P6dov 



d}Q&V 


YOi>viat , 
TtsQicps- ^j,^. ytoviat 

?«^^ toXixai ovtutai 


&q5jv 


yoaviat 
C"'"'' toXacai 


yoaviat 
Ovtvxai 


Kaq%LVOv 




Z V y V 




5 fisarifi 
a 


t8 & 

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9 o 
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H? fi? 

X(i is 


9 
fisarjfi 
a 


Xg o 
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fts Xa 


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Y 

d 

10 « 


fi yC 
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6 
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9 
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To^orov 


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7. x/9] xrj C. 8. xrj] xa A. Qvrj] Qfirj A. 9. Xg] vg C. 10. Xg (pr.)] X- 
in ras. A. 11. g-^alt.)] in ras. D. 13. a] Xa B. 15. q^] post q ras. A, 
corr. ex qXS C^ 17. rta] 7t6 D. 19. vs] D, fis ABC. 21. v] rj A. xs] 
xrj BC. 22. TtS-] 7t- in ras. A. 23. 6] X D. Qvy] Qiy D. 25. x6] xa D. 
X (pr.)] 6 D. 29. r^ vy C. 30. X6] corr. ex Xv in scr. C. 6] corr. ex e in 
scr. AD. Qvy] Qfiy D. 31. vg X] ia ras. D. 32. r^] -f in ras. D. 



MAOHMATIKHS STNTASESiS B' 



181 



a)Qmv id /_' (lOiQwv ^g 


D. 








(tiQmv 


ycovltti 

nSQUpS- '^^„. 

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dvttxal 


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1- 1?] ly D. juC] ("« B C, 8. ra] -a e corr. in scr. B. 9. qX8] 

18 BC. 10. v9-] -d- e corr. in scr. C. qitj] trj B C. 11. 9] in ras. D. 

17. ly] vy D. Xg] -g e corr. D. v-9-] vs C. 19. qx^] x(i A. 24. Jidv- 

fiojv] om. D. 26. ftS^] vd- BC. 28. ^y] 1* D. xy] y D. 32. xa] -a 
euan. B. 33. Qxrj'] qx- e corr. A. 



182 



KAATAIOT nTOAEMAIOT 















Tov dici 'EXlr}67t6vtov 


WQ&V 


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5. vq] vi^ C 
Xt] Xs D 



6. rj] V C. 
q/iS] qoS D. 



qxS] -X- in ras. A. rtCalt.)] x^ D. 8. 
qvy] -V- in ras. A. " 10. vd] /id- D. 12. vs] 

/is BC. 14. Aiovtog] -so- in ras. D. 17. vn) /irj BO. 20. ^s] | f^ D. 

fis] /i& B. 21. qvrj] q/irj BC. 23. tg] om. D. vS] va D. 27. /S(pr.)] 

a D. 28. oS] CjS A. 29. q/iy] q/tg D. 30. S] corr. ex s D. rtfj ra D. 



MA0HMATIKHS STNTA3ESiS B'. 



183 



mgmv vb (lOtQcov fi vi. 


\ viovlai , 
&qS>v ^^Qi<P^- hva- Ytovlai 
^ Qsuav toltxai ovtixal 


&Q(bv 


fteQUpe- 
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ycavlai 

itva- 

toXtxai 


yorviai 
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5. I?] e corr. A. 6. »/] v BXJ. 7. o] o A (h. e. oij6h). 8. r/?] vy D. 

9. vr]] firi D. 10. Qi6] corr. ex Qte in scr. D. 14. 'Y^QOxdov] corr. ex 

iX&ixav D. 15. of] og BC. 20. x6] X6 D. 22. Qig] corr. ex Qvg A. 

26. v6 (alt.)] va D. 27. S (pr.)] corr. ex a in scr. D. o (pr.)] in ras. A. 

30. Qis] Qs D. 31. a] X D. 32. X] e corr. A. 



184 



KAATAIOT nXOAEMAIOT 















Tov dicc fisaov 


Ilovtov 


tb^&v 


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hva- 

toXixai 


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ytoviat 
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5. fiearifi {t^t.)] ftsari D, ut saepius. qiy] qirj D. 6. qtg] qXg D 7. 

2(pr.)] s D. 8. 017] Jtri C. 9. qv6] -v- in ras. A. 10. oS-] corr. ex orj 

in scr. C, 16. qx6] qxa D. 17. X6] Xa D. 19. vs] corr. ex vy D. 26. 

Xe] Xfi D. ^g] -g e corr. in scr. D. 27. 0] A. 28. 0] o A. 29. x] 
tS C. 30. 6] in ras. A, corr. ex e in scr. D. 



MA0HMATIKHS STNTASESiS B'. 



185 



a)Qcav is U noLQoav ftf a. 



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in ras. D. |^] in ras. D. 16. ^(pr.)] j/ BC. ^y] in ras. D. tt^] in 

ras. D. 17. o] o A. tf] in ras. D. o] in ras. D. 18. fiq (pr.)] fia D. 
19. xd] xa D. 20. y] v D. 26. v?] fig C. 



186 



KAATAIOT nTOAEMAIOT 















Tov ^ia BoQvad-ivovs 


(hQtbv 


ywviai 
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C«^^ toXuiaL 


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fi 


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1. tov 6i&\ tb 6ia rov B, tov 6ta tov C. 7. /J(pr.)] 6 H. X6] in 

ras. D. 9. QXg] Qxtj D. o] S A. 15. tS] S G. 18. X] 6 D. 20. o] 
5 A. 21. o] 5 A. 26. o] 5 A. 27. fi6] fia D. 28. o^j os D. 29. 

0] 5 A. 30. xy] C^ y D, ^] e corr. D. 32. o] 3 AB. 



MA0HMAT1KHS 2TNTASESiS B'. 



187 



WQOaV l<5 flOlQCOV fi/7] X^. 



^^ 


Yoivlat 
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ytatlttt 

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9 
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25 



1. Xfi] fip D. 6. X] « D. 7. 0] 5 A. 9. 9] e corr. C. o] corr. ex i C. 
vr,] vy C. o] o A. fia] fiS C. 16. o] 6 A. |C] 1/ C. fts] fiy B C. 17. 
Xa (pr.)] X- 6 corr. D. 22. vS] v^ D. 25. ^^] ^a D. 26. X^] X- euan. B. 27. 
^J(pr.)] D, vS ABC. g] post ras. C. 28. xr/] -r, in ras. D. 29. ;i/ (pr.)] 
corr. ex Xd' C. v] seq. ras. D. 30. i9] in ras. D. 81. xi/] om. D. fig] in 
ras. D. 32. xt] x- in ras. D. Af] Xy D. 33. x] ia ras. D. 



188 KAATAIOT nXOAEMAIOT 

scpcadsv^svrjg drj xal tijg rCbv yavL&v TtQay^areiag^ 
XsiTtovxog ds rotg ifjtotcd^s^svoig xov xag S7to%ag x&v 
xad'^ sxddXTjv s%aQ%iav S7ti6rj\ia6iag d^ccov itdXscov 
S7ts6xs(p^at, xaxa ^rjocog xal xara TtXdxog TtQog xoi)s 
5 XG)v sv ai)xatg cpatvo^svcjv sjtvloyi6^ovg xriv ^sv xoiav- 
X7JV SKd^E^LV siaiQSXov Tcol yscjyQacptKTJg sxo^svrjv 
TtQayiiaxsiag xad' avxriv vTt^ o^tv Ttotrj^o^sd^a dxo- 
Xov%'ifi6avxsg xatg x&v S7ts^SLQya6^svov Sg svi ^dXt6xa 
xovxo xb sidog i^xoQtatg xal TtaQayQaq^ovxsg^ o6ag 

10 iLOiQag d7ts%SL xov L6rj^SQLV0v xcbv 7t6Xscjv sxd6xrj 
xaxd xhv Sl avxrjg yQag)6^svov ^s6rj^PQLv6v^ xal 
7t66ag ovxog xov dt^ 'AlsiavdQsCag yQacpo^svov fis6rj^- 
^QLvov 7tQog dvaxoXdg rj d\)6SLg STtl xov t6rjfiSQLV0Vy 
dLcc xb TtQbg xovrov rj^tv ^vvL^ra^d^at rovg rov STto- 

15 %G)v %Q6vovg. vvv ds rb ro6ovrov ag V7toKSL^svcov 
r&v d^s^scov S7tSL7tstv dx^Xovd^ov rjyrj^d^sd-a^ dtdrfc, 
OTto^dxLg dv 7tQoaLQG)^sd^a rrjv sv rLVL rcov vtcoxsl^svcov 
r67tcov coQL6^svrjv coQav 6xo7tstv^ ijrLg rjv xard rbv 
avrbv %q6vov scp^ srsQOv rLvbg rcov STtL^rjroviisvcov^ 

20 8rav dLa(psQco6Lv ot dC avrcbv fis^rj^PQLvoL, ka^^dvsLV 
dcpsL^o^sv^ o6ag d7ts%ov6iv dXXriXcov oi)roL ^oiQag STtl 
rov l6riiiSQLVov ^ xal 7t6rsQog avrwv s6rLv dvaroXLXco- 

2. Se] mut. in ts B^, ts D. 3. STCLarKiaGLCig] pr. t supra 

ras. D. 4. iTcscnscpd-ca] -ai e corr. A. v.ttxd (pr.)] %axd 

xs D. "Aaxd (alt.)] om. CD. 5. avxatg] av- in ras. A. 

cpaivofibsvcov] -a- corr. ex ^ in scr. C. 7. TCQayfiaxsLag] -g 

corr. ex v D\ noifiGov D. 8. sTts^sQyac^svav D. 9. xo] 

ins. C. 10. iiOLQag] fi ovxog B, corr. ex ^ov C^ 15. xo] 
om. D, del. A». 17. av] sdv ABCD. xrjv] mg. D^; ^ '^^ 

sed eras. 18. a>QL6a^sv7]v C, corr. C^. ^xLg] rjXTqg C, 

riX7\g C^. v.axa xov] corr. ex xar' avxov D. 20. fis6r][is- 

QLVOL D. 21. cc7tsxov6Lv] corr. ex sn^xovaLV C^ ovxol] 

renouat. B^. 22. avx&v] corr. ex savx&v D^. saxLv] om. D. 



MA0HMATIKHS STNTAgESiS B'. 189 

teQog rj dvtLXCJtSQog^ to^ovtoig ts xQdvoig l^rj^SQLVotg 
TCaQav^SLV rj ^slovv triv Tiata tov vtcoxsl^svov toitov 
coQav^ Lva tcol&^sv trjv sv tm STtL^rjtov^svc) xatcc tov 
avtov XQOvov d^scoQOv^svrjv^ trjg ^sv av^t^^scjg 0vvL6ta- 
^svrjg^ otav 6 STtL^rjtov^svog tdjcog dvatolLKatSQog fi^ 5 
tr]g 8s ^SL(x)6s(X)g^ orai/ dv6^Lica)tSQog 6 ifjcoxsL^svog. 



1. ri dvTL^KmrsQogl xat D. 2. xonmv C. 3. otara] corr. 
ex ita D^ 6. ftftcbryfcog] corr. ex fislcscog D, 6 vnoyieLpLsvog 
SvtLy.mtSQOg D. In fine: KXuvSlov IltoXE^ocLOv (la&rjfiatLyLrig 

cvvtd^ecog f ABC, KXuvSlov IltoXefiaLOv ft^a&rifia § D. 



r'. 

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%•'. 7t£QL tfjg tcbv vvx^rj^iQCDv dvL06tritog. 
15 'E(pc3d£v^ivcov iiiiXv iv totg iCQh tovtov 0wt£tay- 
fiivoLg tcbv t£ blo0x£Qcbg d<p£LX6vtC3v jC£ql t£ ovQavov 



1. r'] om. ABC, Tisq^dXaLa tov xqlxov D. 2. y'] AD, 

xQLxcp B, om. C. TTjg] x&v D. ficcQ-7][iccxLyifig Gvvxd^scog] 

lia&T^ficiXLyiav D. 4. a'] om. D. ivLccvaLov^ corr. ex ivir- 

avaCag C. Post xqovov add. x^ rjd (sLd D^) fl^ D. 5. |3'] 

om. D. yiavovog D. 6. et 8. permutauit D. 6. y'] om. D. 

8. d'] om. D. 9. «'] om. D. 11. g'] om. D. 12. t'] 
om. D. nccQodovli om. D. 13. tj'] om. D. xfjg] xfj C. 

xov ijXLOv'] TjXiayifjg D. 14. -9''] om. D. 15. IlxoXsfia^ov 

^iaQ^riiiaxLTi&v y ABC, nsQl xov (isyid^ovg xov ivLavaiov %q6vov D. 

s(podsv(isvcDv C, corr. C^ ytQo] corr. ex -jtQdg C. 16. 

rs (alt.)] supra scr. D. , 



KAATA. nTOAEM. MAOHMATIKHS STNTASESiS P'. 191 

xal yrjg ^ad-rjnatLxag TtQolricp^rivaL xal hi tcsqI xfjg 
iyxXL^scog tov dia ^e^cov t&v ^adicov riXiaxov xvxXov 
xal t&v xata ^SQog jtSQl avtbv 6v^paLv6vt(X)v iitc ts 
tfjg OQd^fig 0(paCQag xal iitl trjg xad^' sxd6trjv ol'xrj6iv 
syxsxXL^svrjg dxoXovd-ov rjyov^sd^a xal sips^flg rovTov 5 
tbv JtSQl Tov rjliov xal trjg 6sXr]vrjg 7toirJ6a6d-ai, Xdyov 
td ts TtSQi tdg xivr]6Sig avr^v S7ti6v^^aCvovta dis^- 
sld^slv firjdsvbg tcbv TtSQl tovg d6tsQag (paivo^svcov 
avsv tfjg tovtcov JtQodiaXijxpscog xatd tb Ttavtslsg 
svQsd^fjvac dvva^svov, xal tovtCDv dh avt&v TtQorjyov- 10 
^svrjv svqC6xo^sv trjv tfjg r}Xiaxf}g xivtj^scog jtQay- 
HatsCav^ fjg dvsv ndXcv ovds td TtSQi trjv ^sXi^vrjv 
olov t dv ysvoito dis^odiXGyg xataXa^s^d^at. 

a' . TIsqX tov fisysd^ovg tov sviav6Cov ;|r^dvov. 

IlQcotov d?) TtdvtcDV tcov TtSQi tbv YlXiOV dTtodsiXVV' 15 
lisvcov vjtdQxovtog roi) rov sviav6iov xq6vov svqsIv 
tdg iisv t&v TtaXai&v jtSQl tijv djt6g)av6iv tov toiov- 
rot> diacpG)vCag ts xal djtoQCag ^dd-oi^sv dv sx tcov 
6vvtstay^8vcov avtolg xal ^dXi6ta rc3 'IjtjtaQXG) dvdQl 
(piXojt6vc) ts o^ot) xal (piXakrid^Si. dysi yaQ fidXi6ta 20 
xal toihov slg tijv totavtrjv djtoQCav ro did (isv tcbv 
jtSQl tdg tQOJtdg xal tdg i6rj^sQCag cpaivo^svcov djto- 
xata6td6scov sXd66ova tbv sviav6iov xq6vov svQC6xs6d^ai 

1. (la&r^ficcTiyimg] corr. ex fiad^qfiatLti&v D^. 2. rjXiayiov] 
rov 7}XLa-iiov CD. 3. avT&v C. 5. tovtoov] corr. ex rd D*. 
9. TcavrecXsg C. 11. svQLGTiofiiv] dg&^ev D, mg. ^^ 14. a'] 
mg. BC^, om. AD. nsQL — xqovov] om. D. 15. dTJ] corr. 
ex 8l A^. 16. £VLav6Latov CB^, ivLavOLEOv B. 17. cltco- 

cpaGLv CD, supra -a- ras. D. 18. dnoQLag] ante q ras. 1 litt. D, 
anoQSLag C. av] D, om. ABC. 19. Post tc5 ras. 1 litt. D, 
item post ^lnnccQx^p. "^l. dnoQLav] ante o ras. 1 litt. D. 23. 
ivLavGLaiov C. 



192 KAATAIOT nTOAEMAIOT 

trjg STtl raig r^s rj^EQaLg rov Tfrc^^rov JtQOiyd-yjTcrjg^ dca 
ds rmv tcsqI rovg ajtXavstg a6rsQag d^scoQov^svcov fisi- 
^ova. od^sv STtipdXXsi rm xal rijv rav aTtkavcbv 6(paiQav 
fisrd^a6LV Ttva TtoXvxQoviov Jtotstad^ai, xal avrrjv^ \ 
5 S67tSQ xal rdg rcbv jtXavcj^svcsVj slg rd sjtoiisva rrj$ ^ 
r^^v TtQcbrrjv TtSQiaycoyriv 7tOLOV0rjg (pOQdg Kard rbv 
did rmv JtoXov d^tporsQcov rov rs i6i^^SQLV0v xal rov 
Ao|oi) yQa(p6iisvov xvxkov. rj^stg ds^ rovro ^sv ort 
ovrcog rs s%si xal riva yCvsrai rQOJtov^ sv rotg jtsQl 

10 rcjv ditkavcbv d^rsQcov STtidsi^o^sv ovds ydg rd TtSQl 
sxsivovg dvsv rr]g rikia%r\g xal 6skr]Via3ifjg TtQodialrj^scjg 
olov r dv ysvoiro di okov d^scoQrjd-fjvai' Tcara ds ri^v 
7taQov6av STti^KS-^iv TtQog ovdsv dkXo rjyovfisd^a dstv 
dno^XsTtovrag rbv sviav6i0v rov rjliov xqovov 6K07tstv 

15 ;jj rrjv avrov rov riXCov %Qbg savrov^ rovts^nv rbv 
yivo^svov V7t avrov Aolov xvxXov^ d7to%ard6ra6iv 
bQCis6%-aC rs rbv sviav6iov %q6vov^ ota^' bv d7t6 nvog 
dxivrjrov 6rj^sCov rovrov rov xvxXov xard ro i^fjg 
S7tL ro avro TtaQayCvsrai^ ^6vag dQ%dg oixsCag rfjg 

20 roiavrrjg d7toKara6rd6scjg rjyov^svovg rd "b^tb r&v rQO- 
7tLxcbv xal i6rj^SQiVG)v 6r]^sicov d(poQit^6^sva 6T^^sta 
rov 7tQosiQr]^svov kvkXov. sdv rs ydQ ^ad^rj^atiKcbg 
S7tipdkXcj^sv np k6y(p^ ovrs oiKSLorsQav d7toKard6ra6LV 
svQrJ6o^sv rfjg i7tl rbv avrbv 6%r]^ari6^bv (psQ0v6r]g 



1. rjfiigai C. did] - - did B. 2. nsQi] corr. ex Ttgos D*. 

3. Tc5] corr. ex ro D^ (to). zi]v] supra scr. D^. 6. rryv] 

-TJ- in ras. 2 litt. A^. 9. yBV7\tai C. 13. 6v.Btpiv D. ~] mg. D. 



. 14. ccno^Xmovtsg D, corr. D^. 15. tovtsati D, comp. B. 

triv yLV0(i8vrjv D. 16. vTt' avtov^ {-n' ccv- renouat. D^) 

vTc' avtov nqbg tov AD, Ttgbs tov del. A^. 18. 67\ii8iov] -ov 
renouat. D^. tov] om. A. 21. ^r^^eicav] corr. ex 6rjfistov C^. 

22. sdv'] D, ccv BC et post spatium 1 litt. initialis A. 23. 
Xoycai] svXoycp ex renouat. D^. 24. tov] t&v A. 



MA0HMATIKHS STNTASESiS T'. 193 

tbv ijhov roTttx&g rs ocal j^^QovLX&g fjroi TtQog rovg 
dQi^ovrag rj rbv ^s6r]^PQtvbv tj ra ^sysd")] rav vvx^^- 
fisQCJv Toi) roLOvrov d^sciQoviisvov ovrs aXXag aQxag 
sv r(p dia ^s^cov rcbv t,codCc3v zvx?.g), fiovag ds rag 
nara rb ^v^^s^rjxbg dq)OQi,^onsvag vTto rs rofv rQO- 5 
7tLKG)V Tcal i6riiiSQLVcbv ^rj^SLCOv sdv rs (pv^LXcbrsQOv 
rLg S7tL6K07tfj rb olxsloVj ovrs d7toxard6ra6LV svXoyca- 
rsQav svQ7]6SL rfjg aTtb rov b^oCov 7tSQL rbv dsQa 
xata6rr]^arog STtl rb o^olov xal rrjg avrrjg c3Qag S7tl 
rr]v avrr^v (psQov6rjg rbv rjXLOv ovrs dkXag dQ%dg tJ 10 
liovag^ xad"^ dg at G)QaL ^dU6ra dLaxQCvovraL^ ^isrd 
tov trjv 7tQbg tovg djtXavstg d6tSQag d^scjQov^svrjv 
d7toxatd6ta0Lv ato7tov (paCvs^d^aL d^d ts dlXa xal 
(idXL6d'\ otL xal rj avtcov OtpatQa 7tOLOV^svr] tuvd 
tstay^svrjv ^std^a^tv sCg td S7t6^sva tov ovQavov 15 
^sc^QSLtau' ovdsv yaQ tovtcov ovtcjg sxovtcov XG)kv6SL 
IsysLVy to6ovtov slvaL tbv svLav6L0v tov rjXCov xQOi^ov^ 
sv 06C!) tbv tov Kq6vov d6tSQa X6yov svsxsv i) xaC 
tLva tcbv dXXcov 7tXavco^svcov 6 ijhog ^tSQLxatakafi^dvsL^ 
7toXXoL ts dv ovtcog xal dLd(poQOL ysvoLVto oC svLav6L0L 20 
XQOVOL. dLa ^sv dij tavta 7tQo67JxsLv oC^^sd^a tbv 
svql6x6^svov d^d tcbv tr]Q7]6scov tcbv cog svl ^dXL6ta 
d7tb 7tXsCovog dLa6td6scog Xa^^avo^svcov d7t6 tLVog 



1. 7]xoi\ 7) x6v BC, corr. B^ 2. vvxQ-ri^iqGiv] post q 

ras. 2 litt. A. 3. d'£coQ7i^Evov D, xe- ins. D^. 4. (lovag 

8t] 7] fiovag D. 6. iciv ts] si^zs D. 7. ng] corr. ex te D^ 

STtLGKOTtsi ABCD. 8. svQT]aEL] corr. ex svqsivsl D. 9. 

tfig] t- in ras. A. 12. tov] om. D, tov -AaC supra scr. D^ 

13. Ante atonov ras. C. 14. \ji,aXiG\G%' D, sed corr. 17. 
xov\ -V in ras. A. 18. KqOvov] comp. B, corr. ex i^ovov C. 

21. ofy^s^a A. 22. svi\ corr. ex sv Dl 23. ano (pr.)] 

fx D. nXsLvog C. 

Ptolemaeus, ed. Heiberg. 13 



194 KAATAIOT nTOAEMAIOT 

tQOTtfjg t) t6r]^£Qtag ml trjv avtijv xal i^ps^TJg xq6vov 
tovtov rjyst^d-ac tbv ivLav6L0v tov rjXiov, 

iTCsl ds d^OQvfist TCGyg tbv "iTtTtaQxov i^ ^^^ %bqI 
avtrjv triv totavtrjv d7toxatd6ta6Lv VTtoTttevoiiivrj dta 
6 tc3V %atd tb i%r{g yivoybiviov 6vv£xa)v trjQTJ^scjv dvt- 
66trjg^ jteLQa^o^sd^a dst^at did PQaxicjv ^rjds tovto 
d^oQvP&dsg VTtaQxov^ nstOiia fisv slXrjipotsg itSQl tov 
^rj dvL6ovg sivai tovg ;u()dz/ovg tovtovg^ i^ av xal 
aiftol did t&v dQydvcov zatd tb i^ijg tvyxdvo^ev 

10 tstrjQrjxotsg tQOJtcbv ts xal LGrj^SQcav ovdsvl ydQ 
d^iok6yco diaipiQovtag avtovg svql6ko^sv trjg xatd tb 
titaQtov i7tov6Lagy aAA' ivCots 6xsdbv o6G) jtaQa ts 
trjv xata6}csvr}v xal trjv ^i6Lv tcbv OQydvcsv ivdixstai 
dLafiaQtdvsLV 6toxa^6^svoL ds xal i^ avtcbv^ Sv 6 

15 "iTtTtaQxog inLXoyL^staL^ iiaXXov tcbv trjQr]6scov slvaL tijv 
TtSQl tdg dvL66tr]tag d^aQtCav. ixd^i^svog ydQ tb 

TtQCbtOV iv t& IIsqI tfjg ^Sta7ttG)6SG)g tWV tQOltLK&V 

xal L6r]^SQLVcbv 6rj^SLG)v tdg doKov6ag avr» dxQL^ag 
xal icps^fig tstrjQrj^d^aL d^SQLvdg ts xal x^i^i^^^Qt^ydg tQO- 
20 %dg bfioloyst xal avtbg ^ij to6ovtov iv avtatg sivao 
tb didfpG^vov^ C96ts Sl avtdg dvL66trjta xatayvG)vat 
tov ivLav6L0v XQ^'^^'^' iTtiXiysL ydQ avtatg ovtcsg' 
„£>c ^sv ovv tovtcov tcbv tr]QrJ6SG)v dfjXov^ otL ^LXQal 
7tavtd7ta6LV ysy6va6LV at t&v ivLavtcbv dLacpoQaL 



3. 7 iJag. D. di] corr. ex d^q C, i) Kai] mut. in yiccl 
7} B^ 5. Twv] renouat. D*. 7. nsLaiia] BD*, nL6(ia ACD 
(corr. uoluit C^). 8. firj'] supra scr. D, 11. avrovg] -ov- 

in ras. A, 12. xhaQGxov C, sed corr. 14. dLaybaQxsiv D. 

18, avtcp] seq. ras. 2 litt. A, corr. ex avxcbv D. 20, elvai 
> 
Bv avxaig D. 23 sq. ^ mg. ABCD. xovxcov'] supra scr. D*. 
> 
HiyiQUL] corr. ex iiL'/.Qd A^, 24. TravxaTtaaLv] -v eras D, 



•«,■ 



MA0HMATIKHS STNTAjEjESiS V. 195 

dXX' i%\ fihv tcov XQOTt&v ovx a.TiBlTtCt.Gi ocal '^^dg xal 
xhv ^AQXLiiridri xccl iv xfj xr}Q7]0€L ocal iv xw 6v2,XoyL6^^ 
dLa^aQxdveiv xal smg xsxaQXov ^SQOvg ti^SQag. cckql- 
^&g ds dvvaxai xaxavo£L6d'aL rj dvco[iaXLa xcov ivLav- 
6Cgjv ;updvcov ix xcov xsxrjQrj^ivcov iitl xov iv Als^av- 5 
dQsCa xsL^ivov xaXxov xqCxov iv xt] xsxQay(hv(p 
xaXoviiivri 6xoa^ og doxst dLa6rjy.aCvsLv triv £6rj^SQLvriv 
'fj^iQav^ iv fi dv ix xov sxiQOv fiiQovg aQxrjxaL xijv 
xoCXrjv iitLcpdvsLav (pcoxC^s^d^aL." 

sixa TtaQaxC^sxaL itQcbxov fisxojtcoQLvcbv L6rjfiSQLCov lo 
XQOVovg G)g dxQL^i6xaxa xsxrjQrjfiivcov ^ iv fisv xa l^' 
sxsL xfjg XQCxrjg xaxd KdkLitTtov TtSQLodov xov Ms60Qr} 
A' TtSQl xrjv dv6Lv xov rjXCov^ fisxd ds y sxrj iv xa 
X sxsL xfj TtQaxrj xav iitayofiivcov TtQcoCag^ diov xijg 
fis6rjfiPQCag^ co6xs dLansfpcovrjxivaL xsxaQXOi fiLdg rjfiiQag. 15 
fisxd d' ivtavxov iv X(p xa sxsl coQag g\ OTtsQ xal 
rjv dxdXovd^ov xfj jtQO axjxijg xrjQ7]6si, (isxd ds Td hrj 
X(p A/3' sxsL xfj xqCxtj x&v ijtayofiivcov sig xijv xsxaQxrjv 
xov fiLS6ovvxxCov, diov TtQcotag.^ co6xs xa d' TtdUv dLaits- 
(pcovrjxivaL. fisxd ds ivLavxbv sva xa Xy' ivLavxm xfj 20 



1. aTfsXnitoi] WD, atpsXiti^ai ABC. 2. 'J^^^tju-^^^rj] mut. in 
'AQXniridr]v B^. 4. rcov] e corr. D*. svlccv6l(ov] -co- in ras. D, 

6. v.ttXov[i8vrj xEXQaycovcp B. 7. 6toa\ ato&i C, t eras. 8. 
aq%ritai\ corr. ex ap^rjrat D*. 10. ybBton(OQLV&v\ -m- e corr. D*. 

ler^fiSQL&vl corr. ex lar]pL8QLv B^, iarjfifQLVcov D, larjusQLvdav D^. 

11. Ante sv ras. 1 litt. D. t^'] corr. ex ^l Dl 12. 

KctXLTtnov] ABC, KaXunnov D. Msgoql B. 13. X'] 

ABC, r^ tQLa^noatjj B^D. 14. tfj'] corr. ex tf] A^ nQmtrj] 
B^D, vso^n^Ca ABCD^ 15. &ats] AD, J,? BCD^. 16. 

S'] 8s D. sv ro5] svatco D, supra a ras. v,a'] nQmtca xal 
sly(.oatco D. rjv xat C. 17. avtfig] corr. ex tavtrjg D^ 18. 
ty] tov tjj B. 19. tov] eras. B. 20. Ss] S' BC. Xy'] 

seq. - - in ras. B, X'y C (similiter saepe), X tQLtco D. svl- 
avtoi] stSL D. 

13* 



196 . KAATAIOT nTOAEMAIOT 

d' rav STCayo^svGyv TtQCoCag^ otvsq xal ^v axdXovd^ov xfi 
TtQO avtrlg rrjQ7]0SL. ^sra ds y srrj ra X<s' £tSL rfj rs- 
raQrri r&v STtayo^svcov s67CSQag^ dsov rov ^s6ovvKriov^ 
wg r« d' ^ovip Ttdkiv dLajtscpcovrjxsvaL. 
5 ^sro: ds ravra SKrCd^srai Tcal rag b^oCog dxQtPcog 
rsrrjQrjfisvag saQivdg L6r]^sQCag' iv fisv ra A/3' srsv rrjg 
rQCrrjg xard KdkcTtTtov TtSQiodov^ MsxIq k^' JtQCoCag' 
xal 6 XQLXog df, (prjdCv^ 6 sv 'Aks^avdQsCa t6ov s^ 
sxarsQOv ^SQOvg JtaQrjvyd^d-r] TtSQu s' coQav co^rs rjdrj 

10 xal ri]v avrijv i^rj^sQCav diacp^Qcog rsrrjQrj^svrjv f coQatg 
syyL6ra dLSvsyTcstv. xal rdg scps^fjg ds cprj^Lv iisxql 
rov Xt^ srovg 6v^7tscpc3vrjKsvaL rfi JtQog rb d' STtovaC^. 
fisrd ds Td srrj r& y' Kal ^i' srsL rov Msj^Iq rfj Kd'' 
fisrd rb ^sdovvKrLov rb slg rrjv X' ysvsed^aL cprjalv rijv 

15 saQLvijv C^rj^SQCav^ oitSQ Kal dK6kov6%'ov rjv rfj sv r& 
Xp' srsL rrjQrj6sL Kal ^vpLcpcovst^ cprjaCv^ Jtdhv Kal TtQbg 
rdg sv rotg sxopbSvoLg srs6L rrjQrj^stg pis%QL rov v' 
srovg' sysvsro ydQ rov ^a^svcod" rfj TtQcorrj jtSQl dv6LV 
ijXCov (jLsrd piCav rj^SQav Kal r]^L6v Kal rsraQrov sy- 

20 yL6ra rrjg sv t& ^y' srsL^ ojtSQ kol STtL^dXXsL rotg 
lisra^i) S hs6Lv. ovd^ sv ravraLg ccQa ratg rrjQrj6s6LV 



1. Bnayo^isvoiv'] -o- in ras. A^ 2. Si] -s in ras. Bl y 
iri]] corr. ex ye rrjv B, xqlxov hoq (corr. ex txsi m. 2) D. In 
D numeri plerumque omnibus litteris scripti sunt. 4. ndXiv'] 
supra scr. D*. 5. Bv,xi%'sxaC\ corr. ex sv.xiQ^Evxca D^ a.v,Qi- 
|3c6s] corr. ex &tiQi§s6xaxa D^. 6. iGrjfiSQivds D. X^'] 

l §' AC. 7. KdUnTtov^BCD et corr. ex Unnov A^ 

MsxiQ] MsxoDQ D, MsxsiQ D*. 9. naQvydG^r] C, corr. C^. 
. TCf^t] supra scr. D^ 11. qotjat D. 12. A^'] corr. ex Zy D^. 

13. rc5] corr. ex x&v A. y' v.al ft'] fly D. MsxsCq A. xjj\ 
om. D. 14. cpTqGiv'] -v del. D^ 15. ^v] corr. ex slsv D^. 

16. 6vyicp(ovsi\ del. B^, mg. yp. ^vvstpoovsi; Gvvscpmvsi D. 

qp7](7i D. %at(alt.)] om. D. 18. syivsxo^ -sv- supra 

scr. Cl nQmxrj] AD^, a BC, vov}ir}Via D. 21. f] snxd BC. 



MAeHMATIKHi: STNTAtSEiiS V. 197 

yiyovE tig d^idkoyog diacpOQa KaCxoL dvvatov ovtog 
ov ^ovov 7C£qI tag tQOitiKag tr]QYJ68Lg^ akka xal tzsqI 
tocg iOrj^sQivdg^ yoyvedd-ai tu itaQ' avtag dLa^ccQtrj^a 
xal iidxQi d' liLdg rjnsQag' xav yaQ rw tQL6xLlL06t& 
Tcal s^axo0LO6t^ [iovg) ^sqsl tov d^a tcbv TtoXcov tov 5 
i6rinsQLV0v TcvxXov TCaQaXXd^rj tfjg dxQL^SLag r] d^s^Lg 
rj xal dLaLQS6Lg t&v OQydvcov^ tijv to6avtrjv xatd 
TCldtog 7taQaxG)Qrj6LV 6 rjXLog diOQd^ovtaL TtQog totg 
Cerj^SQLVotg t^r]^a6LV tstaQtov ^Lccg ^OLQag xatd ^rjxog 
STtl tov Xo^ov xvxXov XLvrjd^SLg^ wdts xal trjv dta- 10 
(pcavCav ^sxql d' ^Lccg rj^SQag syyL6ta dLSvsyxstv. stL 
d' dv dLa^aQtdvoL nXsov STtl t&v ^ij xad^aTta^ L6ta- 
lisvcov xal JtaQ avtdg tdg trjQr]6sLg dxQLpovfisvcjv^ 
dXXd 6vvs6trjQLyfisvc3V OQydvcov d%6 tLvog dQxr^g totg 
VTtoxsL^svoLg sddcps6Lv TtQog t6 ^ovCfirjv sitl Ttokv trjv 15 
&S6LV sx^iv, yLyvo^svrjg tLvbg TtSQt avtd vjtb tov 
XQOvov XsXrjd^vCag JtaQaxLvrj^scjg^ hg inC ys tcbv TtaQ 
rj^tv sv tfi 7talaC6tQa ^jaAxwv xqCxov sv tcj tov L6r]- 

^SQiVOV STtLTtsdG) doXOVVtCJV f^V d^S^LV £%£tl/ IdoL tLg 

dv to6avtr] yaQ rj^tv tr]Q0v6L xatacpaCvstaL dia^tQOcpr] 20 
tfjg ^s6scog avtcbv xal ^dh6ta tov ^sC^ovog xal 
dQxaLotSQOv^ d)g svCots xal dlg sv tatg avtatg i6r]- 
^SQCaLg ^stacpcjtC^s^d-aL tdg xoCkag avt&v sitLcpavsCag. 



1. ysyovs] seq. ras. 1 litt. D. 3. yivEeQ-ai D. 4. ya.Q\ 
ins. D^ 6. larniBQLvov\ in ras. D^ 7. ri] postea ins. D. 

-AaC] %al 17 D, i^ add. B^. 9. tfn^^iaGLv] -v del. D^, r/irj- 

(laOL B. 12. dLa[ibaQxdvEL AC, dLayLaQ%r]^sCr] D. nlstov D. 

{iri\ del. B, supra scr. D-. 13, v.aC'] comp. B, v.al (i-^ B^ 

ayiQL^ov(i8vcov] aKQL^ovfi^vcov OQydvcov D. 14. 6vvE6xr}QLyfis- 
v<ov\ corr. ex 6vv86xr]Qi6}iiv(ov D^. oQydvcov] om. D. 15. 

idd(ps6L D. 16. yLvofisvrig D. 17. uts snC] corr. ex a^itC C^, 
renouat. D. ys x&v'] renouat. D. 18. italai^xa D, corr. D^ 

20. dtaffT^oqp^ 17 ^tafftr^og)^ D. 



198 KAATAIOT nTOAEMAIOT 

aXXa yaQ r&v fiev totovtcov ovdsv ov8' avtbg 6 
"iTtTcaQiog oLstac tvyxdveLV a^LOTti^tov TtQog trjv VTto- 
ipCav tijg dvL06trjtog tcov ivLav^ccov iqovcov^ dno de 
tLvov tTjg ^eXTJvrjg ixlsLtl^scov imXoyL^onsvog svQL^xeLV 
5 q)rj6LV^ otL ri dvcainaXCa t&v ivLav0Ccov %q6vg)v TtQog 
tov ^iedov d^ecjQOv^evr] ov ^eC^ova iteQLeieL dLatpoQav 
/.' nal d' fieQovg ^L&g rnieQag' OTteQ dv r^v T^drj ttvbg 
i7tL6td6ecDg d^LOv^ elneQ ovtcog el%e xal fn) i^ avt&v^ 
av TtQOcpeQetat^ dLezf^ev^^evov id^ecoQetto. ijtLXoyC^etat 

10 ^ev yccQ dtd tLVcav 6vveyyvg aTtXavcjv d6teQcov tetrjQrj- 
lievcov cfelrjvLaTccbv iKkeCrl^ecov ^ 7t66ov xad'' exdatrjv 6 
xaXov^evog Zltd%vg TtQorjyettaL tov ^etOTtcoQLvov 6rj[ieCov, 
xal dLd tovtcov evQCoxeLv otetaL Jtote fihv tb Ttlet^tov 
avtbv dite^ovta totg xa-O"' eavtbv %Q6voLg ^oCQag g/.', 

15 Ttote de tb iXd%L6tov [loCQag e xal d\ 6vvdyeL de 
ivtevd^ev^ ort, i^ceCTteQ ov dvvatbv tbv Utd%vv iv 
ovtcog oXCyq) %q6vg) to6ovtov netaxLvrjd^fjvaL ^ tbv 
7]Xlov eLx6g^ dcp^ oh tovg t6jtovg tcbv ditlav&v 6 'Iit- 
7taQ%og i7tL6xe7ttetaL ^ ^r] iv l6co %q6vco 7tOLet6&aL trjv 

20 d7toxatd6ta6LV. leXrjd^e de avtov^ otL tov i7tLloyL6^ov 
firjd^ oXcog dvvafievov 7tQO%coQetv dvev tov tbv xatd 
tijv exkeLipLv tov rjXCov t67tov v^toxet^d-aL avtbg eCg 
tovto xad"' exd6tr]v ^taQaka^L^dvcov tdg dxQL^&g iv 
totg ete6LV ixeCvoLg i(p eavtov tetr]Qr]^evag tQOTcdg 



6. ^sGov'] corr. ex fisLov D^, -sa- supra scr. D^. 7. [_'] 
7}liLaovs D. 8. slxs] corr. ex slxsv D^. 9. STtLXoyC^EtaL] corr. 
ex insXoyL^sto D*. 15. (lOLQag s %at] I D. avvdysL] post 

ras. C, -ys- in ras. A. ds (alt.)] d' D. 16. dwatov] -tov 
ins. B^ 17. (istaKLvr^LQ-fivaL A. 18. "Inaqxog D. "20. df] 
8" D. 21. ngoxoiQSLv] -co- in ras. A. tov tov] corr. ex 

tovtiov D*. 23. naQalafi^dvcov] AB^C^D^, naQaXa(i§dvov 

BCD. 24. Ig)'] ABC; vcp' D supra scr. s, quod del. Dl 



MAeHMATIKHS STNTASES^S V, 199 

xal l0r]fi€Qiag ccvrod-ev dfjXov Ttoist ^rjdsfiLav tzsqI riji/ 
^vyxQL6LV r&v ivcavrcbv v7tdQxov6av Ttaga ri^v rov 
rsrccQrov sjtov6tav diacpoQav. 

cag yaQ scp' svbg vTtodsiyiiarog sx ^sv rfjg sv rco 
A/3' srsL rfjg rQLrrjg xara KdXvTtTtov TtSQtodov TtaQarsd^st- 5 
^svrjg sxksLTtriKfjg rriQr]6sG}g svqlGxslv olsrat rbv Erd%vv 
JtQorjyov^svov rov ^sro7tG)QLVOV erj^SLOv ^OLQag g i\ 
did ds rfjg sv ra ^' xal rQLrcp srsL rfjg avrfjg TtSQLodov 
nQorjyovfisvov ^OLQag s d\ xa\ biioCcog TtaQarLd^s^svog 
eCg rovg jtQoxst^svovg koyL^iiovg rdg sv rotg srs6L lo 
xovroLg rsrrjQrj^svag dxQL^&g saQLvdg lerj^SQLag^ Xva 
did ^sv rovrcjv Xd^ rovg sv rotg ^s6oig XQOvoLg r&v 
ixksL-ipsov rjhaxovg roTtovg^ djtb ds rovrcov rovg 
fSskrivLaxovg^ dnb ds rcbv rfjg csXrjvrjg rovg rcov d6rs- 
Qcov^ rfjv fisv iv ra A/3' srst cpr^el ysyovsvaL rov 15 
MsxLQ xt^' jtQcoLag^ rf^v d' iv rc5 ^y' srsL rfi xd"' ^srd 
rb ^s6ovvxrLOV ro slg rrjv X' (isrd ^L! 8' rj^sQag 6%sdbv 
rfjg iv rc3 A/3' srsL ysysvrj^svrjg^ o6ag xal jtOLSt ro 
rsraQrov ^ovov ijtLXa^^avo^svov sxd6r(p r&v ^sra^v 
Td ircbv. slitSQ ovv firjrs iv itlsCovL ^r^rs iv iXd66ovL 20 
XQOvcp rfjg xard ro d' ijtov^Cag 6 ijXLog rfjv itQbg rdg 
VTtoxsL^svag i6r]^SQCag d7toxard6ra6LV jtSTtoCr^raL, ^r]rs 
rbv Urdxvv iv ovrcog oXCyoLg srs6LV ivds%sraL fiCav 



5, KdXiTtTtov] ABC, KccXlLTiTtov D. Ttagats&SL^^vrjg] corr. ex 
naQccTLd^siiEvrig D^ 6. STilrjTtziHTjg C, corr. C^. 7. [_'] /_' j' D, 
corr. D*; j" ins. B^ 8. fi.' ital tQLtoj'] ]Ly D. 9. «] s [_ D, 
« 8 D^ ojdotcoff] o/Ltcoff D, 10. slg tovg TtQoyiSLfiivovg] mg. D. 

XoyLC^ovg] BC, mg. A^; STtLloyLGiiovg D, sed sitL- renouat. 

15. qprjcrr D. 16. Ms%lq] ^isxslq tjj D. k^'] supra scr. C. 

S' sv ta] corr. ex ds t&v D^ 17. l'] tQLaKoida D. d'] 
mut. in tstaQtov B^ 20. SLTtsQ ovv] corr. ex sTtsi ovv D^ (yQ-)- 

21. y.ata to] v.ax6 A. inLOvaCag D. 



200 ' KAATAIOT nXOAEMAIOT 

fiOLQav Tcal TStccQtov xsxivrj0d-aL,, Jt&g ovx aroitov ta 
Slcc tcbv 'bTtoxsL^Bvov aQ%G)v S7tLk8koyL0iiBva TtagaXa^' 
pdvsLV TtQog triv avtcbv tcbv 0v6tr}6a^avcov avta dLa- 
^oXiiv xal tijv altCav tov TtSQl trjv to0avtrjv KLvr]6LV 
5 roi) Utdxvog ddvvdtov ^rjdsvl ^sv dXXG) 7tQ06d7tt£LV 
TtXsLOvcjv ys '6vtC3V t&v SfiTtOLrj^aL f^v toaavtrjv 
d^aQtLav dvva^svcov^ ^ovaLg ds tatg vTtoxsL^svaLg iarj- 
fiSQLaLg dyg d^a dxQL^cbg xal ^ri dxQLpcbg tstrjQr]^svaLg; 
dvvatbv yaQ dv do^SLS ^dlXov i]toL tdg sv avtatg 

10 tatg sxXsLtl^s6L dLa6td6SLg trjg 6sX7Jvrjg jtQog tovg 
syyLGta tov d^tSQCHv bko0%SQS6tSQOv xatsdtoxdad^aL -§ 
toijg iTtLkoyLC^ovg rjtOL tcbv TtaQalXd^scjv avtrjg TtQog 
tijv tG)v cpaLVO^svov toTtov STtLdxsipLV rj trjg tov 
ijXLOv xiv7]6scog trjg djtb tcbv i6rj^SQL&v S7tl tovg 

15 iis6ovg tcbv sxksL^scov iQovovg r] ^rj dXrjd^&g t) ^-^ 
dxQLpog SLXfjfpd^aL. 

dXk' ol^aL xal tbv^lTtitaQxov 6vvsyvcoxsvaL ^sv xal 
avtov^ otL ^rjdsv sv totg tOLOvtoLg svs6tLv d^LOTtL^tov 
JtQbg ro dsvtsQav tLvd to riXiGi TtQO^dittSLV dvcj^aXLav^ 

20 ^s^ovXri^d^aL ds fidvov vitb cpL^aXrjd^SLag ^rj ^LConri^aC 
tL tcbv svCovg sCg vTtoiJ^Cav b7tco6diJ7tots dvva^svcov 
ivsyxstv. xs%QritaL yovv xal avtbg tatg 'i)7tod's6s6Lv 
riXCov xal ^sXrjvrjg og ^Ldg xal tfjg avtfjg V7taQ%ov6rig 
7tSQl tbv rilLov dvco^aXCag trjg 6vva7toxad-L6ta^svr]g 

25 to 7tQbg tdg tQ07tag xal tdg L6r]^SQCag svLav6C(p %q6vg). 



1. xBxaQXOv] j' B, j J). HfxtVTjcr-O^at] post %£- ras. 1 

litt. A. 5. 117)8 evl |u.£V] corr. ex iilv (ir^dsvi: Dl 6. xoi- 

wvxTjv D. 7. dvvccfi8V(ov] des. fol. 68" A, „deest folium" mg. 
m. rec. (desunt reuera 4 folia). (lovaLg] sqq. om. A. 8. Post 
&(ici del. xat Dl 9. do^sLs] D, do^si BC. 10. sv,lsC^saLV C. 
11. iyyvs D. 13. t) xfjg] om. B. 14. tGrjfisQiv&v D. 15. 
6cXr}d-&g] aXrjd-rivog D, Zr supra add. D^, ccXrjd-Lv&g D^. 



MA0HMATIKH2 STNTASE^S T\ 201 

xal ovda^fj dicc t6 l6o%qovCovg vTtotLd^s^d^aL tag ex- 
KEL^svag tov riXCov jcsQLodovg to; tvsqI tag ixXsCilfSLg 
(paLvdiLSva d^scjQOV^sv d^LoXdyo) tLvl dLaq)6Q0vta t&v 
xatd tdg szxsL^svag VTtod^s^SLg STtLXoyL^o^svcov^ ojtsQ 
dv ai6d"rjtov Jtdvv Cvvs^aLvsv ^rj 6v^7taQaXaiipavo^svr]g 5 
Tijg TtsQl tijv dvL66t7]ta tov sviav^Cov xqovov dLOQd^co- 
6scog^ sl xal fiLdg ^ovov i^v ^oCQag^ dvo ds coq&v sy- 
yL^ta C6rj^SQLVG>v. 

sx ts drj tovtcov aTtdvtcov^ xal s^ (bv rj^stg a^dtol 
dtd tcbv icps^rjg rj^tv tstrjQrj^svayv tov rjlCov TtaQoScov 10 
xatakafi^avo^sd^a tovg tcov d7toxata6td6scov ^t^dvovg, 
ovts dvL6ov svqC6xo^sv t6 ivLav6Lov ^sysd-og, idv 
JtQog sv tL xal ^i) itots fisv TtQog td tQOitLxd xal L6r]- 
fisQLvd 67]^sta^ Ttots ds TtQog tovg djtXavstg d6tsQag 
d^scoQiltaL^ ovts dXkr]v oCxsLOtSQav djtoxatd6ta6LV trjg 15 
d7t6 tLvog tQOTtLXOv 7] xal L6r]iisQLVov r) xal dXXov 
tLvbg 6r]^sCov tov dLa ^s6cov tcbv ^mdCcov xvxXov 
TtdlLV iitl t6 «vt6 (psQov6r]g tbv 7]Ilov. oXcog ds 
r^yov^sd^a 7tQ06r]xsLV di d7tlov6tSQcov cog svl ^dXL6ta 
v^tod^s^scov td (paLv6^sva dTtodsLXVvsLv., icp' 66ov dv 20 

^7]dsV d^L^XoyOV ix tCOV t7]Q7]6SC0V dvtLTtCjttOV tf] tOL- 

avtf] 7tQ0%-s6sL (paCv7]taL. oti ^sv toCvvv 6 TtQbg tdg 
tQ07tdg xal 7tQbg tdg L67]^SQCag d^scoQOv^svog ivLav6Log 
XQ6vog ild66cov i6tlv tr]g i7tl tatg t^s r]^SQaLg tov d' 



1. iyKSifi4vag D, corr, D*. 3. cpuLvofisva] C'D, cpcavo- 

(i^vag BC. d^eooQovfiEv^ corr. ex d-sooQOviisva D. tav] corr. 
ex ta>L D^. 6. av c(L6d"r}t6v~\ corr. ex ccvaiGd-rjtov B^, corr. 

ex av aia&^qtcog D^ 6vve§aLvev] -v del. D^. 7, (lovov tjv^ 
corr. ex (i6vr]g D^ 15. -S-fcop^Tat] E, dscoQSLtaL BCD. 19. 
Sl'] di B (h. e. ^ta). 20. aitodsL-KvvsLv] corr. ex dno- 

SSL-HVVSL B^, dSLKVVSLV D. 21. dvtLltLTttCOV C. 22. tOLvvvl 

ovv D. 7 mg. D. 23. TtQ^e] om. D. 24. s6tL D, comp. B. 



k 



202 KAATAIOT nXOAEMAIOT 

%Q06%"rixrig, cpavsQOv rj^tv ysyovsv kuI di d)v b^^lTtTCaQ- 
%og aTtsdeL^ev^ no^ca de ekd66mv e6xCv^ d6(pake6xaxa 
^ev ovx oiov t' av yevoixo la^elv xfjg xs xov d' naQ- 
av^7]0e(os ejcl TtXeCova exrj TtQog ai6d^6iv aTtaQakkdxxov 
6 (isvov6Yjg did xb sXdxL6xov xfjg diacpoQag xal dtd xovxo 
xaxd xiiv dtd ^axQoxsQov xQOvov ^vyxQL^tv dvvanevrjg 
xfjg evQL67co^ievr]g xcbv rj^eQ&v enov^Cag^ tjv det xotg 
^exa^v xfjg dtaexdaecog exe6iv STti^SQC^siv^ Tcal iv 
7tXsCo6i xal sv sldxxo6iv sviavxotg xfjg avxfig d'sa)QSi6%'ai' 

10 kafi^dvoixo d^ dv syyi6xa dxQiP&g rj xoiavxrj dTto- 
xaxd6xa6ig^ b6(p dv b ^sxa^v xav 6vyxQivo^svG)v xrjQij- 
6SG)v XQ^^^S ^lsCcov svQC6xrixai. xal ov fiovov sitl 
xavxrjg xb xoiovxov ^v^pe^rjxev^ dXXd xat eiti %a6G)v 
XG)v 7teQiodiXG)v d7toxaxa6xd6eG)v' xb yaQ TtaQa xrjv 

15 avxcbv XG)v xrjQ7]6eG)v d^&eveiav^ xdv dxQi^cog ^ed-odev- 
ovxai, yivo^evov didi;ev6^a ^Qa^v xal xb avxb eyyi6xa 
VTtaQxov G)g TtQbg xfjv jtaQ avxd al^&rj^iv e%C xe xmv 
did (laTCQOv xal eTtl x&v 8i bXCyov XQ^'^^'^ (patvo^e- 
vov eig ekdxxova ^ev eTti^eQi^o^evov exrj fiet^ov itoist 

20 xb eviav6iov d^aQxrj^a xal xb ex xovxov xaxd xbv 
^axQbxeQov xQ^^^ov S7ti6vvay6}isvov^ slg TtksCova d\ 
^ka66ov. 

bd^sv avxaQXsg 7tQ067]xsi vo^C^siVy sdv^ b6ov 6 
fisxa^v ;u^oVo? rj^av xs xal d)v ys e^o^ev Ttakaicbv 



1. yeyovE D. 2. ccnadsi^s post. ras. 1 litt. D. sotLv 

iXdaGoiv D. 3. ts'] BC, ys B^D. 8. iv nlsCoai] corr. ex 
i(i nXsioaiv D^ 10. kocfipdvoivto D, corr, D^ 12. XQOvog] 
corr ex xQovoig C^; bis D, corr. D^. 13. tavtrjg'] tavtji BC, 
avtf]g corr. ex avtog in scr. D, tavtr]g D^ 15. t&v] bis D, 
corr. D*. iisd-odsvovzai CD, corr. C*D^. 16. ycyvoiisvovJ). 
didtpsvafia] corr. ex didipsv^a D^. 18. xqovcov D. 20. 

%ai] del. C^Dl 21. 8s] corr. ex dt' C^D». 24. sxoi^sv] 

corr. ex ^;^Gj/xfi; in scr. D, sxcofisv BC. 



MAGHMATIKHS STNTASEiiS T'. 203 

a^a ocal ocxql^cov trjQYJ6scov dvvatai 7tQO07Coif}dac tfi 
TG)v TCSQLodcKCJV VTto&d^scov iyyvtrjZL, to6ovtov Tcal 
avtol JtstQad^a^sv 6vvsL6svsyxstv xal ^rj ixovteg dfis- 
X'tj6c3^sv tfjg 7tQ067jxov6r]g i^stdascag^ tag ds tcsqI oXov 
tov aicbvog rj xal tov ^axQa tLVC 7CoXka7tla6Cov tov 5 
xata tag trjQ7]6sLg xqovov dLapsPaLco6SLg dXlotQLag 
(pLlo^ad^SLag ts xal cpLlaXrjd^SLag rjycy^sd-a, svsxsv ^sv 
ovv TtaXaLOtrjtog a% ts VTto t&v TtSQl Mstcova xal 
EvTctrj^ova tstrjQrj^svaL d-SQtval tQ07tal xal aC ^istd 
tovtovg 'i)7tb tc3v TtSQL ^AQL6taQ%ov 6q)SLkoLSv dv sig lO 
triv 6vyxQL6LV tcbv xad-' rj^dg ysysvrj^ivcjv TtaQaXa^- 
^dvs6d-aL. svsKsv ds tov xad^olov ts tdg tcbv tQ07ta)v 
triQ7]6sLg dv6dLaxQLtovg slvaL xal 7tQog tovtOLg tdg V7t 
ixsLVcjv 7taQadsdoiisvag 6Xo6xsQi6tSQOv sUrj^fiivag^ d)g 
xal T« ^l7t7tdQ%G) doxst cpaLVS^d^aL^ tavtag ^sv 7taQrjtr]6d- 15 
fLsd^a^ ^vyxsxQTj^sd^a ds 7tQbg tr]v 7tQoxsL^ivr]v 6vy- 
XQL6LV talg t&v L6r]^SQLG)v tr]Q7]6s6L xal toi^tcov dxQi- 
^sCag svsxsv talg ts V7tb tov ^l7t7tdQ%ov ^dkt^ta 
iTtL^rj^avd^sC^aLg d)g d6(paXi6tata sCXrj^^ivaLg V7t 
avtov xal tatg 'btp rjn&v a^vtcov dLa tG)v slg td tot- 20 
avta xatd trjv dQ%r]v trjg 6vvtd^scog {)7todsdsLy[iivc3v 
6QydvG3v ddL6tdxtG)g ^dXL6ta tstr]Qr]^ivaLg' i^ g)V 
s^vqC^xo^sv iv totg t syyL6ta sts6Lv hlcc 'f]^iQo: 7tQ6- 
tSQOv ytvo^ivag tdg tQ07tdg xal L6r]^SQCag tf]g xatd 



1. Svvatcci] mut. in 8vvr]rocv B*. 7. (piXo^ad-Cccg D. 8. 
vitb rmv nsQC] supra scr. D, in textu •/, nsQl tda. 9. Q^eqivuC^ 
om. D, yQ. Y.ul d-SQLvccC supra scr. D^. at] om. D. fitrcc 
rovrovgl jLi.fr' avrovg D, deinde ins. av D^ 17. rars] ratg 

rs D, corr. D^ rriQtiosrGi C, riqQijosoov D. 19. iTtiorjfiav- 
^rjoaig C, corr. C^, sed euan. mg] add. mg. B^. Scocpa- 
Xsorara] corr. ex aoq^aXsotdrag D', ao- corr. ex comp. ao B^. 

22. adiGrd-nrcog] corr. ex ddiord%ra) D^; hic calamum mutauit C. 

23. iv] om. C. srsoi D. 24. rdg] ins. D^ -/lat] >tai tdg D. 



204 KAATAIOT nTOAEMAIOT 

t6 d' inl ratg t^s rjfisQcctg S7tov6iccg. iv ^lv yaQ tm 
A/3' £t£L tfjg y' Kccta KdkiTtnov TtSQcodov iTtedrniYivato 
lndXL^ta tijv fistOTtcjQLvrjv i^rj^SQLav 6 "l7t7taQ%og cjg 
dxQLp£6tata t£triQriii£vriv Tcal ijtLX^koyL^d^aL (prjalv 
5 avtijv y£yov£vaL tfj y' tcbv ijtayoiiivcav tov ii£6ovvxtLOv 
tov £Lg tijv d' <p£QOvtog' TcaL i^tLv tb £tog Qorj' aTtb 
trjg 'AX£^dvdQov t£X£vtrjg. iL£td ds 67t£ £trj tm y' hsi 
^AvtGiVLvov^ i6tLV v^y' ditb tr^g 'AX^^dvdQov t£X£vtrjg^ 
rin£Lg itrjQtjaa^^v decpaXi^tata TtdlLV tijv ^£to7tcoQLviiv 
10 i6ri^£QLav ysy^vrj^ivrjv tfj d'' tov 'AQ-vq ^£td aCav 
&Qav £yyL6ta trjg roi) rjlLOV dvatoXfjg' i7tika^£v ccQa 
ri d7tOKatd6ta6Lg i(p okoLg Alyv^ttLaKotg 67t£ £t£6L, 
tovti6tLv totg dvd t^£ rjy^iQagj tdg 7td6ag o xal d' 
xal £lxo6tbv £yyL6ta ^Lccg rj^iQag dvtl tcov xatd tijv 

15 tOV d' i7tOV6LaV i7tL^aXX0V6G)V tOtg 7tQOX£L^ivOLg £t£6LV 

rin£Qcbv 0« d'. co6t£ 7tQ6t€Qov yiyov£v rj d7toxatd6ta- 
6Lg tfjg TtaQa tb d' i7tov6Lag rjfiiQoc ^ta l£L7tov6fj tb % 
^iQog £yyL6ta. 

G)6avtcog d£ Ttdktv 6 ^hv "l7t7taQ%6g cprj^LV tijv iv 

20 tm 7tQ0K£L^ivC!) Aj3' £t£L tfjg y' Xatd KdkL7t7tOV 7t£QL6d0V 

iaQLvijv l6rj^£QLav dxQLpi^tata trjQrjd^^t^av y^yovivat 
tfi K^' tov M^xIq 7tQOLag' xaC i6tLV tb itog tb Qor{ 
dTtb tfjg 'AX£^dvdQov t£l£vtf]g. rj^£tg d£ tijv ^£td td 



1. rjiiigccg D. 2. KdXLmcov] BC, KdXXiTcnov D. inL- 

crj^i^varo D, corr. D^ 7 ™&- ^- ^^- ^Gr}(iSQLav] larj- in 

ras. C. 11. aiQav] ijfiiQav B. 12. iqp'] renouat. (ex vcp') D^ 

13. TovT^otL C, comp. B. rots] supra scr. D^. o] r^^s- 
Qas o D. 15. iitLpalova&v C. 16. oa d'] corr. ex o oa D^ 

17. jLtta] corr. ex TCQmxri D^. 19. "inaQxog D. cpr]aLv] -v 
del. D*. ' 20. KdlLnnovi BC, KdlXLmcov D. 21. coiQL^Eata- 
trjQrj&SLaav C. 22. tjj] corr. ex tfjg D^. Ms^slq D. iatLv] 
-V del. D^, satL C, comp. B. to (alt.)] y.atd tbv s%atoat6v D, 
xara tov del. D^. 23. ta otcs] ras cri D. 



MA0HMATIKHS STNTAgESiS T'. 205 

67C£ o^oicjg £trj ra v%y' ccito Tijg ^AXs^dvdQov tsksvrrjg 
iaQLV^v L6r]^£0Lccv £VQL6xo^£v y£y£vrj^£vr]v rfj J' rov 
na%a)v ^£ra ^oav coQav £yyL6ra rr]g ^£6rj^PQLag^ (bg 
xal ravtrjv ri^v 7C£qlo8ov £7t£L^rjcp£vaL rag l'6ag rj^^Qag 
o xal d' Tcal % £yyL6ra dvrl rcov TtQog ro d' £7tLpaX- 5 
Iov6g)v rotg 67t£ £r£6LV rj^^QCJV od d\ 7tQ6t£QOv aQa 
7ca\ ivtavd^a y£yov£v r] tr^g iaQLvfjg L6r]^£QLag d^toxatd- 
6ta6Lg trjg TtaQa to d' i7tov6Lag rj^iQa ^La X£L7tov6rj 
To %' ^iQog. C36t£ i7t£l tbv avtbv £%£l loyov td t£ t 
£tr] TtQbg td 67t£ Tcal r] ^Ca r]^iQa 7tQbg tr]v ^tav 10 
X£L7tov6av tb % ^iQog^ 6vvdy£taL, dLOtL xal iv totg t 
£t£6Lv £yyL6ta 7CQ6t£Q6v i6tLv tfjg xatd tb d^ i7tov6Lag 
i] TtQbg td i6r]ii£QLvd 6r]^£la yLVO^ivr] tov r]lLOv d7to- 
xatd6ta6Lg rj^iQa d. 

xdv 7tQbg tr]v V7tb tCov 7t£Ql Mitcjvd r£ xal Evxrt]- 15 
^iova r£rr]Qr]^ivr]v d^^QLvr^v rQ07tr]v cag blo6%£Qi6r£QOv 
dvay£yQa^liivr]v ri]v 6vyKQL6Lv 7taXaL6rr]rog £v£xsv 
TtOLr^^a^^d^a rrjg vcp r^iicbv cog £Vl iidU6ra ddL^rdxrcog 
£7tLl£XoyL6^ivr]g^ rb avrb rovro £VQr]6o^£v. ix^Lvr] ^hv 
ydQ dvayQdcp£raL y£y£vr]^ivr] i^tl 'A^£vdovg dQ%ovTog 20 
Ad^TJvr^^L ;(aT' Alyv^trCovg 0a^£VG)d' %a TCQcoCag^ r^^stg 



2. saQiVT^v^l corr. ex iaQLvf]L D. y£ysvvriiievr]v C, ysy^ysvr]- 
liavrjv D. ^'] t^ B, corr. mg. B^ 3. atQccv'] rjfidQav B. 

syyvata mQav D. 4. ttjv] om. C. i7C7]XsL(pivaL D, 6. 

oa6"] a A D. 10. £T7]] supra scr. C. ta] D, xds BC. 

11. To] D, TtQog x6 BC. 12. iGXLv] comp. B, sGxaL D. 14. 
a] BC, ^La D. 15. 7 ^^g- D. v.av] B, xat CD, -Aal sl 

C^D^. Supra xr\v scr. D, del. D^ xs\ om. D. 17. ava- 



H-, 



ysyQaasvrjv C. 18. noirjamfisd-a] corr. ex noLrjaofisd^a C, 

-amfisd-a in ras. B, TCOLrjadfisvoL D, noLriaofisd^a corr. ex noLr]aoo- 
fisQ^a D^ T?5g] corr, ex xr}v D*. 19. inLXsXoyiafisvr^v D, 

corr. D^ 20. ysysvvr]fisvr] C. 21. TtQcoLas] tcsql xj]v aQxr]V 
xfjg 'qfiSQag D. 



206 KAATAIOT nTOAEMAIOT 

ds rrjv iv tc5 TtQoxsL^evc) v^y' £t£L ccjcb rrjg ^Xs^dvdQov 
rsX^VTTlg a6cpakG}g £7t£koyL6d^£%^a ysyovsvai rij la' tov 
M£€oQ^ (i£ra /3 coQag iyyvg rov £Cg rriv i^' ^£6ovvxrLov' 
Tcat i^riv ra ^hv ccTth rf}g £7il rov ^Ail}£v8ovg dvay^yQa^- 
o ^ivrjg d^^QLvrjg rQOTCrjg ^ixQL rfjg vTtb rcov 7t£Ql Aqi- 
6raQ%ov r^rrjQrj^ivrjg rS v' £r£L rf^g jtQCorrjg xard 
KdlLTtTtov TtsQLodov^ xad^hg xal 6 l7t7taQ%6g (pr]6LVj 
hrj Qvpy td dh djtb rov 7tQox£L^ivov v' irovg^ o ^v 
xard rb ^d' hog d7tb rrjg 'AX^^dvdQOv r£l£vr rjg^ ^^XQ^ 
10 rov v^y' rov xard rijv rifi£riQav rriQrj6LV irrj VLd'. iv 
roig fiera^i) ccQa rfjg oXrjg dLa6rd6£C3g cpoa £r£6Lv^ idv 
r] V7tb tcbv 7t£Ql Evxtrjfiova t£trjQrj^ivrj d^^QLvrj tQO^trj 
7t£Ql trjv dQxrjv tfjg tov 0a^£vhd' xa fj y£y£vr]^ivi]y 
7tQ06y£y6va6Lv i(p oloLg AiyvTttLaxoig £t£6Lv rj^iQat 

15 QJiC y' £yyi6ta dvtl Qfi^L' ^' t^^v totg cpoa £r£6Lv 
xard rrjv rov d' i7tov6Lav i^tL^aXXov^&Vy C36r£ 7tQ6r£Qov 
yiyov£v rj ixx£L^ivrj d7toxard6ra6Lg rrjg xard rb d' 
i7tov6Lag rj^iQaLg dv6L k£L7tov6aLg r» l^' ^Ldg ri^iQag. 
(pav£Qbv aQa xal ovrcog yiyov£v^ orL iv oXoLg rotg % 

20 £r£6LV rdg dvo 7tlriQ£Lg £yyL6ra rj^iQag 6 ivLav6Log 
XQ6vog 7tQoXa^pdv£L rfjg xard ro d' i7tov6Lag. xal dt' 
^XXcjv d£ 7tl£L6vG)v rrjQij^^CDV ri^£tg r£ rb avrb rovto 

6V^PatV0V £VQL6X0^£V Xal tbv "l7t7taQXOV 6QG)fl£V 

7tl£ovdxLg avt& ^vyxatatLd^in^vov £v t£ ydQ rc5 II£qI 
25 ivLav6L0v fisyid^ovg 6vyxQLvag tfjv VTtb AQL6tdQxov 



1. icno^ t&v 6cn6 D. 2. snEXoyL6a,iL£Q-u\ D*, snsXoyried- 

liE^a BC, inLXoyiGdfisd-cc J). 7 ^S- ^- '^V '-^'1 corr. ex 
tfjt a D^. tov^ t- e corr. C. 3. MegoqC BD. mqag 

$vo D. iyyiGta D. 4. iGti D, comp. B. kni\ supra 

scr. BD*. Tov] supra scr. D^ 5. tqonf\i &sQLvfjg B. 

d^sQivfig] e corr. D^ f^^XQ''! "^ renouat. D^. 7. KdXinnov^ 
BC, KdXXinnov D. 9. v.atd to\ om. D. 10. -u^y'] i;|y' 

stovg D. 13. r^s] tfig xa D. xa'] om. D. 15. y'] 

tQLtov e corr. D^ hs6L D. 17. 17 stiyisi^ivr] ysyovsv B. 

18. Td5] corr. ex to C, ex tatg t&v D^ 19. Torg] om. D. 

20. stsGiv] B, stsGL CD. nX7]QTn C. 24. yao] corr. ex 

taQ B^C^ 



MA0HMATIKHS STNTAHESiS T'. 207 

tstrjQrj^evrjv d^SQtviiv xqotc^v rcl v' hai XriyovTi tfjg 
TtQCjrrjg Kata KdXtJtTCov jtSQtodov tfi vcp iavtov jtdXtv 
dxQiP&g sUrjii^evT} r« ^y' stec krjyovtt tfjg tQttrjg 
xatd KdliTtTtov TtSQiodov q)rj6lv ovtcog' ^^dfjXov toCvvv^ 
otL iv totg Q^s £t86iv td%iov yiyovsv rj tQOTtrj trjg 5 
xatd tb d' i7tov6cag td5 rj^t^et tov 6vva^g)ot£Qov i^ 
rj^sQag xal vvKtbg XQOvov"' Ttdkiv te Kal iv ta IIsqI 
i[ipoXc^cov ^rjvcbv te Kal rj^SQCJv itQoentcov^ oti Katd 
^ev tovg TteQl Metcova Kal EvKtr]^ova 6 iviav6iog 
XQovog 7teQie%ei rjfieQag ti,e d' xal og' fitag rnieQag^ 10 
Katd de KdktTtTCov rj^eQag t^e d' ^ovov^ imXeyet Katd 
Xe^iv ovtog' j-^ri^etg de ^fjvag ^ev oXovg evQi6Ko^ev 
7teQie%o^evovg iv totg td" eteGtv^ o&ovg KdKstvot^ tbv 
d' iviavtbv eti Kal tov d' eXa60ov tQtaKo6co6tw ijtt- 
Xa^^dvovta ^dXiGta ^eQet [icdg rj^eQag^ cag iv totg t 15 
eteecv iXXecTtecv JtaQa ^ev tbv Mitcova ri^ieQag i, jtaQcc 
de tbv KdXcTtTtov rj^eQav ^cav"' koc 6vyKe(paXacov- 
fievog de tdg yvco^ag eavtov 6%e8bv dcd tfjg dvayQa- 
q)fjg tcov Idccov 6vvtay^dtcov cprj^lv ovtcog' ^^iSvvtetayx, 
df KoX TteQl tov ivcav6iov %q6vov iv ^cfiXiG) evc^ iv 20 
(p ditoSecKvvco^ otc 6 Kad'^ rjXcov ivcavtog' tovto de 
ycvetac 6 ;c()ovog, iv co 6 r]Xcog ditb tQOjtfjg ijtc trjv 
avtijv tQOTtfjv TtaQaycvetac rj dnb c6rj^eQcag iitl trjv 
avtfjv c6ri^eQiav' neQiixei rj^SQag t^e Kal eXattov rj 
d' ^EQog t(p tQiaKo6io6ta eyyi6ta ^eQet fiidg rj^eQag 25 



2. KdXmnov] BC, KdXXimtov D. t^ — 4. ovtcoq] mg. D^ 

4. KdXin%ov] BCI)^. q)r]olv ovtcog] etiam in textu D. 

5. oTt] ins. D^. 9ft£] corr. ex ^ B. ^'zsglv'] -v del. D*. 
xdxiov] corr. ex xd%siOV CD*. 6. inovGiag'] post n ras. 1 

litt. , -g e corr. D*. :: mg. D. f^] £h te D. 7. Ante 

XQOVov del. Y,ui D^ xt] om. D. 9. Mixmv C. 10. d''] yial 
hi {-i corr. ex rj) J' D. 05'] D, o s' B, Ts B^, d s C. 11. 
KdXmnov] BC, KdXXinnov D. S'] KCii xBxaqxov D. 12. ftfV] 
om. C. 13. > mg. D. 15. fttag] corr. ex ag D^ 17. KdX- 
innov] BC, KdXXinnov D. xat'] om. D. 21, 6] D, om. BC. 
I: mg. D. 23. naQayCyvExai D. 24. sXaacov D. 



208 KAATAIOT nTOAEMAIOT 

xccl vvxtog^ Tial ov% &)g oC ^ad^rj^atLKol vo^it,ov6Lv avtb 
t6 d' STtdys^d-aL ejtl ta eiQrj^svG) TtXYJd^Si tcjv rj^SQ&v^^. 
ori iisv ovv ta ^s%Qi rov dsvQO cpaivofisva jtSQi 
tb ^sysd-og tov sviavoCov %q6vov tfi jtQosiQrj^svr} TtQbg 
5 ri)i/ t&v tQOTtLKcbv ocal C6rj^SQivc3V 6rj^Si(DV aTtoxatd- 
6ta6iv TtrjkLKotrjtL 6vvtQS%Si Tcatd tijv tcbv vvv TtQog 
td ^QotSQov biioloyCav^ (pavsQbv ol^ai ysyovsvai. 
tovtcjv d' ovtcjg s%6vtov^ sdv S7tL^SQi6cj^sv tijv ^Cav 
rjiiSQav sCg td r strj^ STti^dlksi SKd^tco stsi ^iccg 

10 rj^sQag s^rjK06td dsvtSQa i^j ditSQ sdv dcpsXco^sv djtb 
tcjv trjg xatd tb d' S7tov6Cag t^s Ts^ s%oiisv tbv STti- 
^rjtov^svov sviav6iov %q6vov rj^sQ&v t^s id ]irj. 
to6ovtov ^sv dri TtXrjd-og tcbv rj^SQCov strj dv syyi6ta 
riiiiv iog svL ^dXL6ta s% rcov naQ^vtcov sCXrj^iisvov. 

15 svsxsv ds tfjg sitC ts tov r\XCov Tcal tcbv dXXcjv TtQbg 
tdg TtaQ SKa^ta yivo^svag avtcbv naQbdovg S7ti6KStlJScog^ 

rjV 7tQ6%SiQOV Ttai &67tSQ SKKSL^SVrjV TtSCpVKS 7taQS%SLV fj 

6vvta^ig tfjg %atd ^SQog xavovo^toiCag^ ^tQ^d-s^iv ^sv xal 
6K07tbv rjyov^s&a dstv V7tdQ%Siv tm iiad^rj^atiK^ dst^aL 

20 td (paivo^sva sv ta ovQavco 7tdvta di biiakcbv Kal syKVK- 
XCov KiV7]6scjv d^totsXov^sva^ 7tQo67]Kov6av ds xal 
aK^Xovd^ov tfj tOLavtrj TtQod^s^SL iidkL6ta Kavovo7tOLCav 
trjv %coQCt,ov6av fisv tdg xatd ^iSQog b^aXdg KLvfj6sLg 
d7tb tfjg dtd tdg tcbv kvkIcov 'i)7tod's6sLg doKOv6rjg 6v^- 

25 ^aCvsLV dvco^aXCag^ TtdUv ds sk trjg ^C^scog xal tfjg 6vv- 
aycoyfjg tovtcov diicpotSQCov tdg cpaLVO^svag avtcbv 7taQ- 
6dovg d7todsLKVvov6av. %v ovv rj^tv Kal tb tOLovtov 
sidog sv%Qr]6t6tSQ0v Kal 7taQ' avtdg tdg d^todsC^SLg vxb 
%stQa Xa^^dvrjtaL^ ^tOLrj^b^sd^a svtsvd^sv tfjv sKd^s^LV tcbv 

30 Katd ^SQog b^aX&v tov fjXCov XLvfj^scov tQ67t<p tOLSds. 

1. avto] corr. ex ccvTm D*. 4. TtQoasiQrjfiivr] D, -6- eras. 

5. aTto-nciTdGTccOLv] pr. r e corr. C, -lv corr. ex -ft D^. 11. 

STtovoiag] corr. ex sniovoCaq D^ Deinde add. rjiiSQobv D et 

supra scr. B^ Ts] corr. ex id JJLfj D^. 13. Ante tooovtov 

del. ro D^ 14. sllrjfifisvoiv D, corr. D^ 25. ovvaycoyqs D, 
av del. D^ 27. Hva D. 29. TtOLrtGm^sd-a D. 



MA0HMATIKHI; STNTASESiS T'. 209 

trjg yccQ ^tag cc7Coxata6rd0s(Dg aTtodsdsLy^evrjg rjy^s- 
Qav t^s 1,6 jl^, sccv STti^SQL^coiisv sig ravrccg rag rov 
ivbg xvkIov ^oigag t|, s%o^sv rb r}iiSQ7]6LOV fis6ov 
XLvrj^a rov ^jXlov ^olqcov o vd' rj l^ Ty l^ Xa syyL^ra' 
aQ%i6SL yaQ ^s^ql ro6ovrcov s^rixo6rcbv rovg ^SQL6fiovg ^ 
xovrcDv 7tOLSL<Sd-aL. TtcckLV rov fj^SQrjaLov XLvri^arog 
Xaii^dvovrsg rb xd' s%o^sv rb cjQLatov ^olq&v o ^ x^ 
V jiy y a syyL6ra. o^iOLCog rb rj^SQTj^Lov 7tokXa7tXa6id- 
6avrsg STtl ^sv rdg rov svbg ^rjvbg rjfisQag X s%o^sv 
^s0ov KLvrj^a ^rjvLatov ^olq&v xO' Ad ^ Ag Ag ti A, 10 
S7tl ds rdg rov a AlyvTtrtaKov srovg rj^sQag r^s 
s%o^sv svLav6L0v ^s6ov XLvrj^a ^olq&v rvd" jis xd jis 
%a rj Xs. Ttdktv rb svLav6Lov Ttolkaitka^Ld^avrsg STtl 
srrj Trj dLa rb cpavrj^o^svov 6v^^srQ0v rfjg xavovo- 
yQacpCag xal dcpslovrsg olovg xvzkovg s%o^sv Trjsrrj- 15 
QLdog S7tov6Lav ^olqcov rvs X^ xs Xg x Xd X. 

srd^a^sv ovv xavovLa rfjg b^aXfjg XLvr]6scog rov 
rjlLOv y^ sxa6rov STtl 6rL%ovg ^sv 7tdkLV Jis^ ^^QV ^^ 
dvo' 7tSQLS^SL de t6 ^sv TtQ&rov xav6vLOV rd rcbv Trj- 
srrjQLdcov ^e6a XLvrj^ara^ rb ds /3' 7tQG)ra rd sviav6La 20 
Tcal V7t avrd rd cjQLata^ rb ds y' TtQcora ^isv rd ^rjVLata^ 
VTtoxdrco ds rd rj^SQ7]6La^ r&v ^sv rov xqovov dQLd-^&v 
sv rotg 7tQ(oroLg ^eQe6L ra66o^evcov^ rrjg ds rcbv ^olq&v 
TtaQad^s^scog sv rotg /3' xard rdg oizsLag sxd6rcov S7tL- 
6vvay(oydg. xai s16lv ol xavovsg roLovroL' 25 

2. t|«] ante £ ras. 1 litt. D. ravta D. 3. t|] seq. ras. 1 
litt. D. to] toCvvv to D. 4. o vd''} corr. ex ovd' D. 6. r}fi8- 
QLOLov C. 7. 7.a§6vteg D. o ^] corr. ex o^ D. 8. o^oCcos] 
6- corr. ex t D. rjpLSQCGLov C. 9. Post a^ofisv del. 17 D^ 10. 

inqvLccLov fiioov xtVrjju-o; D. i?(alt.)] supra scr. B. 11. a] svog D. 

T^f] -£ e corr. D^ 12. ^f mg. D. 16. oyitojyiaLSsyiastrjQL- 
dog D. 17. td^ofisv D. 19. TfistSQidcov C, oxrcoxat^fxaeT?;- 
QLd oiv D. 20. 'KLVTjiiata] in -V7]fiata rursus incipit A fol. 69. 
Ss] U A. 21. ojQLaLa] OQLa la C. 22. ijfisQCoLa AC. 23. tf]g 
^e'] tmv 8s tfig D. 24. TtaQaO^soso^g] corr. ex TiaQad^Cosoov D. 

§'] dsvtsQOLg BD. 
Ptolemaeus, ed. Heiberg. 14 



210 



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MA0HMATIKHS STNTASESiS T'. 



213 



1 

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c^ - g 


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o o o 


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214 



KAATAIOT nTOAEMAIOT 





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r< *< 


r< 


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MA0HMATIKHS STNTASESiS V. 



215 



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216 KAATAIOT nTOAEMAIOT 

y'. IIsqI tG}v xad"' o^aXijv Tcal iyTcvx^cov KLvrj6iv 

VJtod^S^SCJV. 

^E^TjS d' ovtog Kal tijv (paivo^Evrjv dvco^aXiav tov 
7]XCov dsi^ai TiQoXrjTttaov Tiad-okov^ dioti xal aC tcov 
5 7tXavc3^8V(ov eig ta STtd^sva tov oi)Qavov ^stamv7]6sig^ 
&67tSQ xal ri slg td rjyov^sva ipoQd tCbv oXcov^ 6^aXal 
^sv si6iv 7td6ai xal syxvxXiOi tfi (pvGSi^ tovts6tiv aC 
voov^svai jtsQidysiv svdstai tovg dotSQag tj Ttal tovg 
xvxXovg avtcov snl Ttdvtcav aTtXcbg sv tolg l'6oig XQOvoig 

10 l'6ag ycoviag d7toXa^pdvov6iv TtQog totg TcsvtQOtg sxd^trjg 
tcbv TtSQicpOQ&v^ aC ds cpaivo^svai TtSQi avtdg dvco^akCai 
TtaQd tdg d^s^stg xal td^stg tcov sv tatg 6(paCQaig aijtcbv 
xvkXcov^ di G)v Ttoiovvtai tdg 7av7]6sig^ dnotsXovvtai^ 
Tcal ovdsv dXlotQiov avtcbv trjg didiotrjtog JtSQi trjv 

15 'bTtovoov^svrjv tcbv (paivo^svov dta^Cav tcb ovti 7ts(pvKs 
6v^^aCvsiv. tb d' altiov trjg dvco^dXov (pavta6Cag 
xatd dvo ^dXi6ta tdg TtQcotag xal d%Xag v7to^s6sig 
ivdsxstai yCvs^&ai, tfjg ydQ xiV7J6SG}g avtcbv d^scoQov- 
fiivrjg TtQog tbv b^oKSvtQdv ts tS x66^a) Tcal sv ttp 

20 ijtiTtsdGj tov did ^s6ov tcbv ^ipdCcov voov^svov xvxXov^ 
cog ddiacpoQstv TtQbg tb xsvtQov avtov trjv rj^stSQav 
'otfjiv^ avto^bg rjtoi xatd ^rj o^oKsvtQcov ta x66^g} 
TCvxXcov b^aldg vitoXrjTttsov 7tOist6d^ai tdg XiV7]6Sig rj 
Tcatd o^OKSvtQCov ftfV, ov% djtX&g de sit avtcbv^ 

1. y'] mg. BC^ om. AD. 3. ^'] 8s D. ovrmg C. 4. 
nqolrintaiov J) ^ corr. D^ 7. sici CD, comp. B. 10. £v.d6Tr]g\ 
iq)' sKdGtrjg D, corr. D^ 11. nsQLcpoQ&v^ corr. ex nsQKpSQSi&v D*. 

12. td^sig'] -SLg e corr. D^ ta>v — ccv-'\ in lacuna minore 
ins. D*. 13. noL-'] in lac. maiore ins. D^ dcn-'] in lac. D^ 

14. ovSsv] -sv in lac. mai. D^ dXXotQiov'] -ov in ras. 5 litt. D*. 

16. d*] ds D. 17. %atd] v,cctd. td B. 20. iisGov] [lieoov D. 

24. jicctd] Ticctd to C. dnXwg] d- e corr. D^ ds] d' D. 



MA0HMATIKHS 2TNTASESiS T\ 



217 



dXX' STil BteQCJv V7i ixELvcov (fSQOfiEvov^ 7caXov^8va)v dh 
iTCLXVKXcjv. xa%^ ixatEQccv yaQ tovtcov tcbv 'b7Cod'e6ecov 
ivd8%6^evov (pavTj^etai tb iv i^oig avtovg XQOvocg 
avC^ovg (paCve6^ai tatg 6i^e6Lv rj^&v 8LeQ%o^evovg tov 
dLa ^e6c3v tcov ^(pdCcov xvnXov o^oxevtQov ta x60^<p 5 
7CeQL(peQeCag. 

idv te yaQ ijtl trjg ;c«r' iKxevtQotrjta vTCod^e^ecog 
vo7]0cj^ev tbv ^ev exxevtQOv xvx^ov^ i(p ov b^iakcbg 
j^ 6 d6t^Q XLVSLtaL^ tbv ABF^ TCeQl 

xevtQov tb E otal dLa^etQov t^v lO 
AEzl^ ro de Z erj^etov iic avt fig 
triv rj^eteQav oiI^lv^ w6te xal tb 
fiev A tb djcoyec^tatov yCve^d^aL 
^rj^etov, t6 8e A jteQLysLotatov^ 
dTCoXa^ovteg ts l6ag 7ceQL(peQeCag 15 
t7]v te AB xal f^v AF iTCL^ev- 
^o^ev tdg BE %al BZ %al FE %al FZ^ avt6d-ev 
dfjkov e6taL^ dtoTi tdg AB xal FA ^ceQLCpeQeCag exa- 
teQav iv 1'6g} %Q6vcp TCLvrjd^elg 6 d^trjQ dvC^ovg d6^eL 
tov 7ceQl tb Z KevtQOv yQacpoiievov kvxXov dLeXrjXv- 20 
d^ivaL 7ceQL(peQeCag dLcc tb i'6r]g ov6rjg tfig V7cb BEA 
ycjvCag trj V7cb FEA iXd66ova ^ev yCve^d^aL tr^v vTtb 
BZA exateQag avtcbv.^ ^eC^ova de tijv V7cb FZA 
[EucL I, 16]. 

idv t i7cl tfjg xar' i^cCxvxXov v7Co^e6ea}g vorj^co^sv 25 




1. aXXd D. V7t' Bv,sCv(ov\ vtzo^slii^vcov D. 3. xQovoig 

avxovg D. 4. avLGovg^ a- supra ras. 2 litt. D. Sleqx^^^^'' ^^ 
corr. D^ 5. yivyilov~] y,vv,Iov v.aL D. 7. bdv^ av D. fx- 
MfVT^dTTjTo;] £x- iii ras. 1 litt. D^. vnod^^oscov C. 8. ojLtaiwg] 
6- supra scr. A^ 14. J] A xo D. 18. sgxlv D. 8l6xl\ 
supra scr. D^ 19. dd|£t] 8hLh,SL B, 86\sl supra scr. B^ 20. 
To] corr. ex Tdv D. 22. t^] seq. ras. 1 litt. D. 25. t'] xs D. 



218 



KAATAIOT nTOAEMAIOT 



zbv ^ev 6^6xsvtQOV ta dia ^80(dv tav ^aydicjv zvxlov 

tbv ABFJ TtSQl TcsvtQov ro E xal dLccfistQov tijv 

AEF^ tbv d' STt^ aVtOV CpSQO^SVOV STtiKvxkov^ s(p ov 

nivsttai 6 a6triQy tbv ZH&K 
5 tcsqI KsvtQov tb A^ cpavsQbv 

xal ovtcjg avtdd^sv s6tai^ didtu 

tov STtLocvxXov b^aX&g diSQXO- 

ybsvov tbv ABFzI tcvkXov cjg 

dnb tov A Xoyov svsxa sjtl t6 
10 B xal rov d^tSQog tbv STtC- 

Kvxkov^ otav ^sv xata t&v Z 

xal & ysvYitau 6 d^tTJQ^ ddta^po- 

Qcjg g)av7]0staL rc5 A xsvtQCO 

tov STtLxvxkov^ otav ds xata aXlcjv^ ovxstL^ dXXd 
15 xata \isv tov H ipsQS SLTtsiv yLvb^svog TtXsCova do^st 

TtSTtOLfjad^ai xCvrj6LV tfjg b^aXijg r§ AH 7tSQL(pSQsCa^ 

xatd ds rov K sld66ova o^oCcog tf] AK jtSQL(psQsC(x. 
STtl iisv ovv trjg toLavtrig ;car' sxxsvtQOtrjta VTto- 

d^s^scog dsl Cv^^sprjxs trjv ^sv sla%C6triv xCvyiOlv xatd 
20 ro dTtOysLOtatov TtaQaxoXovd^stv^ trjv ds ^syCdtrjv xatd 

ro TtsQLysLOtatov^ sitsl xal Ttdvtots rj vjtb AZB ycjvCa 

sXd66cov s6tlv trjg vjtb z/ZF, snl ds rijg xat sTtCxvxkov 

d^cpotSQa dvvatat 6v^^aCvsLV. tov yaQ STtixvxkov slg 

td STto^sva tov ovQavov triv ^std^a6Lv JtoLov^svov^ 




1. fi^v] ^ D, ft D^. 3. d'] seq. ras. parua A. 9. ano] 
in ras. B^. A Xoyov] aXoyov C. avstiEV D. 10. B] corr. 
ex a D^ 11. Ante fiiv ras. 1 litt. B. xara] ini D. 12. 
ysvTjrat,'] corr. ex ysCvrixcci A, yCvritai D. adiacpoQOig] A, corr. 
ex dtaq^OQCDg B^C^D^. 13. tov A 'HSVtQOv D. 14. 

15. nXsova D, corr. D^ 17. AK] A- renouat. B^ 
tpEQsCat corr. ex nsqicpiQbiai D. 18. ovv] om. B. 
TTjra D, corr. D^. 19. aisC D. Gvfips^rjyisv D. 
comp. B. 24. ^Etd^aai C. 



XOTT D. 
TtSQL- 

8y%svtQa)- 
22. s6tC D, 



MAOHMATIKHS SiTNTASESiS T'. 219 

(hg Xoyov svsxev aito tov A i%\ ro .B, ikv ^sv 6 
d^trjQ ovtcog iv ta STtLXVKkG) TtouYitaL tijv xivrjeiVj 
a6t6 tijv aTto tov aTtoysiov ^8td^a6iv slg ra STto^sva 
TtccXLV aTtotsXst^d^aL^ tovts6tLv aTtb tov Z cog sjtl tb 
H^ Katd tb dnoysLOv tijv (isyL6tr}v naQodov yCvsed^aL 5 
6v^^7]6staL dLa tb sitl ta aiftd t6v te iTtLxvxXov tdts 
oial tbv d6tSQa XLVSt^d^aL^ sdv ds rj ditb tov ditoysLOv 
tov d6tsQog ^stdpa6Lg stg td TtQorjyovfisva toi) sjtL- 
xvkXov yLvrjtaL^ tovts6tLV djtb tov Z cog sitl tb JT, 
xatd t6 dTtoysLOV dvdnaXLv rj sla%L6tri jtaQodog dito- 10 
tsls6d^ri6staL dLd tb sig td svavtCa trjg tov STtLKVTcXov 
(ista^d^sog tbv d^xsQa tots ^staKLVSt^d-aL. 

tovtcov d' ovtcog s%6vtG)v sg)S^rjg KdKstva %QoXrpt- 
tsov^ otL ts STtl [isv tcbv dL66dg noLOv^svcjv dvco[iaXCag 
d^cpotsQag tdg v7to%^s6sLg tavtag svds%staL 6v^7fs- 15 
%Xs%%aL^ (og sv totg %sq\ avtcbv d%odsC^o^sv^ s%\ ds 
tG)v ^ta Ka\ tfj avtfj KS%Qrj^svcov dvco^aXCg: Ka\ (iCa 
tGiv SKKSLiisvcov v^od^s^scDv dQKs6SL^ Ka\ otL %dvta td 
(paLvo^sva xaO*' SKatsQav avtcbv d%aQaXXdKtcjg d%o- 
tsXs^d^tj^staL tcbv avtcbv X6ycov sv d^cpotSQaLg %sqls%o- 20 
fisvcov^ tovts6tLV otav^ ov s%SL X6yov rj ^sta^v tcbv 
KsvtQCov s%\ trjg Kat SKKSvtQ6trjta v^od^s^scog tfjg te 
oipscog Ka\ tov SKKSvtQOv kvkXov %Qbg trjv sk tov 
KsvtQOv tov SKKSvtQov^ tovtov s^T} tbv X6yov s%\ tfjg 
Kat s%CkvkXov v^od-s^scog rj sk tov KSVtQov tov s%l- 25 
KvxXov %Qbg tijv ix tov KsvtQov tov (pSQOvtog avtbv 
kvkXov^ Ka\ stL sv o6(p %Q6vq) tbv SKKSvtQov kvkXov 

2. TtoLSLtat B. 3. ocTtoyBLOv] e corr. D^. etg \ td corr. 

ex st\6td A^. 5. MccTa] -td supra scr. D^ 8. sig] stil D. 

10. slaG%LGtri ^- l^- ^9H^(7ft] -el renouat. inter duas ras. D^ 
21. sxri D. 1^] mg. D^. 23. Supra xov add. v.bvtQov 

tov D*. 24. sxril A, sxet BCD. 27. stL Jv] corr. ex tGtL D^ 



220 KAATAIOT nTOAEMAlOT 

6 d6rrjQ cjg sig tcc STCo^eva TtOLOv^svog triv xcvrj6LV 
a^stdTttcotov ovtcc diccTCOQevetaL^ iv to6ovt(p xal 6 ^sv 
eTCLKvxXog tbv o^dxevtQov tfj oil^eL xvxXov dLeQ%ritaL 
itdkLv G)g elg td eico^eva ^etaxLvov^evog ^ 6 d' d^tijQ 
5 tbv ejCLXvxXov l6ota%S)g^ hg ^ievtoL tfjg xatd ro dico- 
yeLov ^etapd^ecog eig td TCQorjyov^eva yLyvo^evrjg. 

otL de tovtcjv ovtcjg vTCoxsL^evov td avtd TCeQL 
exat eQav t&v VTCod^e^ecjv (paLvo^eva 6v^p7]6etaL^ dta 
PQa%eG)v eq)odev6o^ev dcd te t&v X6yc3v avtcbv xal 

10 fietd tavta xal d^d t&v itpodevo^evcov ev avtotg eTcl 
trjg tov rilCov dvco^alLag dQLd^^&v. 

Xeycj dri TCQ&tov^ otL xad-^ exateQav avtG)v rj ^e- 
yL0trj dLaq)OQd yCvetaL tfjg b^aXfig XLvrjaecjg TcaQd trjv 
q)aLvo^evrjv dvco^aXov^ xad-' rjv xal rj ^e6r} TCaQodog 

15 tcbv d6teQG)v voettaL^ otav r] q^aLvo^evrj dLd6ta6Lg dicb 
tov dnoyeCov tetaQtrj^oQLOv djco?.a^pdvf] ^ xal otL 6 
dicb rov dicoyeLotdtov {lexQC tfjg eiQrj^evrjg ^86r]g 
7CaQ6dov ;updvog ^eC^mv e6tl tov dicb tfjg fie6rjg enl 
ro 7ceQLyeL6tatov. od^ev 6v^^aCveL xatd ^ev trjv t&v 

20 exxevtQCov vTC^d^e^LV deC^ xal xatd tijv t&v iiCLXvxXcsv 
de, otav ai djcb tcov dTCoyeCcov avtcov ^eta^d^eLg eig 
td 7CQor]yov^eva yCvcovtai^ tbv dnb tfjg eka%C6trig XLvrj- 
6ecog enl tijv fie6i^v iq6vov ^eC^ova yCve^d^aL roi) dnb 



3. di8Qxstca D. 4. ^'] ^^ D. 5. Ante mg del. (lev D*. 
T^g] rfjg I tfjg B. 6. yivoiiivrjg D. 7. — > mg. D. 8. 

cpuLvdfisvcc] alt. V corr. ex q C. 9. ts'] corr. ex S^ D^. 10. 
^ta] seq. ras. 1 litt. D, om. B. s(podsvo(isvcov'] AD, -svcov 
euan. B, stpodsviisvcov C, s(p(o8sv[isv(ov D'. 11. tov iilCov] 

TjlLayifig D. 12. avtcov] -{Jb- in ras. A. 13. b^icclfig] -fj- 

e corr. A. 14. avdtiiaXov] corr. ex avoafiaXLav D^. 15. 

didetaGLg] -6- del. D^ 16. 6] ins. D^ 19. oQ^sv] corr. ex 
OTtSQ D^, supra scr. yQ. onsQ. avv^aivsL A. 22. yCvojvtaL'] B, 
ylvovtai AC, yiyvcovtai D. 23. yCvsG^aC] -i- e corr. D^ 



MA0HMATIKHS STNTAgESiS T'. 221 

rrlg ^86r]g btiI trjv ^6yL6t7]v dia ro Tcata t6 aTtoysiOV 
£v exaxBQa triv ikaxC^triv jcaQodov aTCotsXsidd-ao^ xata 
ds trjv slg tk STto^isva tav S7a7iv%lG)v tag aito tov 
aitoysiov Jtoiov6av TtSQiaycjyag tcov d^tsQCJv dvccTtaXiV 
tbv ccTCo tijg fisyi0trjg xivrjascjg inl trjv ^£6r}v XQOvov 5 
(isi^ova yivs^d-ai tov dito tf^g ^£0r]g iitl tr^v iXaxi6tr]v 
Sid t6 zal svtavd^a xatd tb dTtoysiov tijv ^syidtrjv 
jtaQodov d7tot£Xsi6d'ai. 

s0tc3 drj jtQcbtov 6 sxocsvtQog tov d(5tSQog xvKlog 
6 ABF^ JtSQi xsvtQov tb E xal did^£tQov trjv AEFyj^ 
iq)' rjg ^iXyjq^d^co tb xivtQOV tov 
i&diaxov^ tovtidtiv tb xatd trjv 
oifjiv^ xal £6tco t6 Z, xal did 
tov Z jtQbg OQd^dg ycovCag tfj 
AEF diax^£C6r]g tfjg BZ^ vjto- 15 
7C£C6d-c3 6 d6tijQ ijtl tav B Kal 
A 6i]fi£Cc3Vy Xva drjlovoti t£taQtr]- 
^OQiOv ixatiQcod^^v r] cpaivo^ivr] 
Sid6ta6ig djti%r] tov A djtoy^Cov. d£iXtiov^ oti JtQbg 
totg B %al /i 6r]^£Coig r] ^£yC6tr] yCv£tai dia(poQd tfjg 20 
b^alf]g mvf]6£C3g jtaQa tf]v dvd)y,aXov. 

ijt£^£vx^cj6av yaQ f] t£ EB %al f] E^. oti ^lv 
ovv^ ov dv £xr] loyov r] 'bjtb EBZ ycovCa JCQbg tdg 
d OQd^dg^ tovtov ix^i tbv koyov f] tov JtaQa tf]v dvcj- 




1. to (pr.)] supra scr. D. 2, r-qv] % B, r' B^. 6. yi,Bi- 
^ora] ABC, ilaGoova B^D (renouat. D^, supra est ras.). 7. 
8i6i\ corr. ex ^? B^. aTtoy^iov'] -slov renouat. B^. 9. — 

mg. D. 6] punctis del. D, sed puncta eras. 12. ^codLwnov 
KVTiXov D. t6] om. C, ins. B^ 19. A] renouat. A*. 

SsLTitsov] -i- ins. A\ corr. ex 8si%taiov D^. 20. yCvstai i) 
^syiatr] D. 22. Tf] ins. D^. 23. av] supra scr. D*. exrj] 
corr. ex sxsi D*. tdg] om. D. 24. tov] supra scr. D^. 



222 KAATAIOT nTOAEMAIOT 

fiaXiav diacpoQOv TtSQicpSQSLa TtQog rbv olov xvkXov^ 
avt6d-£v yCvetai (pavEQOv^ STceidiqTtsQ rj ^av vjtb AEB 
ycovia rrjv rfjg o^akfjg ziV7]0ec3g VTtoreCvei TteQicpeQetav, 
7} de 'bjtb AZB rriv rrjg (paivo^evrjg dvcj^dlov^ vneQ- 
5 oxv S£ avrcbv ianv rj 'biib EBZ ycovCa [Eucl. I, 32]. 
g)rj^i drj^ ort rovrov exar eQag dXlri ycjvCa fiei^csv 
ov 6v6rad"^6erai TtQog rfj rov ABF^ xvxlov TteQi- 
cpeQeCa eitl rf^g EZ ev^eCag. 

6vve6rdrG)6av yaQ ycovCai TtQbg rotg ® xal K 

10 6r]^eCoig rj vTtb ESZ Tcal rj vitb EKZ^ Tcal i7tet,ev%- 
d-cj^av rj re @^ otal rj KJ, eTtel ovv icavrbg tQi- 
ycovov r] ^eC^cjv TtlevQa 'bitb rfjv ^eC^ova ycovCav 'bito- 
reCvei [Eucl. I, 19], ^eC^cov de e^nv 'fj @Z rfjg ZA 
[Eucl. in, 7, 3], fieC^cov eerai xal rj 'bitb @z/Z ycovCa 

15 rfjg "bnb A&Z. l'6rj de eenv 'fj vjtb E^® rfj 'bitb 
E&A [EucLI, 5], eTteCiteQ Kal 'f] E® rfi EA e6nv 
i6r]' xal oXr] aQa 'f] 'bnb EAZ ycovCa^ rovre6nv 'f] 
'bjtb EB^^ ^eC^cjv e6rlv rfjg 'bjtb E®Z. itdkiv eitel 
^eC^cov e6rlv r] AZ rfjg KZ^ ^eC^cov e^rlv Kal 'f] 'bitb 

20 ZK/i rf]g 'bitb ZzlK- l'6r] de e0nv 'f] 'bjtb EK^ oAt? 
r?5 'bitb EAK^ eTteCneQ xal 'f] EK Ttdkiv r^rj EA e6nv 
l'6r]' Tcal koiTcf] ccQa 'f] vjtb E^Z^ TOvreWtv 17 'bTtb 
EBZ^ rfjg vtto EKZ eonv ^eC^cov. 

2. cpavsQov] -6- in ras. A^ 4. AZB'] A- in ras. 2 litt., 
-B ins. D^, supra scr. oc^^. Post ccvco^dlov add. 'HLv^GScog 

in ras. 1 litt. B^. vnsQOx^n] v- add. B^. 6. dt]] corr. ex 

$i D^ 7. TtQog] TtQog \ nQog B. 10. 17 (pr.)] 7] xs D. 12. 
vTch xr]v fisC^ova nXevQav 'f] fiSL^cov ycovCa D. /xft^ojv] fisC- 

tcova C. 14. @JZ} mut. in //0Z A^ 15. z^0Z] mut. 

in ©z/Z A*. S6XL D, scxl D^ xri] xfj C (ut saepe), ttJi C^ 

16. Ez/ xji E& D. 18. Supra (isi^cov scr. iXdxxcov A*. iaxlv] 
comp. B, -V del. D^. 19. fieC^cov sgxlv (pr.)] om. D. 20. 

ZKzJ] ZKA ycovCa (isi^cov D. Zz/X] ZKJ C, corr. mg. C\ 

«(jTiD, «WDl 21. EJK^EJKoXrjI). 23. iffrtD, comp.B. 



MA0HMATIKHS 2TNTASESJS T'. 



223 



ovx ccQa dvvarbv aXXag ^SL^ovag 6v6rrj6a6d'ai yca- 
vCag^ Kad'' bv siQTJTca^sv xqotcov^ rcbv %Qog rotg B Kal 
A 6rj^eL0Lg. 

6vva7todetxvvraL d' , on xal 17 AB TtSQLipEQSLa^ 
ijrig 7tSQLS%SL rbv aitb rfig sXaxL^rrjg XLVTJ^scjg sjtl rijv 5 
^s6rjv xQOvoVj [iSL^cjv s6rlv rfjg BF^ iqrLg 7tSQLS%SL rbv 
anb rfjg (is6rjg XLV7]6scog sitl rrjv ^syC^rrjv %q6vov^ 
dv6l ratg rb dLacpOQOv rfjg dvco^ah'ag 7tsQLS%ov6aLg 
TtSQLCpSQsCaLg^ S7tSLdfi7tSQ rj ^sv VTtb AEB ycovCa ^sC^cov 
s6rlv dQd^fjg^ rovrs6rLV rrjg V7tb EZB^ rfj vTtb EBZ 10 
ycovCa^ f] d' V7tb BEF sld66c3V xfi avrfi [Eucl. I, 29]. 

TtdlLv svsKSv rov Tcal STtl rrjg 
srsQag vTto^^s^scog dst^at rb avrb 
6v^^atvov s6rc3 6 ^sv b^oxsvrgog 
r(p x66^a) TcvxXog 6 ABF TtSQl 15 
xsvrQOv ro A %al dLd^erQov rfjv 
AAB^ 6 d' sv rm avr» S7tL7tsda) 
g)SQ6^svog S7t avrov S7tCKVKlog 
b EZ H 7tSQl KSvxQov t6 A^ xal 
V7toKsC6%^co 6 d6rrjQ xard rb if, orav 20 
rsraQrrj^oQLOv d7ts%cov (paCvrjrai, 
rov Tcard rb dstbysLOv 6r]^sCov^ 
xal s^ts^sv^d^co^av ij rs AH xal AHF. Xsyco^ orL fi 
AHr scpd7trsraL tov eTtLKvxXov' r6re yaQ rb 7tlst6rov 
yCvsraL dLdcpoQOV rrjg b^aXfjg KLV7]6sG)g 7taQd rrjv dvd)- 25 




1. (isi^covccg C. ymvCag ovatT^accGd-aL D. 2. xat'] ins. D^. 

3. GTJllSLOLg 4. 7tSQLq>8Q8La] mg. D^ {■KSLflBVOv). 4. TCEQL- 

cpsQSLa] etiam in textu D. 6. £6x1 D, comp. B. 10. tovt- 
ioTLv] comp. B, -V del. D^ Post EZB del. ycovLa (isi^cov 

i6TLv dg^fjg Dl 11. d'] 8i D. Tf^g avTfig D, corr. D". 

17. d'] di D. 21. tElTSTaQTTifjLOQLOV C. 23. i7iL^evx^co6av C, 
corr. Cl xat (alt.)] yial 7] D. 25. oiiaXfig] corr. ex 6(ia?ug A*. 



224 KAATAIOT nTOAEMAIOT 

^cclov. iTCsl yccQ r} ^ev b^aXij ccTtb xov ccjtoysLov 
KLvrj6Lg TCEQiExetaL vjtb rfjg VTtb EAH ycovCccg' i6oxa%G}g 
yccQ Ts d^tijQ rbv i7tL%v%Xov %al 6 iTtLKvxkog rbv 
ABF xvxkov dLSQ%ovrai' rb ds didcpoQOv rrjg b^aXfjg 
6 XLV7]6£C3g TtaQcc rijv cpaLVO^iviqv vjtb rfig VTtb A^H 
ycovLag 7t8QLi%8taL^ (pavsQov^ otL xal 7] v7tSQ0%ri tfjg 
vTtb EAH ycavCag TtQbg f^v vjtb Azt H^ rovricrLv ii 
VTcb AH/i ycivCa^ rrjv cpaLvo^ivrjv rov d6riQog djcb 
rox) aTtoysCov dLd6ra6Lv 7tSQLi%SL. G)6ts i^tsl v^tdxsttac 

10 avtrj tstaQtrj^oQCov^ OQd-rj ^sv s6taL Tcal rj vjtb AH/I 
ycovCa^ icpa^cto^ivrj ds dtd tovto [Eucl. III, 16 cor.] koI 
r} ^HF svd-sta tov EZH i^CLXVKlov. rj AF ccQa 
7tSQL<piQSLa ^sta^v tov A xivtQOv Tcal tfjg icpajcto^ivrjg 
rj ^syC^trj i6tlv dcacpoQa tov jcaQa rijv dvco^akCav. 

15 xal xard rd avrd rj EH 7CSQL(piQSLa^ rjrLg 7CSQii%si 
xard rijv ivravd^a v7CoxsL^ivr]v i^cl rov i^CLXvxkov 
^srdpa6LV rbv dTcb rfjg sXa%C6rrjg XLV7]6scjg i^cl ri)v 
^i6r}v %q6vov^ fisC^cov i6rlv rfjg HZ^ rjrig 7CSQLi%SL 
rbv d7cb rfjg ^i6rjg ZLvr]6scog i^cl rfjv ^syC6rrjv %q6vov^ 

20 dv6L ratg AF 7CSQL(pSQsCaLg^ iTCsCTCSQ^ idv ix^dlo^sv 



2. ■nLvriGig] -7]- e corr. D^; supra est ras. Supra EAH 
ras. 1 litt. D. 5. viio (pr.)] post ras. 3 litt. D. ri)? vTto] 
ins. D*. AJH] AH/J C, corr, mg. C^. 7. tovti6xiv\ tov- 
in ras. Dl i]] om. C. 8. AHJ] corr. ex AzJH B\ 9. 
a6ts ETteC] corr. ex &07t£Q D^. 10. ^arat] icrTt D. 12. EZH] 
corr. ex EZ B. AF aQcc] yccQ seq. ras. 2 litt, D, "ya^" D^ 

13. TitQicp^QSLcc] corr. ex ncpsQSicc D*. iistcih,v — scpccnto- 

yi>ivris] supra scr. D*. 14. htiv] comp. B, -v del, Dl tov] 
seq. ras. 1 litt. D, &vcon,aXLav] a -lCuv inc. fol. 66 m. rec. B. 

15. EH] -H in ras. D^ ijTtg] rj- corr. ex v in scrib. A. 

16. v.cctd] v.al yiatcc C, %at ins. D^ 18. ^soriv] (is6r}v 
'aCv7\6i.v B. xqovov] -V e corr. D, deinde eras. s6tL. s6tiv] 
comp. ins. D^ tfiq HZ] -g H- e corr. D^ 19. ^syC^trjv] 
-yC- e corr. D^. 20. iK§ciXXcoiisv BD, corr. D*. 



MA0HMATIKHS STNTASESiS T'. 



225 



1 



rrjv ^H® xal aydyo^sv rfj EZ TtQog dQd^ag yavCag 
rrjv AK®y i'6aL ^ev yCvovxaL 7] ts vith KAH ycjvCa 
rfj vTtb Ajr [Eucl. VI, 8] Kal rj KH iteQKpiQEia rfi 
AF b^oCa^ ravtrj ds tov Svbg tstaQtrj^oQLOv ^eC^cov 
ILBV iativ ri EKH^ iXd66cov da rj ZH' OTtSQ sdsv 5 
dst^ai. 

oti ds Tcal iTtl tG)v xatd ^SQog xlv7]6scov i(p sxa- 
tsQag tcbv v7to^E6scov iv totg l'6ocg ^Qovoig td ai)td 
yCvstat Ttdvta TtSQC ts tdg b^iaXdg 
Tcal tdg (paLvoiisvag HLvri^sig xal 10 
stL tdg iJTtSQOxdg avtcov^ tovt- 
s6tLV ro TtaQa trjv dvco^alCav 
dLacpOQOV^ ivtsvxtsv dv tLg ^d- 
XL6ta xataudd^OL. 

s6to yaQ 6 ^sv b^oxsvtQog r« 15 
dLa IIS6C0V t&v ^codCcov xvxXog b 
ABF TtSQL TcsvtQov tb ^y b dh 
€XxsvtQog iisv^ l'6og ds ta ABF b^oKsvtQcp^ b EZH 
^sqX xsvtQOv tb 0, xoLV^ d^ d^cpotSQcov dtd^stQog d^d 
rcov A Tial @ xsvtQcov ocal tov E ditoysCov rj EA@A^ 20 
xal dnokri^pd^sC^rig ijtl tov b^oKsvtQov tvxov6r]g TtSQL- 
ipsQsCag tfjg AB xsvtQCO ta 5, dLa6t7]^atL ds t& A@ 
syQdfpd^co b KZ iTtCxvxlog^ xal ijts^svxd^co rj KBA. 




1. /iH&\ JHB. aydyootiEv] -d- corr. ex o in scrib. C. 2. 
teai] 1'g- e corr. D^, oftotat B. 3. tj} (pr.)] seq. ras. 1 litt. D. 

■Kat] ware xat B. xal rj — 4, dfiOLcc] supra scr. D^ 4. 
dpiOLa Tji AF Dl 5. EKH] E- e corr. D, EK B. ansg 
BD, corr. D*. 9. yiyvhxai D. 11. xovxkGXiv] -v del. D^, 

xovxsoxL B. 14. ■aaxafid&oC] seq. ras. 1 litt. B. 15. to5] 

corr. ex xcbv D. 17. ds] 8' BD. 18. to5] corr. ex x6 CDl 

20. x&v] corr. ex toi; C^. E] EA C. ' 22. diacxriiiaxL 

8i] -Aal dLaGxriiiaxL BD. rw (alt.)] xto l'6co xm B. 23. inL- 
tsvx^co D, corr. D^. 

Ptolemaeus, ed. Heiberg. 15 



226 KAATAIOT nXOAEMAIOT 

Xsyco^ oti 6 ^£v d^trjQ v(p iKatsQag tcbv xiv'I]6£G)v 
£7cl f^v Z to^rjv tov £KX£vtQOv %al roi) £7ClkvkIov 
Ttdvtcog ocatd tbv l6ov %q6vov £V£%%"Yi<S£tai,^ tovt£6tLV 
ai y 7t£Qicp£Q£iav o^ocaL £6ovtat dXXTJXaig i] te EZ 

5 tOV £KK£VtQOV Xoi 7} A B tOV 6^0K£VtQ0V Kal 7] KZ 

tov ijtiKVKlov^ Tj dh dia(poQd tfjg o^aXfjg Kivri6£cog 
TtaQd trjv dvcoiLakov Kal ii cpaivo^ivi^ rov d6t£Qog 
TtaQodog KaO"^ £Kat£Qav tav VTCod^ia^cov o^oia ml ^ 
avtri 0vfiPri6£tai. 

10 iTt^^^vxd^co^av ydQ i] t£ Z0 Kal ri BZ Kal ho 
r] ZlZ. i7t£i t£tQa7tX£VQ0v tov B^SZ at d7t£vavtiOv 
7tX£VQal l'6ai £i6lv £Kat£Qa £Kat£Qa, rj ^lv Z@ tfj BZlj 
rj d£ BZ tfi ^®^ TtaQaXXrjXoyQa^^ov £6tai tb B^Z0 
t£tQd7tX£VQ0v. i'6ai ccQa £i6lv at y ycovCai ij t£ V7tb 

15 E®Z Kal ri V7tb AAB xal 7] -b^tb ZBK [Eucl. I, 29]' 
Gi6t i7t£l TtQbg totg xivtQOig £i6i\ Kal tdg v7tot£ivo- 
fiivag 'b7t' avtcov 7t£Qi(p£Q£iag b^oCag dXXijXaig yCv^dd^ai 

t7]V t£ EZ tOV iKK£VtQOV Kal tijV AB tOV 6^0K£VtQ0V 

Kal tfjv KZ tov iTtiKVKkov. Kat d^cpotiQag ccQa tdg 
20 KiV7]6£ig iv ta t^cp %q6v<p i^tl tb avtb 6r]^£iov tb Z 
iv£%%"ri6£tai 6 d6tfjQ koI tfjv avtf]v tov did ^£6cov 
t&v ^codCcov kvkXov 7t£Qi(p£Q£iav dTtb tov d7toy£Cov tf]V 
AA (pavr\6£tai di£Xr]kvd-6g^ £6tai t£ aKoXovd^cog Kal tb 



1. vtp''] B, YQ. iq)s supra scr. B^. 8. 17] postea ins. D. 10. 
ydQ] om. C. JBZ] ZB B. Eti'] fj hi C. ^ll. BJ&Z] 
BJZ& C. 12. £t6iv l'aca D. ittatsQcc] mut. in iKatsQai? D^ 



STiatsQa] supra scr. D. 13. BZ] ZB B. J&] #z/ C. 

sGtaL] 'iati corr. ex sGtiv D^. 5z/Z0]ABC, BJ@Z !>. 

14. at] snsl v.al svaXla^ at D. 7] om. B. i]] snsl yial 
svaXla^ at tQstg ycovCai rj B. 15. xat (alt.)] ins. C. ZBK] 
-BK e corr. D^, ZBK i'6ai B. 17. yiyvsGd^aL D. 19. v,atd C. 

20. to (alt.)] seq. ras. 1 litt. D. 23. htac — p. 227, 1. TtaQo] 
supra scr. D^ (yp.). 23. ^etai ts] S6tai C, S}6ts D^ et supra 
scr. C^ xal th naQo] etiam in textu D {-d renouat. D^). 



MA0HMATIKHI; STNTASE5>2 r'. 227 

TCaQa rriv avco^aXCav dtdipoQOv rb ai)rb xad'' ixareQav 
rcjv vTtod^e^sGyv^ ETtsidrj rrjv roiavrrjv diacpoQav sdsC- 
^a^sv 7CSQis%oiLSvriv iTcl ^sv rfjg ;car sxKSvrQorrjra 
vTtod^sOscog VTtb rfjg 'bnb AXS yovCag^ sitl 8\ rfjg 
zair' STtCxvicXov 'bitb rrjg 'bitb BzlZ^ %al avrac ds l'6ai 5 
rs xal svaXka^ yCvovrat dia rb TtaQdXXrjlov dsdslxd^ai 
ri)v Z® rfi 5z/. 

dr]Xov d\ on xal sjtl jta^cbv rcov dia6rd6scov rd 
avrd naQaKoXov^ri^Si TtaQaXlrjXoyQd^^ov Ttdvrors yivo- 
^svov rov GzJZB rsrQaitXsvQov Tcal yQa(po^svov rov lo 
SKTcsvrQov TcvxXov 'VTt «vTiJg rfig xara rbv ijtCzvxKov 
rov ddrsQog ^sra^d&scog^ orav ot Xoyoi xad'' ixarsQav 
rcjv 'V7tod'S6scov o^oioC rs xal l'6oi 6v^PaCvco6iv. 

ort de, Tcdv o^OiOi ^ovov a^iv^ dvidoi ds ra ^sysd^si^ 
rd a^vrd TtdXiv cpaivo^sva 6v^p7]6srai^ q^avsQOv xal ovrcog 15 
ysvr]6srai. s6rco ydQ Sda^urcog 6 ^sv o^oxsvrQog np 
Tco^iica xvxXog 6 ABF jtSQl zsvrQOv ro z/ zal did- 
[nsrQov^ xad'' rjv djcoysiorarog rs xal TCSQcysiorarog 6 
der^TjQ yCvsrai^ r^rjv A^F^ 6 ds tcsqI ro jB ijcCKVK^og 

taTCsxcjv dicb rov A dnoysCov ri^i/ AB rv%ov6av tcsqc- 20 
g^sQSiav^ Kal KSKivrjad^co 6 der^rjQ r^rjv EZ 7CSQi<psQSiav 
^fioCav ycvo^svrjv drilovori rf] AB did ro i6o%QovCovg 
1. To] seq. ras. D. 2. xriv] tJiv (i£v BD, 4. z/Z0] J- 
/9 a 

in ras. A^, ^ZED, JZ@ B^. 6. vno (alt.)] addidi, om. 
ABCD. Ez/Z] corr. ex BZ D^. foai] i'6- renouat. A*. 

6. yLVOvxaL] yCvoix' av B. 8. 8'] di D. 10. GJZB] 

AC, BzlZ@ BD, eJBZ Halma. 11. vtio tavxj]? D. 13. 
avfi^aLvovOLv C. 14. ^ovov] post -6- eras. t A, -d- in ras. 2 
litt. B. 15. xd avxd] xa av- in ras. C. 16. ysvijosxaL] avfi- 
^-^aofisv B (supra -ao- ras.), noLi^aofisv D. 17. tceql — 19. 

Ajdr] mg. D^ {yiSLfisvov). 18. xs y,aL nsQLysLOxaxog] om. CD. 

21. y.aL] 6 EZ yiai BD. KLvrja&a) C, corr. Cl 22. t^] 
seq. ras. 1 litt. D. 

15* 



228 



KAATAIOT nTOAEMAIOT 



£ivac tag tGiv xvkXcov ajtoicata6t()c6£ig^ %a\ STte^svx^to- 

6av 7] ts ^BE xal rj BZ %al rj JZ. 

oti ^sv ovv l'6aL ts slciv Ttdvtots ij ts i)7Co AAE, 

yGivCa xal rj vtco ZBE^ xal otL stcI trjg AZ svd^sCag 
5 6 d6triQ (pav7J0staL^ xatd 

tavtrjv trjv VTtod^s^iv avt6- 

&SV s6tl drjXov. 

XsyG) d\ oti xal did 

trjg ;car' SKTCsvtQotrjta^ sdv 
10 Tf ^sC^cjv sdv rs skdttov 

ii 6 sxKsvtQog tov ABF 

b^onsvtQov^ tr\g ts tmv X6- 

ycov 6fLOL6trjtog fi6vrjg vTto- 

KSL^svrjg xal tfjg t&v djto- 
15 xata6td6sc3v C6oxQOVL6tr}tog 

STtl tfjg avtrjg TtdXLv svd^sCag 

tijg A Z (pav7J6staL 6 d6t7]Q. 

ysyQdcpQ-G) yaQ ^sC^cav ^sv^ ag stpa^sv^ sxKsvtQog 

6 H® TtSQl xsvtQov STtl tfjg AF t6 K^ sXd66c3v ds 
20 6 AM TtSQL KsvtQov 6^oCcog tb iV, xal sxp^rjd^SL^av 

tfjg ts AMZ& Tcal tfjg AAAH sits^svx^co^av 7] ts 

@K xal rj MN. STtsC s6tLV^ cog r] A B jtQbg BZ, ov- 

tcog rj ts ®K %Qbg KA xal r} MNjtQog NA [p 219,21], 

Ttal ycovCa rj 'bjtb BZA ycovCa tfj vitb MAN l'6r] dtd 




2. Tc] rs BZ %al i] BD, corr. D^. /IBE -nccl j} BZ tkxI 
7}] om. B, JBE yial 7] D, corr. Dl 3. ts] om. B. Etal 

BD. 13. a7C0'iisL(i^v7]g C, sed corr. 19. KsvtQovl xfW(o D, 
v.svt^v Dl sldttcov BD. 20. AM'\ corr. ex z/M B. 

d^OLcog to] -g to e corr. D. sy.^XT]d'si6&v] in -d^SLO&v rursus 
inc. m. 1 B fol. 68. 21. trjg (pr.)] corr. ex tfj A^ Post 

JAAH lac. paruam ob naturam pergameni C, Xsltcsl svtavta 
mg. P3. 22. STtsL — 23. MN] mg. D. 22. insL] g' sttslJ). 
B Z — 23. MN TtQog] postea add. A\ 



MA0HMATIKHS 2TNTASE5i2 T\ 229 

t6 TtaQccXXrjXov elvai, rrjv AA tfj BZ [Eucl. I, 29], 
L6oyc6vLcc iotLV tci y tQLycova [Eucl. VI, 7] xal at 'bjtb 
tag avdkoyov TtlsvQag ycovLav l^ai § ts 'bjtb B^Z 
xal rj vitb /l®K xal 7] vjtb ^MN' TtaQaXXriXoL aga 
Mv at Bzf xal &K zal MN sv^etaL [Eucl. I, 28]. 5 
co6te xal ycovCaL rj vTtb A/iB xal rj vnb AK0 xal 
rj VTtb ANM L6aL ei^C [Eucl. I, 29]. xal ejtel TtQbg 
totg xevtQOLg ei6l tcbv xvxXcov^ o^oLaL e6ovtaL xal aC 
eii avtcbv JteQLcpeQeLat ij te A3 xal H@ xal AM' 
ev ta l'6(p ccQa ;tpc)i/a> ov fiovov 6 ts eitCxvxlog tijv 10 
AB TteQLCpeQeLav xal 6 d6trjQ triv EZ dLeXrjXvd^a^Lv^ 
dXXd xa\ enX t&v exxevtQCOv 6 d6triQ ttjv te H@ xal 
trjv AM dLelrjlvd-cog e6taL^ xat enl rijg avtrjg evd^eCag 
Ttdvtote tfjg AMZ& dLa tovto d^ecoQrjd^TJ^etat xal 
xatd ^ev tbv ejtCxvxXov ejtl tov Z 6rj^eCov yLvo^evog^ 15 
xatd de tbv ^eC^ova exxevtQov enl tov 0, xatd de 
tbv eXdttova enl tov M, xal eTtl 7ta6cov tcbv d^e^ecov 
b^oCcog. 

e7tL6v^paCveL d\ otL xaC^ otav L6rjv TteQLCpeQeLav 6 
d6triQ dTteLXrjcpcog cpaCvrjtat djto te roi) dnoyeCov xal 20 
tov JteQLyeCov^ l'6ov e6taL xad'' exateQav d^e^LV ro 
TtaQa tijv dvco^aXCav dLacpoQOv. eitC te yaQ trjg xat 
exxevtQotrjta^ edv yQaipco^ev tbv ABFzf exxevtQov 
xvxXov TteQL xevtQOV tb E xal dLa^etQOv tr^v AEF 



2. iativ^ comp. B, mut. in §6x1 aqu D^. y] A, om. 

BCD. TQiyGivu^ -iy- e corr. D^ 6. 17 (pr.)] scripsi, at 

ABCD. 7] (alt.)] om. D. AKS^ A@K B, corr. ex AziKG D. 

7. 17] om. D. bIgCI comp. B, corr. ex eIolv D^. 8. at] 
ins. D< 9. 7] H& v.al 7} AM D. 11. dulriXv^s D, corr. Dl 

13. avTf]g'\ supra scr. D^. 14. ^m] 8iav C. 19. laag 

nsQicpsQsCag D. 22. inC ts] corr. ex snsinsQ D^ 24. AET'] 
AETJ C. 



230 KAATAIOT nTOAEMAIOT 

dia rov A aTCoysiou rrjg o^jscjg vjtoxeL^svrjg ijt^ avrijg 
xara ro Z 6rj^Siov xal d^a rov Z rijv BZ^ rv%ov6av 
diayayovrsg sjtL^sv^coiisv ro^g EB xal ^z/, au rs cpauvo- 
lisvai TtaQodoL tCai^rs xal aTtsvavrCov s^ovrai^ rovr- 
5 i6riv 7] rs vjcb AZB yovCa rrig aTto rov aitoysCov 
xal Yj vTtb TZA ^S ocjtb ^q^ 
icsQiysCov^ rd rs ita^a r^v dvco- 
ybaXCav didtpoqov rb avrb s6rat 
did rb l'6r]v slvat rrjv ^sv BE 

10 rfi EA^ r^v ds VTtb EB Z ycovCav 
tfi 'bTtb EAZ [Eucl. I, 5]- co6rs 
ra avra 8ia(p6Q(p rfjg cpatvo^svrjg 
7tsQiq)SQsCag^ rovrs6riv rrjg v<p 
SKarsQag r&v^vTtb AZB xal TZA 

15 ycoviGiv TtSQisyoyisvrig ^ ^isC^ova ^sv yCvs^d^ai rrjv ditb 
rov A dTtoysCov rr]g o^alrjg mvri^sGig %sQi(psQSiav^ sld6- 
6ova ds rrjv dTtb rov T jtSQiysCov rr^g o^aXrjg Kivr}6sG)g 
7tsQi(psQSiav^ did rb xal rrjv ^sv VTtb AEB ycovCav ^sC- 
^ova sivai rfjg vjtb AZB^ rr^v ds vTtb TEA sld66ova 

20 rrig {)7tb TZA [Eucl. I, 32]. 

xal STtl rrjg %ar sitCxvxXov vjtod^s^scjgj sdv y^d- 
ipco^sv rbv ^sv b^oKsvrQOV o^oCog xvxlov rbv ABT 
TtsQi TcsvrQOv To A xal did^srQov rrjv AAT^ rbv d' 
STtCTCvxXov rbv EZH jtSQl TcsvrQOv rb A^ xal diaya- 

25 yovrsg r^^v AHBZ rv%ov6av siti^sv^cj^sv rdg AZ 




2. v.aC] Kccl dLayccyovtsg D. BZJ] corr. ex Bz/Z D. 3. 
dtccyayovrss'] om. D. 4. trf] ins. D^. 6. vtto] v- renouat. 
B^ (propter fig.). 7. Post TtaQcc lac. ob naturam pergameni C. 
Item ante i'6r}v lin. 9. 13. ttJs — 14. AZB'] mg, D^, rfjg 

vrcb ABZ in textu D, AZB supra scr. Dl 16. eXaaaov BC, 
corr. C^ 18. TtSQKpsgstav] om. D. 19. AZB] corr. ex 

ABZ J)\ 23. d'] ds D. 25. JHBZ] corr. ex JBHZ D*. 



MA0HMATIKHS 2TNTASESiS T'. 



231 



Kcd AH^ 1] iLav xov TtaQcc tijv dvcj^aXiav dua^p^QOv 
nsQKpBQSia ri AB 7] avtrj TtdXiv £0tai vjcoKst^svrj 
oiat d^<pot£Qas tdg %-B6£ig^ tovt£6ttv idv ts xatd tb 
Z idv t£ xatd tb H f] 6 ddtTJQ^ ;cal l'6ov dh djtixcov 

(pavYi6£tat dito t£ tov xatcc tb diio- 5 
y£tov 6rj^£tov tov dtd fi£6a)v tcbv 
^codtcjv^ otav fi xatd tb Z, xal djcb 
rov xatd tb jt^Qty^tov^ otav fi 
xatd tb H^ i7C£td7]7t£Q rj ^£v ditb 
tov ditoy^tov cpatvo^ivrj 7t£Qtcp£Q£ta 10 
7t£Qt£%£tat VTtb tfig vTtb ^ZA yc3- 
vtag' VTt£QO%ri yaQ ov6a id^txd-rj 
tfjg t£ o^aXfjg xtv7]6£cog xal tov 
jtaQd tijv dvco^aXtav dtacpdQOV rj 
dh djtb tov 7t£Qty£tov cpatvo^ivrj 7t£Qti%£tat {)7tb trjg 15 
V7tb ZHA ycovtag' l'6rj yaQ iattv ;cal avtrj tfj t£ d^cb 
rov 7C£Qty£tov b^akfi xtv7]6£t zal tp TCaQd tijv dvco- 
liaXtav dtacpoQCp' t6ri di i6ttv xal rj VTcb AZA 
ycovta tfj V7tb ZHA [Eucl. I^ 5] dtd tb xat trjv AZ 
xfi AH t6rjv £tvai. Gi6t£ xal ivt^vd^^v 7cdltv 6vv- 20 
dy£6%at^ ott t& avtm dtacpoQCO^ tovti&ttv tfi {)7tb AAH 
ycovtcc^ lit£Lt,cov ^iv i6ttv rj JCQbg ta dTCoy^icp ^i6rj 
trjg cpatvoiiivrjg^ tovti^ttv rj V7cb EAZ ycovia trjg 
V7cb AZA^ iXd66cov dl rj 7CQbg tg5 7t£Qty£i<p ^i6rj tfjg 




1. avco^aX^ccv D, 2. nsQiq^iQEia 17] corr. ex nsQLcpBQSt-ccv 

C^D. 7] (alt.)] ins. D^ 6. orifiSLOv] corr. ex arnLBLov C^ 

15. di] 8' D. 16. vTto] om. C. sgtlv] comp. B, -v del. D^. 

17. To5] corr. ex ro C^ 19. to] om. B. 21. xovtiGtLv] 

comp. B, -v del. D^. AJH] AJB D. 23. tovtsatLv — 

p. 232, 1. ov6r]g] supra scr. D^ 23. tovts6tLv] r D^ 24. 

AZzJ] AzJZ B. 



232 KAATAIOT nXOAEMAIOT 

tpacvo^Evrig tijg avtrjg ovarjg^ rovxBdxiv rj vtco HA/J 
ycovCa rfjg vTtb AHZ [Eucl. I, 32]* oiteQ TtQoeKsvto 
dstiai. 

d\ IIsqI tfjg tov rikCov q^atvofisvrjg dvcoiiaXCag, 

5 Tovtcov drj ovtcjg TCQOSXtsd^si^svcDv JtQovTtoXrjTttsov 
xal trjv TtSQl tbv rjlcov (paivo^svrjv dvo^aXCav svsxsv 
tov ^Cav ts sivai xal tbv ditb tf^g sXa%C6trig iavr]6scog 
STtl tijv ^s6rjv %q6vov ^sC^ova jtOLSiv Ttdvtots tov ditb 
tfjg ^s6rjg htl tijv ^syC^trjv xal tovto yaQ 6v^(pcovov 

10 ov svqC67co^sv totg (paivoiLSvoLg' dvva^d^ai ^sv xal dt' 
STcatSQag tcbv TtQOKSc^svcDV vTto%^s6SG)v aTtotsXst^d^atj 
8i,d trjg xat sitCxvaXov yisvtoi^ otav xatd tijv ditdysiov 
avtov TtSQicpSQstav rj tov rjXCov nstd^a6ig sig td 
TtQorjyov^sva yCvrjtat, svXoycotSQOV d' dv sl'rj nsQi- 

15 a^p^rjvat tfj xar' sxTcsvtQotrjta vjtod^s^st d7tkov6tsQ(f 
ov6ri xal 'bnb ^iag^ ovjl 8s vjtb dvo XLvr}6sG)Vj 6vv- 
tskov^svri. 

TtQorjyov^svov toCvvv rov tbv Xoyov tfjg TtSQL tbv 
riXtaKbv xvxXov STCTCsvtQOtrjtog svQstv^ tovts6tLV tCva 

20 Xoyov s%SL r] ^sta^v t&v TcsvtQcov rov ts sxxsvtQov 
xal tov xatd tr]v ot^tv xsvtQOv tov d^d ^s6cov tojv 

^CodCcOV KVXkoV TtQbg tfjV ix tOV XSVtQOV tOV SKXSVtQOVy 

xal stL xatd Ttotov ^dXL6ta t^fj^a tov dLa ^s6cov tcov 
^GodCoov kvkXov tb ditoysLOtatdv s6tLv tov SKKSvtQOV 



1. xfiQ civtfjg ov6r}g] etiam in textu D. xovtiGXL D. 2. 
un8Q D, corr. D^. 4. d'] C, om. ABD. 5. "^^^noXrintiov D. 

9. 6v(itpcovov 6V] corr. ex 6v^cpcovov D^, 12. xara] f) 

yiaxfx, D, 17 add. B^ xriv'] corr. ex ro B^ 13. 17] om. D. 

14. 8' av eVri\ corr. ex av D^ 19. xovxE^tiv] comp. B, -v 
del. D^ 20. th\ om. C. 21. tov (alt.)] -0- corr. ex co in 

scrib. D. 22. nvv.Xov'] -v e corr. D^. tov (pr.)] supra scr. D. 



MA0HMATIKHS STNTASESiS T'. 233 ' 

iSrjfiEtov^ dedsLTitai ^sv TavTo; xal t(p ^IjtTtaQx^ ^sto^ 
67Covd^g' vjtod^s^svos yaQ thv ^av aTtb iaQivijg l6ri- 
^SQLag insxQi d^SQLvfjg tQOTtrjg xqovov ri^SQ&v gdi\ tbv 
ds aitb d^SQLvrjg tQOitrlg ^sxql ^stOTtcoQLvfjg i^rj^SQLag 
rj^sQG)v 9/3/.', dLa ^ovcov tovtcov rav cpaLvo^svcov djto- 5 

dSLKVV6L tflV ^SV ^Sta^V tCJV TtQOSLQrj^SVCOV TCSVtQCOV 

svd^stav SLXO0totstaQtov syyc^ta ^SQog ov6av trjg sx 
tov TcsvtQov tov sxKSvtQov^ TO 6' ccTtoysLOV avtov 
jtQOiqyov^svov tf]g d^SQLvfjg tQOJtfjg t^rj^adtv zd/J ^y~ 
yL6ta, oXcov s6tlv 6 dLa ^s6cov t&v ^codLcov xvxXog r|. 10 
Tcal rjnstg de tovg ^sv tcov TtQOXSL^svcov tstaQtrj- 
^OQLCov XQ^'^^'^^ ^^^ tovg Xoyovg tovg TtQOXSL^svovg 
tovg avtovg syyL6ta xal vvv ovtag svql6xo^sv^ cog 
dca tovto %aC^ otrt tfjv avtfjv dsl \ts6Lv 6 STCxsvtQog 
tov fikCov KVicXog 6vvtr]QSt JtQbg td tQOTtLxd %al i6ri- 15 
^SQLvd 6r]^sta^ (pavsQbv f][itv yCvs^d^ai. svstcsv ds tov 
fif] TtaQaksXsLii^svov slvaL tbv toLovtov toitov^ dXXk 
Tcal Slcc tcbv f]^stSQCov dQLd^^&v sq)codsv^svov STCKst^d^aL 
t6 ^'scoQriiLa^ TtOLrj^ofisd^a ocal avtol tf]v tcov TtQOKSL- 

flSVCOV dst^LV COg Sltl SKKSVtQOV KVTckoV %()1^^a/[l£V0t 20 

Tot^ avtotg cpaLvofisvoLg^ tovts6tLV^ cog scpa^sv^ ta tbv 
fisv dnb saQLvfjg i6r]^SQCag ^sxql d^SQLvfjg tQ07tf]g XQOvov 
TtSQLSxsLV r]^eQag (jd L\ tbv d' djtb d^SQLvfjg tQ07tf]g 
lisxQL ^sto7tcoQLvf]g i6r]^SQCag 9j3/.'. xal yaQ dtd tcbv 
dxQL^s^tata tr]Qr]d-SL6c)v vcp f]^c)v %atd t6 i;|y' stog 25 



1. ar]^SLCov C. tTtccQxco A. fieTa] y^sta ndcris D, TtccGrjg 
add. B^ 3. tov — 5. [_'] mg. D^. 5. &7todsi'nv'v£L B, dcno- 

dsiv.vEL C. 11. ds] seq. ras. 2 litt. A. 16. ysviad-aL D. 

18. ^fistsQcov A. scpoidsvofisvov B; scpodsviiivav C, co corr. 
in o; scpoSsv(isvov D, corr. D^. 23. TjiisQag'] -i- eras. C. 24. 
9^] f]fiiQag 9§ D. yccQ] yccQ g' D. 



234 • KAATAIOT nXOAEMAIOT 

dTib rrjg 'AXs^dvdQov tsX£vti}g L6rj^SQL&v ts xccl dsQivrjs 
tQOTtrig 6v^(p(x)vov tb tcbv dcaetdascov TtKrjd-og t&v 
riiiSQcbv svql6xo^sv^ STCSLdTJTtSQ, Sg stpa^LSv [p. 204, 10; 
205,2; 206,2], r] ^sv iistoTCcoQLvii torj^sQLa ysyovsv tfi 0*' 
6 tov 'Ad^vQ ^stct trjv rjlLov dvaxoXriv^ r\ 8\ saQLvij rg 
^' tov na%G)v lisxd trjv ^sarj^^QLav^ wg ^vvdysiSd^aL trjv 
dLd6ta6LV fiiiSQ&v Qorj d\ trjv ds d^SQLvrjv tQOitriv t^ 
La tov Ms60Q'^ yista tb slg trjv l^' ^s6ovvKtLOv, Sg 
xal tavtrjv ^sv trjv dLd6ta6LV, tovts6xLV trjv ditb trjg 

10 saoLvfjg L6rj^sQLag stcI f^v ^SQLvrjv tQOTtrjv^ rj^SQag 

6vvdysLv ^idl_\ TcatalsLTts^d-aL d' sig trjv djtb trjg d^SQLvrjg 

tQOTtfjg STtl trjv s^rjg ^stOTtcoQLvrjv t6rj^SQLav tdg koi- 

Ttdg slg tbv svLav6Lov %q6vov rj^sQag syyL6ta 9/3/.'. 

s6X(o drj 6 dLa ^s6(ov tCbv t^codCcov %vKXog 6 ABF^ 

15 TtsQL xsvtQov tb E^ xal dLrjxd^co^av sv avrw dvo d^d- 
^sxQOL TtQbg OQd^dg dXlrilaLg dLa tcbv tQOTtLX&v xal 
L6riyiSQLVcbv 6rj^SLCov rj ts AF xal rj jBz/, VTtoxsL^d^co 
ds t6 ^sv A saQLvbv ^rj^slov^ tb d\ B d^sQLvov^ zal 
td s^flg dxo^.ovd^cog. 

20 orfc ^sv ovv t6 xsvtQov tov skksvxqov kvkIov 
^sxa^i) tcbv EA xal EB svd^SL&v 7ts6sitaL^ (pavsQbv 

SK tOV t6 ^SV ABF rj^LKVKhoV TtXSLOVa TtSQLS^SLV 

XQOVov tov rj^L6ovg tov svLav6L0v xqovov xal dtd 

tovto ^SL^ov djtoXa^pdvsLV tov skksvxqov t^fj(ia rj^L- 

25 kvkXlov^ t6 ds AB tsxaQxrjuoQLOv Kal avxb TtksCova 

1. iG7]ii8QiGiv\ D^, tarj^SQSL&v D, to7i(i£Qivf]g ABC. 4. ys- 
yovE xfi D, -f T- renouat. D^ 7. t^] tfj AD, rjyt B et C (tj 
e corr.). 8. la'] i- e corr. D^. [isgoqL B. 11. /_'] corr. 
ex g D^. Q'BQivfig\ ^- corr. ex c in scrib. C. 16. aUrj- 
Zatg] ycoviag cciXrjXaLg xat D. 18. ori^stov'] -ov e corr. D^ 

' 20. '^ivzQov'] X- in ras. A. 21. EA] -^ renouat. D^. 23. 
XQOvov] om. D. 24. TUTj.ao:] v.vv.lov xiifi^a D. 25. nlsiova^ 
itXsCova XE D. 



MA0HMATIKHS STNTASESiS F'. 



235 



7CSQLi%SLV %q6vov Kal ^SL^ovcc TtSQLipsQSLCCv aTtoXcc^^dvsLV 
rov sxxsvxQov TtaQcc rb BF rsraQrrj^oQLOV, rovrov ds 
cvtcog sxovrog VTtoxsC^d-co rb Z orj^stov xsvrQov rov 

sxxsvrQov^ xal Sl- 

t^X^G) flSV 7] 8l 5 

d^(potSQ(ov rcbv 
ocsvtQCjv^Kal rov 
ditoysLOv dLa^s- 
rQog 7] EZH, 
KsvrQO) ds r^ Z lO 
Kal dLa6tYiiiatL 
rv%6vrL ysyQacp- 

%"&) 6 SKKSVtQOg 

rov rjlLOv kv- 
^log 6 ©KAM^ 15 
Kal dLa rov Z 
fjxd^co^av JtaQaX- 
XrjXoL rri fisv AF ^i NSO, rfi 8s BA 7] nPE, 
xal stL ri%d-G)6av Kad^stOL ditb ^sv tov @ STtl trjv 
NIHIO ii @TT, dTtb ds roi) K sjtl rijv UPZ ij KOX. 20 
STtsl roLvvv 6 rilLog rbv &KAM kvkXov bfiaXcbg dtSQ- 
x6^svog rrjv ^sv SK TtSQLcpsQSLav dLaTtoQsvsrat sv 
rj^SQatg <ddL\ trjv ds KA sv rj^SQaLg 9/3/.', KLVsttat 
Ss b^aX&g sv ^sv tatg gd/J rj^SQaLg ^OLQag ^y ^ sy- 
yL^ta, otW s6tlv 6 KVKXog r^, sv ds ratg 9/3/.' ^oLQag 25 
9« Td-) strj dv rb ^sv &KA r^fj^a ^olqcjv Qitd jc, 




3. To] corr. ex t^ Dl 18. NS^O] corr. ex NS 6 C^, 

-O e corr. D^ 20. NSO] corr. ex NIh; 6 C\ K] e corr. 
D^ seq. ras. 1 litt. K^X] K- e corr. J)\ 21. @KAM] 

-A- supra scr. A, 6>- e corr. D^ 22. 6)X] corr. ex K@ D^ 
23. rrjv — /.'] mg. A^ 25. h] -v e corr. Dl /_'] renouat. 
D^. 26. Supra Ta scr. F D. 



236 KAATAIOT nXOAEMAIOT 

6vva^g)6t£Qcc de to ts N@ xal th AO tav XoiTtGiv 
[lata tb NJJO ii^ixvxhov ^olqcov d tc^ ri ds dtjrA^ 
[Eucl. in, 3] 7t6QL(p8QSLa tTJg ®N 'fj ®NT tcbv avt&v 
d X. &6ts ical rj ^sv VTt' c^vr9)v svd^sta rj ®T toLOvtov 
6 £6taL d A/3 syyL6ta^ oIlcov s6tlv rj tov sxxsvtQOV dLcc- 
^stQog 'qtc^ rj ds rj^L6sLa avtrjg r] ®T^ tovts6tLV 17 
E^^ tG)v avtcbv /3 Tg, jtcchv sitsl tb ©NUK t^rj^a 

OAOV ^OLQCbV S6tLV 9^ ^•) S6tLV ds Xal tb ®N ^OLQ&V 

/3 fc, TO ds Nn tstaQtrj^oQLOv ^olq&v 9, ^al loLTtri 

10 iisv s6taL ri IIK itSQLCpSQSLa ^olq&v o vd', r] 8\ dLJiXfj 

avtrjg 17 KTIX TtSQLcpSQSLa ^olqcov a 'vrj. w6ts xal ri 

^sv vjt avtriv svd^sta r] K0X tOLOvtcov s6taL /3 d^ 

oiG)v i6tlv rj tov socKSvtQOv dLcc^stQog 'qtc^ ri d' rniC- 

6SLa avtfjg r] K^^ tovts6tLV rj ZtBl^ t^rjfidtcov a /3. 

15 t&v d" avrwv sdsLxd-rj Tcal rj E^ svd-sta ^ Tg. xal 

STtsl ta ccTt^ avt&v ^vvtsd^svta JtoLst tb djtb trjg EZ 

[Eucl. 1,47], s6taL xal avtrj ^r]7CSL tOLOvtcav /3 x-S-/.' 

syyL6ta^ oIcdv s6tlv r] sk tov ocsvtQov tov sxxsvtQOV ^. 

r] ccQa s% tov xsvxqov tov sxxsvtQov xvxkov tstQaxaLSL- 

20 K06a7tla6LOv s6tlv syyL6ta tf]g ^sta^v tcbv xsvtQCOv 

avtov ts xal tov ^mdLaxov. 

1. 6vti(p6tEQcc C, corr. C^. iV0] @N D. AO] in 

ras. A^. 2. fistcc to] BC et post ras. 2 litt. D, mut. in tav 
ds to A*. NnO'] seq. ras. 2 litt. D. x] A, x v,cil sv.dtE- 
Qov (isv ccQcc avt&v S6tai (ioLQ(bv ^ r BCD. 3. nsQLq)SQSia] 

corr. ex nsQicpiQia k^. 4. x] ins. C^ 6>T] OTT D. _7. 
Ante ^ ras. 1 litt. D. ^NUK D. 8. oXov] om. B. 9y] 

-y in ras. A. s^tiv] comp. B, J supra scr. D^, om. D. ro] 
t6 (liv D. 9. 1] corr. ex y A. fioiQ&v] om. D. 10. 

S6tai] i6tiv C. JI^] Kn D. 0] 6 BD. v&] -& euan. D. 

11. TtSQicpsQSia — 12. K^X] mg. D. 12. (liv] om. D. 

K^X] K^X TcsQicpiQSia (comp.) D. ^ ^] p^ AC, ut sae- 
pius. 13. d'] ds D. 14. ZST] £rz D. 17. Post avtrj 

del. tiifjiia D^. 18. tov (pr.)] supra scr. D^ 20. yiivtQOJv] 
comp. supra scr. D^, -nivtQav rj B, 



MA0HMATIKHS STNTAgESJS T'. 237 

TcdXiv STtEL^ olcov Tj EZ idsvx^V P ^^L\ totovtcjv 
^v Tcal rj ZlBl sv^sla a /3, Kal olcsv dga i6rlv '^ EZ 
v7tOTSLVOv6a ~QX^ toLOvzcDv s6xaL xal 7] iisv ZS svd^sta 
fid' ]JLg syyLdta^ ri d' iit' avrfjg TCSQLCpsQSLa rov yQa- 
<po^svov kvkXov tcsql rb EZS OQd-oycovLOv roLOvrcov 5 
^'9' syyL6ra^ oXcov i6rlv 6 KvxXog r^' zal t} vTtb ZElSl 
ccQa ycovLa^ olcov ^sv s16lv at dvo OQxtal tJ, ro^ot^iroi/ 
s6raL ^-9" 5 oXov ds at d bQd-al t|, roLOvrcov xd A. 
S6r' iitsl utQbg ra TtsvrQG) i6rlv rov ^G^dLaxov^ zal i^ 
B H TtSQLcpSQSLa, 7}v TtQOTjystraL rb xara rb H aitoysLov lo 
rov B d^SQLvov rQOjtLKOv ^rj^SLOV^ ^olqcov i6rLV ocd X. 
XoLTtbv ds^ iitSLdri rb ^sv OU rsraQrrj^OQLOv xal rb 
2JN sxdrsQOV ^olqcov i6rLv 9, s6rLV 8s ;cal 'j^ 
fisv OA 7tSQL(psQSLa avrri rs %al i^ ^^ sxarsQa 
^OLQ&v /3 1, i^ ^^ M27 ^oLQcbv o vQ'^ scal 17 ^sv 15 
AM TtsQLcpsQSLa s6raL ^olq&v stg 'vd^ rj ds M& ^ol- 
Q&v Ttr} ^d'. dXXd rdg ^sv Ttg vd ^OLQag b^aXcbg 6 
ijXLog dLSQXsrat iv rjfisQaLg jtrj xal rj\ rdg ds Ttrj ^d' 
fiOLQag iv rj^SQaLg 9 xal rj syyL6ra' &6rs Tcal rrjv fisv 
Pz/ TtSQLcpsQSLav ^ ijrLg i6rlv djtb fisroTtcoQLvrjg l6rj- 20 
^SQLag iitl ^^ffcftf^^iv?)!/ rQoitriv^ g)av7]6sraL dLSQX^^svog 



2. 7}v] corr. ex ?] C^ 3. tovovtcov D. Post sffrat add. 
KCil ^ ^L' C, del. C^. xat'] supra scr. C^. ZS/] ^TZ D. 
5. EZS;] ZES: corr. ex ZS D. 6. t|"] r- e corr. C. 

■ ZES] ZE- in ras. D\ 7. ^Qd-uL A. 8. d] posfc ras. 1 
litt. D. 9, t6 yi^vtQov D, corr. D^ saxCv'] -v del. D^, 

comp. B. 10. 7t£Qiq>^Qsvci A. tjv] corr. ex 7] C^ 11. sctlv] 
-V del. D^, comp. B. 13. s-ncctsQov] -o- mut. in co C*, sed 

rursus corr. iativ] ^ati D, comp. B. 14. ts] in ras. D^. 



0N] corr. ex OiV Dl 15. 0] ovSsv D. 16. (iolq&v (alt.)] (i 
supra scr. A^ 18. SisQxstaL] corr. ex SQ%stai D^. 19. 7\'] 
dxTob D, 6yd6(p D^ 



238 



KAATAIOT nXOAEMAIOT 




6 i]hog iv r]^bqaig Ttri xal rj^ trjv Se A A, 7]tLg iatlv 
aith %ELiL8QLvfig tQOJtrjg iitl trjv iaQivriv larj^SQLav^ iv 
rj^igaLg 9 ^ccl ri ByyL(3ta. xal svQr^taL rj^tv ta jtQO- 
xsL^sva 6v^(pG)V(og totg vno tov 'l7t7tdQ%ov Xsyo^ivoLg, 
5 Tcato:^ tavtag ovv tag nrjXLXotrjtag ^xstl^cb^sd^a jtQO- 
tSQOv^ 7t66ov ictlv tb 7tkst6tov dLacpoQOv trjg oiiaXfig 
oiLV7]6scog TtaQa trjv dvco^aXov^ 
%al TtQog tL6L 6rj^SL0Lg tb tOL- 
ovtov 6v^p7]6staL. 

10 s6tc3 drj sxxsvtQog ocvxXog 6 
ABF TtsQl xivtQOv tb A xal 
dtd^stQov dLa tov A d^toysCov 
tijv AAFj i(p^ rjg s6t(D tb xiv- 
tQov tot) ^G)dLaKov tb Ey xal 

15 7tQbg OQd^dg y^ovCag tfj AF 7]x&c3 

rj EBy xal i^ts^svx^f^ rj AB. i^tsC^ oXgjv i6t\v rj Bzl 
ix tov xivtQOv I, tOLOvtcov iatlv ri AE ^ista^i) t&v 
xivtQcov j3 A xatd tbv tstQaxaLSLXo6a7tXa6Cova Xoyov^ 
xal OL(ov aQa i^tlv rj Bzf v7totsCvov6a 'qx^ tOLOvtcov 

20 s6taL xal rj ^sv AE svdsta £, rj d' i7t avtrjg 7tSQLcpiQSLa 
tOLOvtcjv d JLtg syyL0ta^ oC(ov i6tlv 6 7tEQl ro BAE oqQ^o- 
ycovLOv xvxkog t|. G)6ts xal r] V7tb ABE ycovCa^ r^tLg 
7tEQLi%SL tb 7tlEt6tov dtdcpoQov tfjg dvco^aXCag^ oIlcov ^iv 
EL6LV aC dvo hQQ^al t|, tOLOvtcav ^6tai d jilg, olg)v d^ 

1. 7j'] rj A, rj D. 7]tig sgtlv'] -g la- et -lv in ras. A^ 

2. ano — ■P90-] d- in ras., cetera in mg. A^ xr\v'\ om. D. 

3. 7j'] r\' AC. 4. XEyo[iBVOLg] inLXsXoyLGybivoLg J). 5. tzqo- 

xEqov^ 7tQox8Qcov A, TCQmxoDV D. 6. ioxC D, comp. B, 8. rtdt] 
seq. ras. 1 litt. A. xolovxov] corr. ex xolovxo D^. 13, 

sffTO)] iaxL D. 14. xat'] &7tb xov E ticcl D, nal anb xov E D^ 
_ 16, inL^svxd-co BC, corr. B^Cl BJ] corr, ex BA Cl 18. 
§] pQst ras. 1 litt. B. 19. BJ] corr. ex BA A. 20, d'] 

ds D. 24, d'] di D. 



MAeHMATIKHS STNTASES^S T'. 



239 



ai 8 OQ^al t|, roLOvtav /3 liy. tav (f avt&v i^tiv 
xal tj ^6V V7C0 BEJ OQd^rj ycovca ^^ rj ds l'6rj tatg 
dv6lv vTtb B^ A drjXovotL 9/3 x^. xal iTtel %Qog totg 
xevtQoig elolv r] ^ev vjtb B^A tov eTcxevtQov^ ij ^^ 
vTtb BEA tov t^GidLaHov^ e%o^ev ro ^ev 7tXet6tov did- 5 
(poQOV tov jtaQa tr]v dvco^aXCav ^olqg)v /3 jcj^, tcjv de 
TteQLcpeQei&v^ TtQbg alg tovto yCvetaL^ tr^v ^ev tov eoc- 
xevtQov xal o^aXrjv ^olq&v 9/3 'ycy ditb tov ditoyeCov^ 
trjv de tov ^cjdLaxov xal dvco^aXov cpaLVO^evrjv tcov 
tov tetaQtrj^oQCov^ xad^aTteQ %al jtQoteQov ditedeC^a^iev^ 10 
^OLQcbv 9. (paveQOv d' eK tcbv 7tQoe(pGidev^evcov ^ oti 
xatd t6 dvtLKeCnevov t^rj^a rj ^ev (pacvo^evr] ^e6r] 
jtaQodog xal tb 7tlet6tov didcpOQov trjg dvco^aXCag 
e6taL xatd rdg 6o ^oCQag^ r] d' o^aXr] xal xatd tbv 

exxevtQOv xatd tdg ^|J AJ. 15 

Lva de Tcal dLa tcbv dQLd^^cbv^ 
cjg ecpa^iev^ tdg avtdg 7tr]XLx6tr]tag 
deC^cj^ev Cvvayo^evag xal e7tl trjg 
Tcatd tbv e^tCnvnlov v^tod^e^ecog^ 
otav OL avtol XoyoL, Tcad'' bv elQr]- 20 
xa^ev Tpdjrov, TCeQLexcovtaL^ e6tc3 
6 (lev o^oxevtQog tip dLa ^e6cov 
tcbv ^adCcov xvxlog 6 ABF jteQl 
xevtQov tb /i xal dLa^etQov ti]v A^F^ 6 ^' ejtC- 
xvxlog EZH TteQl xevtQOv tb A^ xal ^-O-co d^tb tov 25 

1. iotL D, comp. B. 3. 9|3] ft 9(3 D. 8. (iolq&v] fiOLgag 
corr. ex iioiQav D. 11. cpavsQbv d' iv,] in ras. B^ TtQoscpodsv- 
^ivcov C. oxi\oxiv.atI>. 12. rfiTjfia] i^/xtxvxAioi' D. l^. v.ata, 
— liOLQag] et in textu in ras. et renouat. D^ (jso ^oiQag) et supra 
scr. D^ d'] di D. 19. Kata tov] Y,at D. 21. iiSQtixovtaL CD, 
corr. D. 22. 6 [jbiv'] om. D. Slo, — 23. ^cpdlcov] ^cp8Lav.&i D. 
24.T17V] corr. ex tov C^ -- - - - 

uel R KK 




8'] di D. 25. EZH] E- corr. ex iV 



240 KAATAIOT nTOAEMAIOT 

A iq)a7tto^evrj tov STaTcvKXov svd^sta ij ^ZB^ zal ijt- 
stsvxd^co rj AZ. yCvstai dri coeavtag [p. 219^ 21] sv 
OQd^oycovLG) tm A/IZ tstQaKatSLK06a7cXa6LG)v ri A/l 
tfjg AZ^ w6ts KaC^ oig)V i6tlv rj AA 'bjtotsCvovOa ~q7c^ 
5 toLOvtcjv TcdXiv Kal trjv ^sv AZ yCvsGd^ai i, tr^v d\ 
iii avtrjg TCSQicpSQSiav toiovtcov d jitg, olcjv ictlv 6 
TtSQi to A/dZ OQd-oycovLov yQacponsvog KVKXog t|* Kal 
rj vTtb AAZ ccQa yovCa^ oZov ^sv s16lv at dvo dQd^al 
r^, tOLOvtcov s6taL d ^g, ol^cjv ds ai d dQd-al t|, toi- 

10 ovtcav /3 xy. tb ^sv 7tksl6tov ccQa dLccipoQov trjg avco- 
laaXCag^ tovts6tLV rj AB TtSQLCpSQSLa ^ Kal ivtsvd^sv 
svQrjtaL 6v^cpd)vcjg ^olqcjv /3 jc/, rj ds dvd)^log TtsQt- 
cpSQSLa^ ijtsCitSQ ifTtb trjg 'bjtb AZA OQ^r\g ycovCag 
TtSQLSxstaL^ liOLQcbv 9, ri ds dfLaXtj^ JtSQLSxoiisvrj ds V7tb 

15 tfig vTtb EAZ yovCag^ ^olqcjv TtdUv 9/3 '^y. 

s. IIsqI tfjg TtQbg td Katd ^SQog t^tj^ata trjg 
dvcjfiaXCag i7tL6Kitf;scog. 

"EvsKSv 8s tov xal tdg Katd iisQog dvco^dXovg 

KLV7]6sLg SKd6tots dvva^d^at dLaKQCvsLv dsC^o^sv jtdXtv 

20 icp^ SKatEQag tcbv vjtod^s^scov ^ itcbg dv fiLdg tcbv iK- 

KSLiLSvcov %SQL(psQSLG)v dod^sC^r^g Xa^pdvoL^sv Kal tdg 

XoLTtdg. 



1. sn£^Ev%(o C. 13. inCnEQ A, corr. A^ AZJ] corr. 
ex AJZ Dl 14. ^£(alt.)] om. B. 15. vTto] D, om. ABC. 
EAZ] D, corr. ex EZ A, Ez/Z BC, corr. C^. 9^ xy ] in 
ras. Bl 16. «'] mg. C, om. ABD. T(iri(iaTcc'] e corr. B^, 

supra scr. D^ rryg ccvcofiaXLag] t&v ccvcofiaXi&v 'Kavovonouag D, 
corr. p^ {yQ-)i '^^'^ avcofidXcov %avovonoUag e corr. B^, yq. nsQi 
Ta>v %ara fiSQog Ti~]g avco^allag B^. 17. 8ni6v.iip£cog] ABC, 

om. D. 19. dBi^oiLBv] -si- e corr. D^ 20. syiyiSL^ivcov] -v,si- 
e corr. D^ 



MA0HMATIKHS STNTASESiS V. 



241 




e6TC3 drj 7CQG3TOV ^sv o^oKSVTQog rd3 Jcodtaxco 
KvxXog 6 ABF tisqI KavtQOv t6 z/, 6 d' sxxsvtQog 6 
EZH TteQL TcsvTQov t6 0, Q^ ^^ 
df-' d^cpotBQCJV tcbv xevtQcsv Tcal 
tov E djtoysLov dLcc^stQog ri 5 
EA®^H^ xccl dTCoXrjcpd^Si^rjg tfjg 
EZ TtSQLCpSQsCag S7ts^svx,^co6av r^ 
ts Z/i xal ri Z0. dsdoGd^cj ds 

TtQCOtOV r] EZ TtSQLCpSQSLa ^OLQCJV 

ov6a loyov svsksv A, xal SK^Xrj- lo 
d-SL^rig tf]g ZS zdd^stog sit avtriv 
i^Xd^cj djtb tov ^ ri ZfK. STtsl 
roLVvv r] EZ TtSQLcpsQSLa vjtoxsLtaL ^olqcjv A, xal 
7] vito E0Z ccQa ycavCa^ tovts6tLv rj v7to ^®K^ 
o^Ccov iLSv SL0LV at 8 oQ^^al t|, toLovtav s6tlv A, oXcov 15 
8s c^t 8vo oQd^al t|, tOLOvtcav |. Tcal r] ^sv STtl trlg 
^K ccQa TtSQLcpsQSLa tOLOvtcov s6tlv 5, o^LCJv 6 tcsqI t6 
^&K oQd^oycDVLOv KVKkog t|, r] 8s sitl trjg K& tcbv 
koLitSiv slg t6 rj^LKvxXLov [Eucl. III, 31] ^. xal at 
4)% avtdg ccQa svd^staL s6ovtaL rj ^sv ^K toLOvtov 20 
4, oXcav s6tlv rj ^& v7totsCvov6a ^, 17 8s K& tcbv 
avtav oy vs' C36ts Kal oHcjv s6tlv rj ^sv z/0 svd^sia 
§ k^ r] 8s Z® s% tov xsvtQOv |, toLOvtcov xal 7) ^sv 
jdK s6taL d Ts^ ri 8s ®K t&v avtcjv pT, rj 8s K@Z 



2. ABT] ABF^ B. 6. EAO^H] EAGzl D. 7. EZ] 

corr. ex ES D^. inL^svxd^coGav BC, corr. B^C^ 1]] ai' D. 

8. 7]] om. D. 13. EZ] corr. ex Ea D-. 14. vtto (pr.) — 

ij (alt.)J mg. C^ E0Z — zl0K] mg. A^B. r) (alt.)] ins. D^, 

supra scr. ^/ D. 15. iati D, comp. B. ^] D, in ras. 

A^B^C-. 17. JK] in ras. A*. 18. K@] @K^^ 20. ^jr'] 

vTio D. 21. iGtlv rf] corr, ex. iGtL D^ 22. gy vs] in ras. D. 

23. X] in ras. A*. 24. @K]K@I>. K@Z] corr. ex XZ D-- 

Ptolemaeus, ed. Heiberg. 16 



242 KAATAIOT nTOAEMAIOT 

oXyj 1/3 7. xal STtsl ra djt avrwv GvvxE^ivta TtocsV 
t6 aTcb rfjs ZzJ [Eucl. I, 47]^ e^xaL xal i] Zzl vTto- 
TBivovda roiovTCov |/3 Ta eyyi0ta. Tcal olcjv aga ictlv 
7] Z^ ^, toiovtov e^tai xal yj ^sv ^K sv&sta /3 %Sy 
5 ri d' ST^ avtijg TtSQKpSQSia toiovtov ^ Trj^ otcov s6tlv 
6 TtSQl tb Z/IK oQd-oy^vLOV ocvxXog tJ* a6ts xal 'fj 
vjtb ^ZK ycDVLa^ olcov ^sv st0Lv at dvo dQd^al tJ^ 
tOLOvtcjv s6tlv /3 Trj^ olcov ds aC d oQd^al t|, tOLovtcov 
a ^. to6ovtG)v aQa s6tlv t6 TtaQa triv avco^alCav 
10 TOTf dLd(pOQOV. tcjv 6' avt&v rjv rj VTtb E@Z ycovCa 
X' xal XoLTf^ [Eucl. I, 32] clQa rj vTtb AziB ycovCa^ 

tOVtS6tLV rj AB tOV i^CodLaKOV TtSQLCpSQSLa^ ^OLQCbv 

S6XLV 'xrj vd. 

otL ds^ xdv dlXrj tLg tcov yavLCOv do&fj^ xal aC 

15 XoLTtal do^ri6ovtaL^ (pavsQbv avtod-sv s6taL xad-stov 
dxd-sC6r]g sjtl trjg avtrjg xatayQacprjg ditb tov & STtl 
trjv ZA trjg @A. sdv ts yaQ trjv AB tov ^codLaxov 
TtSQLcpsQSLav vTtod^co^sd^a dsdo^svrjv^ tovts6tLV tijv vjtb 
0AA ycovCav^ dLa tovto s6taL xal 6 trjg A& TtQbg 

20 ®A koyog dsdo^svog [Eucl. Dat. 40]. dsdo^svov ds 
xal tov tfjg AQ TtQbg &Z dod-r]6staL xal 6 trjg @Z 
TtQbg @A [Eucl. Dat. 8], dta tovto ds s%oy.sv dsdo- 
ybsvag tr]v ts vitb @ZA ycovCav [Eucl. Dat. 43], tovt- 
s6tLV t6 TtaQa trjv dvco^alCav dLdcpOQOv^ xal trjv VTtb 

2. ^Gzai — vTto-] supra scr. D^ (vno- etiam in textu D). 

3. eyyioza] eyyLCta olcov t] ^K ^v a Ts D. 4. ?; (pr.)] bis B. 

QTi 7] Zzi D. 6. 6 TTf^i] corr. ex onsQ C^. ZzJK] JZKD. 

8. TOLOvxcov — t|] supra scr. D^. sgtl D^, comp. B. at] 
in ras. A^ 9. iativ] -v del. D^, comp. B. H- ■?]] post 

ras. 1 litt. D. vno AJB] corr. ex ^iE D. 17. @A] -A e 
corr. A*, @J B. idv] ccv D. 18. tovtsgtl D, comp. B. 

19. @JA] rJA B, BJA Bl Ante dLct del. dtdo^ivog 

fiBV D^ 21. J@] A@ e corr. A^ 22. di] corr. ex d' D-. 



MA0HMATIKH2 STNTASESiS F'. 



243 




ESZj tovtE6ri,v trjv EZ tov ixxEvtQOv TtSQKpsQSLav. 
idv t£ t6 TtccQcc tfjv avaiiaXiav did^pOQOv VTtod^cofisd^a 
dedo^evov^ tovtedttv t^v 'bno 
0Zz/ ycovCav^ dvaTCaXLv td aiitd 
6vyb^ri6Etai^ dsdo^svov ^ev dtd 5 
tovto tov tijg @Z TtQog ®A Xo- 
yov [Eucl. Dat. 40], dsdo^evov 
ds i^ dQxyjg ^al tov tf}g @Z TtQog 
©z/, w6t£ dEdo^d-at ii£v xal tbv 
tfjg z/0 TtQog ®A Xoyov [Eucl. lo 
Dat. 8], dEdo^xtai dl did tovto 
xal trjv vjtb ®zIA ycoviav [Eucl. 
; Dat. 43], tovt£6tiv t^v AB tov ^aydiaKov 7t£Qi(piQ£iav^ 
ocal t^v vTtb E®Z [Eucl. I, 32], tovti^tiv triv EZ 
roi> ixxivtQOv 7t£QicpiQ£iav. 15 

ndXiv £6tco 6 ^£v 6^6x£vtQog ta did ^iocov xvxXog 
6 ABF TtEQv xivtQov tb A xal did^£tQov trjv Az/F^ 
, 6 d£ xatd tbv avtbv Xoyov iitixvxlog 6 EZH& tieqI 
xivtQOv tb A^ xal ditoXr^cpd^Et^rjg trjg EZ 7t£Qi(p£Q£iag 
i iTtE^Evxd^co^av 7] t£ ZBA xal r] ZA' vTtoxEiad-co df 20 
Ttdkiv rj EZ 7t£Qi(piQ£ia tcbv avtcbv ^OiQCJV X' xal 
rjj(^d^cj d7tb rov Z xdd^Etog iTtl tf^v AE rj KZ, 

ijtEi fi EZ 7t£Qi(piQ£ia ^oiQcjv i6tiv A, £i!yi dv xal 
rj ^£v V7tb EAZ ycovia^ oXcov ^iv £i<5iv at d oQd^al 
r|, toiovtcov A, otW de at /3 OQd-al r|, toiovtcov J* 25 
«^rf xal 1] ^£v i7tl tf]g ZK 7t£Qi(piQ£ia tOiOvtCDv i^tlv 



1. tovT^an D, comp. B. 6. 0Z] Z0 D. 8. df] d' D. 

0Z] Z0 D. 11. dh Slo] -s 8- e corr. A. 12. ttjv] tyiv 
T£ D. 13. T0VT86TL D, •conip. B. 14. T0VTS6TL D, comp. B. 

16. dicc nEGcov] ^oodicc^a» D. 18. EZHQ] corr. ex ZH@ 

D2. 21. 1^] supra scr. C'-. 22. AE] A@ J). KZ] ZK D. 

23. EZ] ZE D. ioTL D, comp. B. 



16 



244 



KAATAIOT nTOAEMAIOT 



J, otW 6 tcsqI t6 AZK OQd^oycovLov xvjclog t|, rj d' 

STtl tijg AK tav Xoltccov etg tb rj^ixvxliov [Eucl. 

III, 31] 'qz. xal ai vtc avtag ccQa svd^stai e^ovtat ri 

^£V ZK toiovtov I, oZg3v 
5 £0tiv 7] AZ did^etQog ^, 

ri ds KA t&v avtcov ^ 

ve' C36te Kai, oicov eatlv rj 

^ev AZ v7toteivov6a /3 A, 

ri de AZl ex tov TcevtQov 
10 5, toiovtcDv e6tai zal 7] 

^ev ZK evd^eta a Te, rj 8e 

KA tcov avtcov /3 1, rj de 

KAA oXrj 1/3 t. xal ejtel 

ta aii avtOiv 6vvte^evta 
15 itoiet t6 d%o trig ZBA 

[Eucl. I, 47], e(5tai xal rj 

Zz/ ^7]xei toiovtcov |j3 Td^ 

OiG3v r] ZK rjv d Te. xal oicov ccQa e6tlv rj A Z v7to- 

teivov6a ~Qx^ toiovtcov e6tai xal 7] ^ev ZK evd^eta /3 
20 3^5 V <^' ^'^' ccvf^VS TteQicpeQeia toiovtcjv /3 Trj^ oZcov 

6 TteQi t6 AZK oQd^oyd^viov xvxXog t|* S6te xal rj 

vjtb ZAK ycovia^ oicov ^ev el^iv at dvo oQ^al t|, 

toiovtav e6t\v j3 fc^, oXcov d' al d oQd^al t§, toiovtcov 

d d'. to6ovtG}v ccQa e6tlv Ttdliv t6 itaQa trjv dvcj- 
25 ^aliav didcpoQov trig AB iteQiq^eQeiag. tcov d' avtcov 




1. d'] A, ^£ BCD. 8. ;i] D, in ras. B^, ^ A, corr. ex 
J C^. 13. ip 1] corr. ex | seq. ras. 1 litt. D^ 14. ovv- 

xiQ-ivxa D, corr. D^. 15. rd] t6i/ BC, corr. Cl ZBz/] 

z/Z D. 17. Zz/] z/Z D. 18. Tiv a] corr. ex i] va C^D^, 
cc in ras. A*. z/Z] Zz^ D. ^ 21. 6] ot C. i)] ins. Dl 
23. saxL D, comp. B. d'] da D. 24. xooovxov D. i art D, 
comp. B. 



MA0HMATIKHS 2TNTASESiS T'. 



245 



^v xal rj vjtb EAZ yavCa A* koLTtri [Eucl. I, 32] ccQa 
ri vTtb AZ/1 yoovCa^ tovraatcv r] cpaivo^avrj tov ^cjdLa- 
7C0V TtBQKpeQSia^ iioiQCbv s6tiv %rj va 6v^q)G)va)g tatg 
iitl tfig SKXSVtQotrjtog aTtodsdsiy^ivaig 7tr}li7c6tr]6iv. 

o^oiGtg ds xal iv^dde^ Tcav aXXrj dod^f] ycovia^ dsdo- 5 
fiivai £6ovtai xal au loiital ajfiei^rig Kad-itov inl tfjg 
avtrjg xatayQacprjg aitb tov A ijtl trjv z/Z tfjg AA, 
idv te yccQ itdliv tijv g^aivo^ivrjv 
tov ^mdiazov TteQicpsQeiav dcb^ev^ 
tovti6tiv tijv vTtb AZA ycaviav^ 10 
dedo^ivog ^ev 8id tovto e6tai xal 
6 tfjg ZA TtQbg AA Xoyog [Eucl. 
Dat. 40], dedo^ivov de e^ dQxfjg 
xal Toi) tfjg ZA TtQbg AA do- 
d^ij^etai xal 6 tfjg A A TtQbg AA 16 
[Eucl. Dat. 8]. dicc de tovto xal 
7] te vTtb AZlB ycjvCa do^r]6etai 
[Eucl. Dat. 43], tovti6tiv rj AB jteQicpiQeia tov 
TtaQcc tfjv dvcj^aXiav diaq^oQov^ Tcal rj VTtb EAZ 
[Eucl. I, 32], tovti6tiv 1] EZ tov ijtixvKXov TteQi- 20 
(piQeia. idv te to naQa tfjv dvc3^a2.iav didcpoQov vito- 
^cb^ed-a dedo^ivoVy tovti6tiv tfjv vjtb AAB ycoviav^ 
dvditaXiV (ii6avtcog 8o%f\6etai \iev 8id tovto xal 6 tfjg 
AA TtQbg AA Uyog [Eucl. Dat. 40], dedo^ivov de £| 
^QX^ig 3<«t tov tfjg A A TtQbg AZ dod^TJ^etai xal 6 tfjg 25 

1. XoiTcfi] v.aX XoLnfi D. 2. xovxiexiv i]] xovxeott D. 4. 
syfnsvxQOxrixos] post -d- ras. 1 litt. A. ccTtodsdsiYfiEvccig] -ai- 
in ras. D. njiU-noxriXog D, sed corr, 8. eccv'] ccv D. 10. 
X0VXS6XI D, comp. B. 12. TCQoq] corr. ex 11^6 A. 13. df] 

d' D. 14. AJ] corr. ex AA B^C^, AA D. 17. A^B] corr. ex 
A^ A.'^. 22. rovTfWBD. 23. -g do-] e corr. D. 24. ^z^] in 
ras. C^, /iA D. iiQog — 25. /d A] supra scr. D^ 25. nQog AZ] 
supra Z scr. A post ras. D^, eadem uerba supra scr. D^, sed del. 




246 



KAATAIOT nXOAEMAIOT 



ZA TtQos AA [Eucl. Dat. 8], ^ik df tovxo %a\ r^ xb 
vno AZA ycovia dsdo^ivrj e6xai [Eucl. Dat. 43], rovr- 
£0rLV ri (paLvoiLBvri rov t,(pdiaxov TtSQicpeQSia^ ;cal r} 
vitb EAZ [Eucl. I, 32], rovri^riv r^ EZ rov im- 

5 %VXl0V TtEQiCpBQEia. 

Ttdliv iiti rfjg TtQOxeiiiivrjg roD 
ixxivrQov kvxXov xarayQacprjg aTt- 
Eilrjcpd-co ccTto rov H itEQiyeiov 
rov ixxivrQOV rj HZ TtSQicpi- 

10 Q£ia VTtOKSi^ivr] rcbv avrcbv ^Oi- 
Qcjv ly jcal i7ts^svx^cj6av rj rs 
ZlZB Tcal r] Z0, %al xccd-srog 
rix^(io djtb rov z/ iitl rr^v @Z 
^ JK. 

15 iTtsl r] ZH TtSQicpiQSia ^oiQCJv ionv A, Sirj dv xal 
r] vjtb Z@H ycovia^ oYcjv ^iv si6iv at d oQ^al t|, 
roiovrcjv /l, 0iG)v ds at dvo OQd-al r|, roiovrcjv ^. 
&6rs xal r] ^sv iitl rfjg AK svdsiag TtSQicpiQSia roi- 
ovrcDv i6rlv f, oicjv 6 TtsQl rb ^®K oQd^oycoviov 

20 KvxXog t|, -j^ <^' i^\ T^VS -^® '^^*' XoiTtcov [Eucl. III^ 31] 
Sig rb r]HiKVKliov rfir^^drov 'qk' Kal aC v7torsivov6ai 
aQa avrdg sv^stai s6ovrai r] ^sv ^K roiovrcov |, 
Oicov i6rlv 7] AS did^svQog ^, r] ds K® rcov avrcov 
'oy vs. Ktti oZcov aQa i6rlv r] ^sv z/@ v7torsivov6a 

25/3 A, 17 ds 0Z iK rov KivxQov |, roiovrcov i6rlv Kal 




1. Ts] om. D. 2. AZJ] AZ BC, corr. C\ 9. HZ] 

H- in ras. D. 12. Z@] 0Z D. 13. @Z] "Z@' B. 14. 
7]] A, in ras. D^, 17 8i BC, corr. C^, 8i eras. B. 15. bgxi D, 
comp. B. 16. Z@H] H@ C, @H C\ 17. dvo] § corr. ex 
t^ D. 21. xfirjiidrojv] om. D. vTtotSLVovGai] corr. ex ccno- 
xtLvovGccL C, corr. ex vnoxBivovaa D-. 23. isxlv i]] corr. ex 
SGXL D^. 25. sGXLv] comj). B, tcxuL D. 



MA0HMATIKHS STNTASESiS T'. 247 

71 ^£v ^K evd-sta a Ts^ 'fj ds ®K o^otcog ^ T^ '^ ds 
KZ rcbv koi7tG)v vt, v, xal stcsI ra ai^ avxobv Ovvrs- 
^eWc^ Ttotet t6 aTtb rrjg z/Z [Eucl. 1,47], e(Srai, ocal 
avxri fi7]K£L roiovrcDV v^ va eyyi^ra^ oZcav 'fj zfK ^v 
d Te. xal oZcav aga e6r\v r] AX 'b7toreivov6a ^, roi- 5 
ovrGiv Tcal 'rj ^ev zfK ^6rat )3 Ad Ag, i^ ^' ^'^' avrrjg 
^eQtg)£Qeia xoiovxov /3 xt,^ oXov 6 Ttegl rb AXK 
dgd^oyavtov xt^xXog r|* ^ere xal 'yi 'VTtb ^ZK ycovCa^ 
oZov ftfV et6tv aC dvo d^^al tJ, roiovxcov e<5rlv /3 xS;, 
oY(ov 8' aC d oQd^al t|, rotovrov a td eyyt6ra. ro6ov- 10 
xav aQa e6rl rb TtaQo. r^^v avco^altav dtd(poQOv. xal 
eTtel r&v avr&v 'VTtoxetrat xal 'fi 'vitb ZSH ycovia A, 
e6xai xal 'rj 'vnb jBz/P oAi^, rovre6rtv i^ J^B rov Jco- 
Staxov TteQtcpeQeia^ ^olqcjv Xa td. 

zaxa xa auTft; de nal evd^dds expXrjd^ei^rig xr]g 5z/ 15 
^al xad^exov eit a^vxrjv dxd^ei^rjg xfjg ®A^ edv xe x^rjv 
FB xov ^(pdtaKo^v TteQtcpeQetav dcb^ev^ xovxe6xtv xrjv 
VTtb @^A ycjviav^ dod^yj^exat ^ev dtd xovxo xal 6 
xrjg A0 TtQbg ®A koyog [Eucl. Dat. 40], dedo^evov 



1. ©K] corr. ex OK D^. ofioLcog] -o- e corr. in scrib. C. 

r] corr. ex ui C^ 4. Supra v^ va scr. v^ v fid- D^. rjv a] 
corr. ex T} v^ C^D*. 5. xat'] %a&' BC,^orr. C^. 6. Xs] 

Is^ f in ras., D^, l supra add. D^ Zg] Xd in ras. D^, g 

supra scr. D; cfr. p. 249, 20. «5^'] 8s D. avrf^g] C^D, avrrjv 
ABC. 7. JZK] corr. ex ^Z A^. 9. Svo] A, ^BB, dv C. 

sGTLv] comp. B, sGxaL D. 10. 8'] di D. a lS] corr. ex 
ccL A D^. zoaovtcov] corr. ex toaovrov D^ 11. iatC] AD^, 
comp. B, satLv CD. 12. Z@H] corr. ex ZH@ C^ 1] 

tQLay.oatij D, tQLd-aovta D^. 13. ^ataL] corr. ex satLv C. 

Bz/r] mut. in BJH Cl 14. s^^g ^ %at ayQacpi] fol. 70"^ D, 
fig. seq. fol. 70^. 15. ta avtd] corr. ex tavtd D^ BJ] 

BA C. 16. rs] corr. ex ys D^. 17. tovtiatLv] comp. B, 

-V del. D-. 18. 0JA] corr. ex z/0^ D^ ycoviav] corr. 

ex ycavia C^ 



248 



KAATAIOT nTOAEMAIOT 




ds i^ o^QXVS 5c«^ '^ov rrjg 0^ nQos ®Z do&YJ66taL xal 

6 rrjg Z0 TtQog @A [EucL Dat. 8]. dia rovxo d^ 

£^o^sv dedo^Bvag %v\v rs vjtb &Zzi yovCav [Eucl. 

Dat. 43], rovrs6rLv rb JcaQa rrjv 
5 avc3iiaXCav didfpOQOv^ xal rrjv VTtb 

Z@J [Eucl. I, 32], rovrs0rLV 

rrjv HZ rov sjcxsvrQOv tcsql- 

(psQSiav. sdv rs rb TCaQa rijv dvcj- 

liaXCav didcpoQov d&^sv, rovr- 
10 s6riv rijv vjtb QZzJ ycovCav^ dvd- 

TCaXiV dod"]^6srai ^sv did rovro 

xal 6 rfjg Z& TCQbg @A koyog 

[Eucl. Dat. 40], dsdo^svov d' s^ 

dQX^yjg ^ocl rov rfjg Z® TCQbg 0z/ dod-7]6srai Tcal 6 rrjg 
15 ^0 ^Qog &A [Eucl. Dat. 8]. did ds rovro dsdo^svag 

s%o^sv rr\v rs vTcb &^A ycovCav [Eucl. Dat. 43], rovr- 

s6riv rijv FB TCSQicpsQSiav rov ^adiaxov^ Tcal rrjv 

vTcb Z®H [Eucl. I, 32], rovrs6riv rr^v HZ rov sk- 

XSVrQOV TCSQiCpSQSiaV. 

20 c}6avraig sjtl rrig TtQoxsi^svrjg rov o^oKsvrQov xal 
rov STtiXvxkov xatayQaq)rjg d7to2,rjq)d'sC6r]g dicb rov @ 
TCSQiysCov rfjg ®H icsQicpSQsCag rcbv avrcjv fioiQav X 
s%st,sv'i%'G)6av [Lsv ri rs AH xal rj ZlHB^ xdd^srog ds 
dicb rov H stcI rrjv AA ^ypco r\ HK. sicsl ovv 

25 TcdXiv ii ®H TCSQicpSQSia ^oiQ&v s6tiv A, slrj dv xal 



1. ds] S' D. @J] J@ D. 2. Z0] corr. ex ZE D. 3. 

0ZJ] 0Z BC, corr. C^ 4. xovxbgxl D, comp. B. 6. rovt- 

sGxi D, comp. B. 9. xovxiGTi D, comp. B. 16. @/JA\ corr. 

ex J&A C^ xovxicxi D, comp. B. 18. xovxegxl D, comp. B. 
23. Supra JHB scr. Z D. ■ndQ-sxog] ante -g ras. 1 litt. D, 
ds] d' D. 25. 0H] H@ B. hxiv] s- e corr. C, comp. B, 

ioti D. 



MA0HMATIKHS STNTASES^S T\ 



249 



-j^ VTtb ®AH yovCa^ oXcav ^ev 8L0iv aC d OQd-al r|, 
tOLOvtcov A, oicov d' aC dvo dQd-al tI, toiovtcov |* 
co6ts xal ri ^sv ijtl trjg HK TtSQicpsQSia toiovtcov 
£6tlv I, 0LC3V 6 7C6qI to HKA OQd^oycbvLov xvTcXog t|, 

Yi ds iitl trjg AK tcbv XoiTt&v 5 
[Eucl. III, 31] £ig t6 riiLixv%Xiov 
Qoc. xal tcbv VTt avtag ccQa £v- 
^£iav rj ^£v HK £6tai toiovtcov 
I, 0LC3V iatlv rj AH v7tot£LVOv6a 
Q^^ r] d£ AK tcbv avtcjv p/ v£. lo 
ocal oLcov ccQa i6tlv rj ^£v AH 
£v%-£La /3 A, rj dh A^ ix tov 
xivtQOV 5, tOLOvtcov xal rj ^£v 
HK £6tai a ~i£.) rj ds AK o^OLcog 
Kzf tG)V Xoiitcbv vt, V. xal iitsX tk 15 
aTt' avtcov 6vvt£^£vta 7toi£i t6 aTtb tijg ^H [Eucl. 
I, 47], iiiYiK£i ccQa £6tai xal avtij toiovtcov vt, va 
^yyi^ta^ olcov ri KH £v%-£ia rjv a Ti. Tcal oicov 
ccQa i6tlv ri /IH {)7tot£ivov6a qx^ toiovtcov £6tai xal 
r] ^£v HK ^vd^^la p Xd Xg^ rj ds iTt avtfjg 7t£Qicp£Q£La 20 
toiovtGov p K^^ oZcov 6 7t£Ql t6 zfHK xvxXog tJ* 
m6t£ xal r] V7tb HAK ycovCa^ oXcov ^iv £i6iv at dvo 
OQ^^al t|, tOLOvtcov i6rlv /3 Tct,., oXcov d' aC d oQd-al 




P 



2. 8'] da D. dvo] § B. 4. HKA] AHKJ). 5. 8t] 
S' D. 9. AH] JH BC, corr. C^. 12. ^ X r]] §17] A. 

A^] -J in ras. D*. 13. |] post lac. 4 litt. B, post lac. 11 
litt. C. 15. 1] X AC. 1] ^g KA] renouat. D^. 16. gvv- 
Tt-O-^VTo: D, corr, D*. 17. avxi] B. 18. av-^-fta] om. D. 

7\v a] corr. ex 17 va C^. 20. ~§ U Xs] JX6^ D. Se] d' D. 

21. JHK] JHK oQ^oywvLov D (co corr. ex D^). 23. 

iatc D, comp. B. 6'] ds D. 



250 



KAATAIOT nTOAEMAIOT 



t|, tolovtcov a id eyyt^ta. xodovxcov ccga i6tlv xb 

TCaga tiiv avoiiaXCav didcpOQOv Kal ivtavd^a^ tovti^tiv 

vi AB TtEQKpEQeia. %al ijtel tS)v avt&v VTtoxsitai r] 

vjtb KAH ycovCa A, 86tai Tcal rj vitb BHA o2,rj 
6 [Eucl. I^ 32], TJtLg 7tBQLi%si triv cpaLvo^ivrjv Toi) ^cDdLa- 

xov 7tsQL(piQ8LaVj ^OLQ&v ka Ld 6v^q)G)VC3g tatg inl 

tov ixxivtQOv TtrjkLKOtrj^LV. 

xatk ravra 6e xal iv^dde xad^itov d%^eC<5rig iitl 

trjv AB tfjg AA^ idv te trjv tov ^cydLaxov 7teQL(piQeLav 
10 da^ev ^ xovxi(jXLV xijv vjtb 

AHA ycjvCav^ dod"^6etaL ^hv 

dLa tovto 6 trjg HA TtQbg 

AA loyog [Eucl. Dat. 40], 

dedofiivov 6' i^ aQxrjg xal tov 
16 tfjg HA TtQbg AA dod"i]0etaL 

%al 6 trjg A A itQbg AA [Eucl. 

Dat. 8]. dta 6\ tovto dedo- 

[livag e%o^ev tiqv te i)7tb AAB 

ycjvCav [Eucl. Dat. 43], rovr- 
20 i6tLv xrjv AB TteQLtpiQeLav xov 

jtaQcc triv dvco^alCav dLacpoQOv^ 

xal tijv vTtb ®AH [Eucl. I, 32], tovxi6xLV tijv @H tov 

inLXvxlov TteQLCpiQeLav. idv te ■xdkLV tijv AB jteQLcpi- 

QeLav dcj^ev tov naQcc tijv dvco^akCav dLacpoQov^ tovvi6tLv 




1. a — saxLv] supra scr. D-. b6xC D^, comp. B. Deinde 
del. h6xiv aqu Dl 3. i] (alt.)] ins. D^. 4. KAH^ HAK D. 

5. 7;Ttg] 1]- corr. ex v D^. 7. fxHfVrpov] iv,- supra scr. D^. 

8. xccvxd] xccvxa A, xccvxcc mut. in xa avxd B^C^D^ 10. 
xovxi6XLv] comp. B, -v del. D^. 14. ■aaL — 15. ^z/] supra 

scr. Dl 15. HA] H- corr. ex N in scr. Dl 16. AA] 

renouat. D^. 19. xovxsaxLv] comp. B, xovts6xl D. 20. Trfv] 
in ras. 1 litt.Dl 22. @AH] HA@ D. xovxs6xl J), comp. B. 

24. xovx^6XL D, comp. B. 



MA0HMATIKHS STNTAgESiS P'. 251 

rriv vjcb AziB yovCav^ dvccTtaXtv d)0avr(og do&TJ^etai ^sv 
dia tovzo 6 rijg AA %Qog AA Xoyog [Eucl. Dat. 40], 
dsdo^Evov (f i^ aQj(^rjg %al tov trjg AA TCgbg AH do- 
%"ifi6Etai xal 6 tfjg HA jtQbg AA [Eucl. Dat. 8]. dia 
de tovto dedo^svag s^o^sv tiqv ts vjtb AHA ycovLav 5 
[Eucl. Dat. 43], tovts6tLv ti^v tov ^GydiaKov TCSQicps- 
Qsiav^ xal trjv VTtb SAH [Eucl. I^ 32], tovts0tLv trjv 
@H tov sjtLxvxXov TtSQLtpSQSiav, ocal dsdsLKtat i^iLiv 
ta jtQotsd-svta. 

TtOLKLlrjg drj Slcc tovtcov tcbv d^scoQrjndtcjv dvva- 10 
^isvrjg 6vvL6ta6%-aL xavovojtOLLag tav 7tsQLS%6vtG)v 
tnriiidtov tdg sx trjg dvo^akCag tcbv cpaLVO^svcov 
TtaQodcov dLaxQCasLg itQbg tb s^ stoC^ov Xa^fidvsLv tdg 
tcbv xatd ^SQog dLOQd^co^scjv TtrjXLXotrjtag dQS0xsL ^akXov 
rjfitv ri tatg biiakatg TtSQLtpsQsCaig TtaQaxsL^svag s^ov^a 15 
tdg TtaQa trjv dvco^aXCav dLacpOQdg dLa ts ro xat' 
ccvtdg tdg v7tod-s6sLg dxoXovd^ov xal d^d tb ditXovv ts 
xal svsTtCpoXov trjg xad'' sxa6ta iprjcpocpoQCag, svd^sv 
dxo2.ovd-'ij0avtsg totg TtQcotOLg xal stcX tav dQLd-^&v 
sxtsd-SL^svoLg t&v d^scjQrj^dtcov xal STtl tcbv xatd 20 
^SQog t^rj^dtcjv sjtsXoyL^d^sd^a dLa tcbv yQa^^cbv 
d)6avtcjg totg ditodsdsLypiSVOLg tdg ixd6tr] t&v biialcbv 
TtSQLcpsQSLCbv i7tLpaXXov6ag trjg dvcj^aXCag dLacpoQdg. 
^caO-dAov ds ta ^sv TtQbg^ ditoysCoLg tstaQtrj^oQLa xal 

■ JB T^^^^ 

1. JJB] a§d D, ad§ D^. 2. AA] corr. ex AA Dl 3. 
S'] om. C, ds C^ 5. s^coiisv C. 6. xovxbgtiv'] AC, comp. B, 
rovTEOtv C^D. 7. TovxiGXLv'] ACD, comp. B, -v del. D^. 10. 
drf] di] xfig D. Svva^^vrjg] corr. ex dvvdfiscog D. 12. xdg] 
xd C. 13. Xa^pdveaQ^dL D. 14. diooQd^mGECov A. dQeGHSi] 
seq. ras. 1 litt. D. 16. yiax' avxdg] corr. ex iiaxci xavxag D-. 
18. ev87ci§oXov] mut. in evenriBoXov D^. ipricpicpoQiag C, 

corr. C^ 21. ineXoyriGd^t^a C. 23. inLBaXXovGag] pr. X 

del. D. 



252 KAATAIOT nTOx^JEMAIOT 

ijtl rov rilCov xul ijtl xcbv aXXov diSiXo^sv slg t^t]- 
^ccra is^ cjg yivs^d^ai rijv Ttaqdd^s^iv iit avtSiv dici 
ILOiQcbv s^, ra ds TtQog rotg TtSQiysCoig slg r^Tj^ara A, 
cjg Tial ijtl rovrcjv yivs^d-ai rijv 7taQdd'S6iv dicc ^oiQcov 
5 y^ iitsidriTtsQ ^si^ovsg Si6iv aC TtQog rotg TtSQiysCoig 
diacpOQal rijg vitSQOxrjg rcov JtaQa rrjv dvoiiakCav iiti- 
^aXlovrciv rotg l'(Soig r^ij^a^iv diacpOQcav r&v TtQog 
rotg djtoysCoig ytvo^svcov. 

rd^o^sv ovv xal rb rfjg rov riXCov dvco^aUag 

10 zavoviov iiti 6rC%ovg ^sv TtdXiv Jis^ 0sXCdia 8s y, cov 
rd ^sv TtQcbra dvo TtSQisxsi rovg dQid^^ovg rcbv rf^g 
o^aXfjg TCiVTJGscjg t| ^oiQav^ rcbv ^sv JtQcorcjv is 6rC%cav 
%SQis%6vrcxiv rd TtQog r& aTtoysCc) p rsraQrrj^oQia^ rcbv 
ds XoiTtav X rd TtQog rcj TtSQiysCc), rb ds y' rdg sxd6rG> 

15 rcbv b^aXcbv aQid^^av ijtipaXXovOag ^oCQag rrjg 7tQ06d'- 
a(paiQs6sG}g roi) jtaQa rrjv dvcj^aXCav diacpoQOv. xaC 
ian t6 %av6viov roiovro' 



6. snL^aXovxcov D, corr. D^. 7. t{iriiicc6i D. 9. xov 

rilCov] ijXLayiiig D. 10. fffAt^ta] ju^^rj D. wv] cog D. 11. 
TtSQLS^SL D. 12. If] dsv.uTtEvts D, ut saepe. GtCxcov^l -ca- 

e corr. D. 13. ra] -a. in ras. D^ 14. X] a BC, corr. C^ 

tb di] AJ), ^i BC. y'] 7 ABC, tQitov D. tdg] corr. ex 
td D. 15. iTtL^aXovGag D. nqocacpaLqEGScog D. 



MA0HMATIKHS 2TNTAaESiS T'. 



253 



g\ Kavoviov rij? riXiccxrjg dvco^aXiag. 



1. g-'] B, om. ACD. 

tfjg ■fjkiaxrjg'] om. D. 

avco/uaXiag'] hvofiaXiag 
ff 
^ D. 2. fxoXqaC] AC, 

om. BD. a' /?' y'] om. 
D ; habet in lin. 4. 6. 
</^] -/? e corr.D». 11. fa 
«00 anoyhiov Svo tstaQtrj- 
/uoQia mg. A*, anoyt'iov 
tetaQtyjfioQtov et mg. et 
inter coU. 1—2 B^ 12. 
fiYl corr. ex ky B^C». 

14. r] seq. ras. A, 15. 
ofjd] -9t5' in ras. A. 16. 
07tt]] corr. ex o-^i? C, -tTj/ 
in ras. A. 17. an^S'] -n^ 
in ras. A. 23. ovy]] 

ortt] D. 31. a] (i D. 

32. o^a] a- e corr. A. 

34. t& tov HaQtysiov 
dvo tstaQtrifioQta mg. A*, 
nsQiYeiov tetaQtrjfioQiov 
et mg. et inter coU. 1 — 2 
B', ^/£] D, -£ inras.B', 
^^^AC, corr. A^. oy.E] 
-e e corr. A. 41. o] e 
corr. D. 42. o] corr. 

ex a D. vy] e corr. D. 

43. o] '^o C, corr. ex 
a D. fig] e corr. D. 

44. o] corr. ex a D. 
X^] e corr. D. 45. o] 

corr. ex a D. //?] e 

corr. D. 46. o] corr. 

ex a D. 48. »;] e corr. D. 

49. Qn] corr. ex Qrj C. 



fioiQat 
ofialwv 
xtvrioiwv 


a' 
aQid-fiol 


/*' 
y.oivoi 


y' 

nQoaStttpaiQsoeig 




«'7 


tv8 
tfitj 
tfifi 


o i8 
o xr] 

O fl(i 






tXq 

tl 

tyd 


o vg 
a ^ 
a xa 






ttrj 
ttli 


a X[i 
a fxy 
a vy 






t 
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anrj 


(i 

(i i8 




.7 

9 


on(i 

aog 

ao 


(i tri 
(i xa 
(i xy 




9/ 
9? 

9^ 


a^a 


(i XY 

/? Xii 




("7 


avr] 
avs 
ov^ 


(i xa 
(i iri 






OfiS- 
Ofiq 
Ofiy 


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aXd 


a vr] 






aXa 
OHr} 
ay.s 


a v8 
a fi^ 
a fi8 




Qfxd 


ax(i 
otS- 
aig 


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a Xy 
a y.: 




QV 

Qvy 


aiy 
ai 
oK 


a xa 

a i8^ 
a : 




Qvg 
Qv9- 
Q^iS 


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o vy 
o fig 




Q$B 

Q^rj 
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Qn^ 


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y.8 




Qo6 
Qo: 
Qn 


Q7tq 

Qny 

Qn 


o ig 

J/ 

o o 



15 



20 



25 



30 



35 



45 



254 



KAATAIOT nXOAEMAIOT 



^'. IIsqI xrig %arcc f^v ^idriv rov riliov TCccQodov 
STtoxrjg- 
AoiTCOv d' ovrog rov rijv S7to%riv rrjg b^aXfig Toi> 

rjXiov xivij^scog 6v6r7]6a6d^ai TtQog rag r&v Tcara ^SQog 
5 STcd^rors TCaQodcjv S7ti6%s^SLg STtoirj^d^sd^a xal rr^v 

roiavrrjv sKd-s6iv dxoXovd-ovvrsg ^sv xad-olov TtdXtv 

STti rs rov rjXiOv zal r&v dXXcov ralg vcp^ rj^cav 

avrGiv dxQips6rara rsrr^Qrj^svaig TtaQodoig^ dva^i^d- 

^ovrsg ds d% c^vrrav rdg rcbv STtoxS^v 0v6rd6sig stg 
10 rrjv dQxrjv rrjg Napova66dQOv ^a6iXsiag did r&v dito- 

dsiKvv^svcjv ^s6c3v KiV7]6sc3v^ d(p^ ov ;^^dvov Tcal rdg 

TtaXatdg rrjQ7]6sig s^o^sv ag STtiitav ^isxql Toi; dsvQO 

dia^cj^o^svag. 

s6rco drj 6 ^sv o^oxsvrQog ra 
15 did ^s6cov %v%log 6 ABF usqI 

TcsvrQOv rb z/, 6 d' sxxsvrQog rov 

rjXiov %v%Xog 6 EZH tcsqI xsvrQOV 

t6 0, ri da di d^fporsQcov rG)v %sv- 

rQcov %al rov E ditoysiov did^s- 
20 rQog rj EAHF^ v7to%si6&G) 8s rb 

B 6r]ustov rov ^GodiaKOv rb ^sro- 

TtcjQivov^ %al S7ts^svx^co6av ^sv 

7] rs BZA %al r] Z0, ^dd^srog ds ditb rov @ sitl 

rr]v ZA s%pir]d-si6av 7]x^cj r] @K. 
25 iTtsl t6 ^sv B ^sroTtcDQivbv 6r]^siov TtSQiSxsi rr]V 




1. ^'] B, mg. A*, k) mg. C^, om. D. 2. inoxvs] om. D. 

3. orog D. rov (pr.)] om. D. rfig — 4. GvezijcaGd-ca] 

zov 7]Xlov TTjg b^alfiq GvGti^Gaa&ai KLvrJGscog D. 5. Tcoiriao- 
[i£&a D. 9. dh an'] 8' in' C, d' D supra scr. an' . 14 tw 
dLa (liacov] x&v ^codiayi&v D. 23. 'Ka&etog] -g add. D^. 8e] 
8' D. 24. @K] corr. ex K© D^ seq. ras. 2 litt. 



MA0HMATIKHI: 2TNTASESi2 T'. 255 

r&v XrjX&v aQxrjv^ zb ds F TceQiyeLOv ra^ tov To^otov 

^OLQag £ L\ V ^^ ^Q^ TtEQiCpBQBia ^OLQCbV i&tiV ^E 

X. xal 7] vnb BJF ccQa ycovia^ tovts6tiv rj vnb 
®^K^ oHcov ^sv £i6iv aC d dQd^al tJ, toiovtcov ^s A, 
oiov ds aC /8 OQ&al r|, toiovtcov Qla. co6t£ xal rj 5 

^£V £7tl t7]g ®K Evd^Eiag 7t£Qi(p8Q£ia tOiOVtCOV £6tiV 

()Aa, 0103^ 6 7t£Qi tb ^&K dQd^oycoviov xvxXog r|, i^ 
dh v7tot£iVOv6a avtijv £vd-£ia r] @K toiovtcov Qd" fc/3, 
oicjv £6tlv r] /iS did^EtQog ^. oHcjv ccQa £6tlv rj 

^£V z/@ £'U'9'£rcU £, rj $£ Z@ V7tOt£iVOV6a ^, tOLOVtCOV 10 

Tial rj ^£v 0K £6tai d ly^ r] ds £7t avtfjg 7t£Qi(p£Q£ia 

tOLOVtCOV d X, OiCJV £6tlv 6 7t£Ql TO &ZK OQd^OyCOViOV 

xvxXog t|. S6t£ xal r] V7tb &ZK ycovCa^ oicov ^£v 
£i6iv aC dvo dQd-al t|, toiovtcov £6tlv d jc, Oicov d£ 
aC d OQd-al t|, toiovtcov /3 l. tcov d* avtSov r]v r] 16 
V7tb BZir ycovCa ^£ k' Tial XoiTti] [Eucl. I, 32] aQa r] 

VTtb Z&H^ tOVt £6tLV i] ZH tOV ixXEVtQOV TtEQiCpEQEia^ 

^ioiQ&v i6tiv ^y %. otav ccQa i7tl tfjg ^£to7tcoQivr]g 
L6r]^£Qiag fj 6 rjXiog^ tov ^hv 7t£Qiy£iov^ tovt£6tiv t&v 
tov ToloToi; ^oiQcbv £/.', 7tQor]y£itai ^86cog Xivov^svog 20 
^oiQag ^y x, tov dh d7toy£iov^ tovt£6tiv tcbv xatd 



2. /.'] X D. 3. X] iii_ras. A. Ez/T] corr. ex BT^ C». 

4. If] 86x\v fe D. 5. ^] iotlv qIci D. 8. ds] S' D. 

7]] om. D. ©K] @- e corr. C. 9. oicov] yiol olcov corr. 
ex yiccl av D. J &] corr. ex dE D^ 10. 1] in ras. 2 
litt. D^ 11. @K] 0- corr. in scrib. C, deinde del. evdsicc D. 

de] d' D. 12. d] post ras. 1 litt. D. @ZK] Z@K D. 

13. 7]] ins. Dl @ZK] ©Z/^ D. 14. Svo] § B. Uxh] 
comp. B, -v del. D^. 16. |f] -f e corr. D*. X] seq. ras. 1 
litt. D. 17. Z@K] Z- corr. ex ^ C. 18. |y"] -y e corr. D^ 

19. xovxiGxiv] comp. B, -?; del. Dl 20. /.'] Aa D. 21. 8i] 
6' D. xovxeGxL D, comp. B. 



256 KAATAIOT nXOAEMAIOT 

roijg ^idv^ovg ^olq&v s A, a7ci%8i ^86cog sig %k aTCo- 
^sva iioiQag Qig ]i. 

tovTov dij d^ecjQTjd^svrog^ iTtsidrj r&v iv ratg %Qm- 
rais rj^iv rsrrjQrj^svcov i^rj^SQi&v ^Ca rcov aycQi^s^rara 
5 Iri^pd^siC&v ysyovsv i6r]^sQia ^sroTtcoQivri rm it,' srsi 
^AdQiavov Tiar AiyvTtrCovg Ad^vQ t,' ^sra dvo syyi^ra 
i6riiLSQivag &Qag rr]g ^s6r]u^QCag^ dfjkov^ on %ar^ 
SKSivov rbv xQovov 6 riUog ^s6c3g Kivov^svog a7tsi%sv 
roi) ajtoysCov Tiara rbv skksvtqov kvkIov sig ra STto- 

10 ^sva ^oCQag qI^ ^. «AA' aitb ^sv rrjg Na^ovaa^aQov 
^aOilsCag ^sxQi tfjg AXs^dvdQov rsXsvrfjg srr^ Cvvd- 
ysrai Kar AlyvxrCovg vk8^ aTtb ds rfjg 'AXs^dvdQov 
rsksvrrig ^s%Qi rfjg Avyov6rov ^a6iksCag srrj (j^d, aTtb 
ds rov a srovg Avyov6tov Kar AlyvTtrCovg rfjg sv 

15 Ta5 003-9' a' ^s^rj^^QCag ^ STtSidri rdg STtoxdg dnb 
^s^rj^pQCag ^vvi^rd^sd-a^ ^^XQ^ '^oi) t^' srovg AdQta- 
vov 'Ad^vQ J' ^srd dvo iOrniSQivdg wQag rfjg ^s6- 
rj^^QCag srr] yCvsrat Q^a Kal rj^SQat |g Kal dyQat 
i^rj^SQival /3' Kal djtb rov a srovg aQa Na^ovaO- 

20 <5dQ0V Kar AiyvitrCovg rf^g sv rfj rov Gcjd' a fis0rjfi- 
^QCag SG)g rov xqovov rfjg SKKSi^svrjg ^sroTtcjQivfjg 
i^riiiLSQCag 6vva%d^ri6srai srrj AiyvittiaKd aoQ' Kal 
rjiisQai Jg Kal G)Qai iarj^sQival /3. «AA' sv tc5 to6ovtc) 
XQOVG) 6 rjXiog ^sacog Kivsltai ^sd'' oXovg Kvxlovg 



3. nQcoruLq^ -xaig add. D^. 4. rniiv] seq. ras. 2 litt. D. 
i6ir]ybf:QL(bv] -L- in ras. 2 litt. D. 6. 'AQ-vq'] 'A- supra scr, A^ 
8. Y,hLvovyiSvo$ C. ccnELXb D. 10. aXl''] aXXcz D. 12. v.ax' 
AiyvTtxiovg] om. D. 13. AvyovGxov] -y- corr. ex x A. 0^8] 
a- eras. in extr. lin., add. init. sequentis A^. 14. a'] jr^to- 

xov D, ut saepius. 15. a'] vov(ir}VLag D, xfjg add. D^; vov^rr 
vlag mg. B^. 16. t^'] corr. ex i C. 18. yCvovxaL D. 20, 
T^] XM B. a'] vovy.TjvLa D. 



MA0HMATIKHS STNTASESiS V. 257 

(lOLQag (Slcc tcs £yyi6ta. mv ovv tatg tijg xata rijy 
ixx6L^8vrjv ^stOTtcjQivrjv l6riiieQCav a7to%fig ano tov 
icTCoysCov tov ixxsvtQov ^oCQaig Qig ~fi jCQ06d'G}fi£v 
ivbg kvkXov ^oCQag r| xal aito t&v yivo^Evcjv a(pi- 
k(xniev tag ola xs ^oCQag tijg xatS: tbv ^sta^i) %q6vov 5 
iitov6Cag^ £%o^ev eig tijv iitox^iv tfjg fiiarjg xivTJescjg 
tc5 a eteL Na^ova66dQov xat AlyvTttCovg ®h%' a' tf\g 
fie^rj^PQCag acpe^tcbta fiev tov aitoyeCov tbv 7]Xlov eCg 
ta eno^eva za-O-' ofiakrjv xCvrietv ^oC^ag 6^e IF, iTti- 
%ovta df ^iacjg tcbv 'Ixd"vc3v trjg a ^oCQag i^rjxoeta ]i€. 10 

rj'. UeQl tfjg riXtaKfjg iffrj(po(poQtag, 

'06dxtg ovv av id^iXcj^ev tijv xa^^ exa6tov tav 
iiCL^rjtov^ivov xqovcov tov rjXCov TttxQodov imytyv^- 
6xeLv^ tbv 6vvay6^evov dnb tfjg iTtoxrjg ;u()di/ov ft£%^fc 
rov vjtoxet^ivov TtQbg tfiv iv ^AXe^avdQeCcc cjQav 15 
ei6eveyx6vteg eig td tfjg oftaAijg xivr]6ecog xav6vLa tdg 
^aQaxeL^ivag totg oixeCoig dQid^^otg ^oCQag iTtL^vvd^rj- 
6o^ev iietd tcbv tfjg aTtoxfjg 6^e 7e ^OLQcbv xal djtb 
rcbv yevo^ivcov ix^ak6vt€g oXovg xvxkovg tdg XoLTtdg 
d(pr]6o^ev d%b tav iv totg ^Ldv^iOLg fioLQ&v e X eig 20 
td enoiieva t&v ^qydCcov xaC^ ojtov dv ixTti^rj 6 aQLd^^ogy 
ixet tijv ^i6rjv rot) rjkCov TtaQodov evQT^^o^iev. eifjg 



1. ovvl comp. ins. D, del. aQcc. xuig xfig\ e corr. D*. 2. 
inoxfig D. 3. ajroysiov] corr. ex STtiysCov D. Ttqoad^&^sv 

svog] -j^ £v(o D^ in loco minore. 5. xs] x' D. 7. Ncc§oaod- 
Qov AC, Ncc^ovvaaccQOv D. a' (alt.)] 6 a C, vsofiTjVLcc D, vov- 
firivicc supra scr. B^ 11. ?]'] mg. AB, om. CD. 12. daccyng} 
6- e'corr. D^ ccv] D, sdv ABC. d-^Xafisv C. 16. td] 
xdg D, 18. S7to%7ig D. 19. yLvofisvoav BD. SK^dXXovtsg D, 

20. (lOLQ&v sH] s X' II J). 21. ^(p8i(ov xat] corr. ex ^coSva- 
v,a>v D. 

Ptolemaeus, ed. Heiberg. 17 



258 KAATAIOT nTOAEMAIOT 

ds xov ccvtbv aQtd^^ov^ tovtsdTLV tbv ccjtb tov ano- 
yEiov in^XQv trjg fi£6rjg jcaQodov^ siOsvsyxovtEg 8lg tb 
tfig dvco^aXLag xavdviov tag JtaQaxsLiievag t& aQL^^iia 
liOiQag sv ta y' CsXidiG) xata ^sv tb TtQ&tov GskCdiov 
6 tov aQid^^ov jCiJttovtog^ tovts6tiv scog QTt ^oiQ&v 
'6vtog^ dcpslov^sv ditb tijg xata tijv ^serjv jtccQodov 
snox^vjg^ xata ds tb /3' 6sUdiov tv%6vtog tov dQid^^ov^ 

tOVtS6tiV V7tSQ7tS66vtOg QTt llOiQagy TtQO^d-TJ^O^SV tfi 

^s6rj 7taQ6d(p xal ovtcog tbv dxQiPrj xal cpaiv6^svov 
10 rikiov s-bQYiaoiisv, 

%•', IIsqI trjg tcbv vvx%"yiilsqg}v dvi66trjtog. 

Td ^sv oi)v TtSQi tbv rjhov ^6vov d^scoQov^sva 
6xsdbv ravT i6tiv' dx^Xovd^ov d' dv strj tovtoig 
TtQo^d^stvai did PQaxscov xal td jtSQi trjg tcov vvx^rj- 

15 ^EQOv dvi66tritog ocpsiXovta 7tQoXrj(pd"fjvai dtd tb td 
fihv SKtsd^SiiiEva ^iiiiv xad'' sxa6tov aTtlcbg fiE6a xivr]- 
[lata Ttdvta xar' l'6ag vjtsQoxdg trjv 7taQav^rj6iv Xafi- 
pdvsiv G)g xal t&v wx^^yj^sQcov 7tdvtcov l6oxQovicov 
ovtcov^ tovto ds firj ovtcog sxov d^scoQSi^d-ai. tfjg 

20 toivvv tcbv oXcov 6tQoq)rjg b^aX&g ts dTtotsXov^svrjg^ 
xal TtSQi tovg roi) i6r]^SQivov 7t6Xovg xal trjg toiavtrjg 
d7toxata6td6scog xatd tb 6r]^sicodE6tSQOv ^tot TtQbg 
tbv dQi^ovta rj 7tQbg tbv ^s6rjfiPQivbv Xa^^avofisvrjg 
x66}iov ^sv 7tEQi6tQoq)rj drjXov oti ^ia s6tlv rj tov 

25 avtov 6rj^siov tov l^rj^SQivov d7t6 tivog r^i^'^aTOff 
^TOt Tov bQi^ovtog rj tov ^s6rj^PQivov STtl t6 avtb 

1. Tovrsctiv} comp. B, -v del. Dl 4. TtQ&tov] a B. 8. 

Qjt] tag QTt D. 11. '&•'] mg. ABC, om.'D. 16. syitLQ-siisva D. 

17. Ttdvta'] om. D. 19. sxcov C. 21. rfjg] corr. ex toig C. 

26. (isar}fi§Qivov] comp. e corr. D. 



i 



MA0HMATIKHS STNTASESiS P'. 259 



cc7toKat(x6ta6igy vvx^yJii£QOv ds ccTiX&g rj tov riXCov 
a%6 tivog t(i7]fiatog ijtOL tov dQc^ovtog rj tov fi£6rf^- 
Pqlvov Ttdkiv BTil to avtb djtoxatd6ta0Lg. b^aVov ^lv 
ovv vvxd^tj^SQOV yCvetaL dLce, tavta tb 7t£QLi%ov jtdQodov 
tav tfig ^Lccg 7t£QL6tQ0(pf}g tov L6rjfi£QLV0v xq6vcov t| 5 
Tcal £tL ivbg ;|j^di/oi; £^rjK06tG)v vd- £yyL6ta^ o6a iv 
tm to6ovtG} ^£0(Dg 6 ijXLog £7tL7CLV£LtaL^ dvco^aXov d£ 
t6 7t£QL£X0v 7tdQodov tcbv t£ tijg ^Ldg 7t£QL6tQ0g)rjg 
tov i6riii£QLV0v ^^dvov t| Ttal £tL tcjv T^tOL 0vvava- 
<p£QO^£vcov r] 6v^^£6ovQavovvtc3v Tc3 dv(j3^dXcp tov 10 

rjXCoV £7tL7CLV7]^atL. 

tovto drj t6 7tQo6dL£Qx6^£vov tov L6ri^£QLVov t^rj^a 
totg tJ %()dvotg dvL6ov dvdyxrj yCv^ed^aL d^d t£ trjv 
(paLVO^ivrjv Toi) rjXCov dvco^aXCav Tcal Slcc t6 td L'0a 
tov dLa ^£6c3v tcbv ^cjdCcov xvxXov t^ri^ata ^r] iv 15 
L'60Lg XQ^^^^^S /*^t£ Tov OQC^ovta ^r]t£ tbv ^£6r]^PQLvbv 
dLa^toQ^v^^d^aL' ixdt^QOV fiivtot tovtcov tr]v ^£v £7tl 
Tov ivbg vvx&r]^£QOv dta^poQdv tr]g b^aXr]g d^toxata- 
6td6£cog 7taQd tr]v dvca^aXov dv£7taC6^r]tov 7toL£L^ tr]v 
d£ £K 7tk£L6vcov vvx&r]^£Q(ov £7tL6vvayo^£vr]v xal fidXa 20 
al^d-r^tijv. 

7taQa ^£v ovv tr]v r^XLayc^v dvco^alCav tb 7tX£L6tov 
yCv£taL dLdcpOQOv £7tl tcov d7tb ^tdg tcbv ^£6cov tov 



1. 17] %v 7} D. 2. (isGTjfi^QLVOv^l ^ D. 3. Post avTo del. 
i-TtL D. 5. T&vl Tcav ts D. tar}fi£QLvov'\ §, D, ^ add. D*, 

ut saepius. 7. tw] om. C. 8. tt)?] corr. ex ri; A. 9. 

GvvavacpBQoafisvcov C, sed corr. 10. 6vv^s6ovQavovvT(ov AC. 

12. ro] om. D. 13. Totg] -oig in ras. A^, -ol- e corr. D*. 

avccyKTii A. 15. rov] corr. ex rd C^ tcvkXov] corr. ex 

y.v-nXcov D*. 17. tovtcov'] t- in ras. A. rifv — p. 260, 23. &] 
mg. D {'KSLfisvov), ad lin. 21 pleraque cum mg. recisa; r^v — 18. 
vvx&ri(iiQov etiam in textu. 23. Tav (pr.)] ins. D^ 

17* 



260 KAATAIOT nTOAEMAIOT 

rjXLOV XLV7]6S(OV STtl f^V BXBQaV dLa6tCC6£G)V' ta yocQ 

ovtcjg avvayo^sva vvxd^T^fiSQa dLOL^st t&v ^sv biialSyv 
XQOvoLg 6 L! xccl d' syyL^ta^ alX^^Xcjv d^ totg dLTtka^CoLg 
XQOvoLg d^L^ ^i« To ocal trjv roi) tiIlov (paLvo^svrjv 
5 TtaQodov JtaQa f^v o^aXi^v nata fisv tb JtQbg t& aTto- 
ysLG) ti^lzvkXlov dC d' ^iOLQag sXXsLTtSLV^ xata ds tb 
jtQbg ta TtSQLysLG) jtXsovd^SLV tatg avtatg' jtaQa dl 
ti^v t&v 0vvavatoXcov rj 6vyxatadv6sc3v dvco^alLav 
tb 7tlst6tov yLVStatt^dLdcpOQOv sjtl tcov vTtb tcbv tQo- 

10 TtLX&v 6rj^SLC3V dq^OQL^o^svcov rj^LTcvKUcov xal svd-dds 
ydQ at sxatsQOv tovtcov tcbv rj^LXvxUcov 6vvava(poQal 
dLOL6ov6LV tcbv iisv bfiaXcbg d-scoQov^svcjv %q6vcov Qjt 
totg dtaipoQOLg tfjg ^syC^trig ri ska%C6trig rj^sQag TtaQa 
tijv L^rjiiSQLVijv ^ dXXTJXcov de, olg rj ^syC^tri tcbv rj^s- 

15 Q&v rj vvxtcbv trjg sXaxC^trjg dLacpSQSL. TtaQa ds trjv 
tcbv 6v^^s6ovQav7]6scov dvL^otrjta tb 7tXst6tov Ttdktv 
yCvstai dtdcpoQov sitl t^v dvo fidXL6ta dcodsxatrjfioQLa 
%SQLS%ov6cbv dLa6td6scov td sxatSQCod^sv d^a ijtOL tcbv 
tQOTtLXcbv ri tcbv L6rj^SQLVG)V 6r]^sCG)v' xal tovtcov yaQ 

20 td TtQog rotg tQOTtLXotg 6vva^(p6tSQa tmv ^sv o^aX&g 
d-scoQovfisvcov dLoC6SL XQbvoLg d i' syyL6ta^ tcbv ds 
JtQbg totg L6rj^SQLV0Lg 6vva^(potSQG)v %dkLv %Q6voLg 
'9', dLa tb ravra iisv skXsCitSLv %aQd rijv ^s6r]v sitL- 



1. dia6Td6£a)v] t&v SiaeTdesoav B, 8ia6Td6 D. 2, ovTm D. 
5. To] T D. 6. /.'] e corr. D. ^']_g a D. to] t D. 11. 
&vucpoqai D. 12. 8loC6ov6i D. q^ xqovcov D. 14. 8b, 

olg\ 8lov6 D. 15. vv-at&v] B^, 99 B. 17. dcod^^aTrjfiOQLai 

L^Tri^OQLa D. 21. 8L0idiJ6£L C. 8] T£VQa6L tiaL D. [_'] B, 
r)iiL6£L ACD, r}(iL6£Lg A*. 22. 6vva{iq)0T£Q0L£ comp. D. 23. 
^] B, %- £yyL6Ta B^. z' £V,£l%£v fol. 73^ D. ^ta — p. 262, 5. 

fiUov] mg. sup. fol. 74^^ D, usque ad 6vvi.6Tdyb£%a p. 261, 3 
recisa. 



|: MA0HMATIKH2 STNTABESiS T\ 261 

^oXriv^ SKstva ds ra l'6c) 6%Edov jtXeovd^SLV. evd-sv 
xal rag sv ratg STtoxatg aQxag t&v vvx^d^rj^SQOV ajto 
tG)v ^s6ovQav7]6s(ov ^vvi^td^sd^a xal ovtc ccTtb tcbv 
dvatoXcbv r) dv6scov tov rilCov dtd tb trjv fisv TtQbg 
tovg bQL^ovtag d^soQOv^isvriv diacpOQav xal ^sxqc %ol- 5 
Xg)v cdqov dvva6%^aL (pd-dvsLV xal ^irj slvaL tr^v avtr^v 
jtavtaxf}^ 6v(iiistapdXksLV ds tfi xad'' STcd^trjv syxXL^tv 
tfjg 6(paLQag vutsQoxfj tcbv fisyL6tC3v rj iXaxL6tcov ii[is- 
QcoVj tijv ds JtQog tbv ^s^rj^PQLvbv trjv avtrjv ts 
sivaL xatd 7ta6av ol'Krj6LV xal ^rjds tovg sx tfjg riha- 10 
xfig dvcj^aUag ^vvayo^svovg tov dLatpoQOv XQ^^^^^S 
VTtSQ^dkXsLV. 6vvL6tataL ds xal soc trjg d^tpotSQCov 
tovtcov ^L^scjg trjg ts jtaQa tr]v tov riXCov dvco^aXCav 
xal tf]g TtaQa tag 6v^^s6ovQavr]6SLg tb didcpoQOV sitl 
t&v xat d^KpotSQag tdg SLQrj^svag dLag)OQdg rjtOL 7tQ06- 15 
d^stLXCDV d^a 7] dcpaLQStLKcbv dLa6td6sc3V^ dcpaLQStLxov 
lisv sxatSQCo&sv iidkL6ta yLVO^svov roi) djtb ^TdQox^^ov 
HS60V iisxQL Xr]Xcov t^rj^atog^ TtQo^dstLXOv dh tov 
djtb UxoQTtCov ^sxQL IIS60V 'TdQOXoov^ d^d tb sxdtSQOv 
tcbv sxxsL^svoov t^r]^dtcov tb %kst6tov rjtOL 7tQo6tL- 20 
^svaL r] dcpaLQstv jtaQa ^sv tf]v r]kLaxf]v dvco^aXCav 
^oCQag y syyL6ta xal dCtQLtov, jtaQa ds tdg 6v^^s6- 
ovQavr]6sLg ;^()di^ov? d xal rS syyL6ta^ cog jtXst6tov 
sx tfjg sxxsL^evr]g ^C^scog 6vvdys6&aL didcpOQOv tcov 



3. &7to] ini D. 5. v.aC'\ om. D. 6. oq&v C. 7. (>v|li- 
iLBxa^dlUi^ C. T^] xriv A. 13. i^Ztov] 17- om. C. 14. 

yi,£6ovQavri68ig D. x6] ABC, xh tiXelgxov B^D. 17. '^T8qo%6ov'\ 
D, comp. B, vdQ7\%6ov AC. 19. iihov] om. B. 'Td^o^doi;] D, 
vdQTixoov AC, -^^ [IB60V B. 21. 7'f] afia t] D. 22. SCxqlxov] 
xqCxov C, Fo D. 6vv[iB60VQavri6ii$ A, fiE6ovQav7]6£Lg D. 23. 
r^] r seq. ras. AB, i^ A^D, r C. wg] ag x6 D. 24. 6vv- 
dys^&ai] yCvE6Q^av D. 



262 KAATAIOT nTOAEMAIOT 

vvxd^rj^BQCOv Ttad'' SKcctSQOv tcbv eLQrj^8V(ov t^rjiidtcov 
TCQbg fi£v ta b^aXcc iQbvoig fj xal y', tovt£0tLV d a^ag 
L! Lr}\ TtQbg dkkrila 6e tcjv dL7tka0L(ov %q6v(ov 7g rS, 
tovt£6tLv &Qav a xal '&•'. tb d^ toaovtov iitl ^ev 
5 rjliov xal t&v dkk(ov TtaQOQCo^svov ovdsvl av l'6(og 
al^d^rjt^ xatapMntOL trjv tcjv TtsQL avta (paLvo^svcov 
£7tL6x£ipLV^ £7tl 6} tfjg <3£X7]vrig dLa tb trjg xLvi]6£(og 
avtrjg td%og d^LbXoyov dv ijdr} trjv dLafpoQav dit^Qyd- 
^OLto xal fi£XQL y £' fiLccg fiOLQag. 
10 Lva ovv Tcal td xad'' 67tOLavd7]7tot£ dLd6ta6Lv dt- 
86^£va vvxd^TJ^^Qa^ Xiycj de td d7tb ^£6rj^PQLag tJ 

^£60VVXtL0V £7tl ^^^rj^^QLaV rj £7tL ^£60VVKTL0V^ £ig 

b^ald vvx^7]^£Qa xad^d^ta^ dvakv(o^£v ^ ^x^ip^^^d^a 

xatd t£ tijv 7tQ0t£Qav £7toxr]v xal trjv v6t£Qav tfjg 

15 dLdo^svrjg tcbv vvx^t^Iibqcov dLa6td0£G)g^ xatd 7toLC3V 

£0tlv tOV dLa ^£6G)V tcbV t,(pdLCOV %VXX0V ^OLQCbV 6 

rjkLog o^aXcbg t£ KLVOv^£vog Tcal dvco^dXcog^ £7t£Lta trjv 
d7tb tfjg dvco^dXov^ tovti^tLv tfjg g^aLvo^ivrjg^ i7tl tr]v 
(paLVO^ivrjv dLd6ta6LV tcbv tfjg i^tov^Cag ^olq&v 
20 £L6£V£yx6vt£g £Lg tdg fjr' oQd^fjg tfjg 6(paLQag dvacpoQag 
£;tt(?x£^o^£'9'a, 7t66oLg 6v^^£6ovQavov6L ;u^d?^otg tov 



2. 'nal] om. D. rovreW D, comp. B. a] AC, (ii&g 
BD. mgag] comp. AC. 3. r^] J^ ABD, r seq. spat. 2 

litt. C. 4. tovtEaTLV coQav a xai] %al w^a? fiL&g D. to — 
5. f}XLov] etiam in textu D (ro postea corr. ex did). In fine 
(io"^' mg. D. 5. aXcov C. ^6. avtovg D. 9. y s'] r e ' ABC, 
tQi&v ns^ntcov D. 10. oiitoiavSriTtotE C. 11. Xiyo)] corr. 

ex Xiysi in scrib. C. 12. inC (alt.)] om. D. 13. 6,aaUa C. 
6cvalvcoii£v] post -co- ras. 1 litt. A, -co- corr. ex o CD^. 6v,s- 
tpa)(is&a C et uoluit D*. 14. yiatcc te] corr, ex tiad^dTtsQ D^, 
yQ. "Ka&d t£ mg. D. 16. iotLv] comp. B, -v del. D^. 18. 
ccvco[iaXLag D. tovteatLv] comp. B, -v del. D^. 19. tfjg 

STiovaCag] ~g i- e corr. D*. 21. noaoL C. avfifisaovQavovaL] 
pr. fi add. A\ avvfiEaovQavovaL C. 



» 



MAeHMATIKHS 2TNTASESiS V. 263 



l^rj^SQivov at trjg avco^dXov dicc6rci6S(X)s-) (hg s(pafisVy 
HotQccL^ xccl ka^ovtsg trjv vtcsqoxyiv tcbv ts svQsd^svtcov 
XQOvcjv ocal tcbv tijg o^aXfjg dLa^tdoscag ^OLQav sm- 
loyi^d^svoC ts tb 7tSQis%6^svov ^isysd^og cjQag L0rj- 
(isQLvfjg 'bno tS)v tfjg 'b7tSQ0%Yig %q6vcdv tovto TtXsLOvog 5 
fLsv svql6xo^svov tov t&v %q6vcjv aQLd^^ov tTJg 6^aXfig 
dLa^tdoscog TCQOdd^rj^o^sv r» dLdo^svip t&v vv^d-ri- 
^SQCJv TtXTjd^SL^ sldttovog ds dq)sXov[isv dit' avtovy 
xal tbv ysvo^svov %q6vov s^o^isv slg td b^aXd vv^d^rj- 
[iSQa dLaxsKQL^svov^ c5 xal ^Qrj^^^sd^a ^dlL^ta TtQbg tdg 10 
S7tL0vvay(oydg tcbv sv totg zav66L tfjg aslfjvrjg ^s6c3v 
iCLV7]6sG)v. svxarav6ritov d' avt^xtsv^ ott xal ditb tfjg 
t&v biiakcbv vv^d^rj^sQCJv V7to(Srd6scog rd xaLQLxd xal 
aTtX&g d^scoQov^sva Xa^^dvsraL rf\g ^tQOXSL^svrjg rcov 
G)QLaC(ov %q6vcov ^tQoad^acpaLQS^scog dvdTtaXLV yLvo^svrjg. 15 

S7tst%sv ^svroL xard rfjv rj^srsQav S7to%fiv 6 rjlLogy 
rovts6rLV tc3 a srsL Na^ova66dQov xar AlyvTtrCovg 
®d)d' a rf{g ^s^rj^^QCag^ b^al&g ^sv XLVov^isvog^ hg 
HLKQm ^tQ^ad^sv [p. 257, 6] d^tsdsC^a^sv^ 'I^d^vcov ^ o "jiZf, 
dvcoudXcjg ds y ^oC^ag xal rj syyL(3ra s^rjKo^rd rcov 20 
^I%%^vcov. 

1. mg] -g ins. D^. 3. $t,aarda£cov D, 'corr. D^. 6. ccQid^iiov^ 

BC^D, &Qi ffc A, ccQLd^fiog C. 7. Sidofisvojl mut. in dLSofiEvcov 
in scrib. C, -v del. C^; dsdofisva) D. 9.' rov] corr. ex rd A\ 
yivofiBvov D. ftg] tov £tg D, xov add. B^. 10. xal XQrjao- 
usd-a} corr. ex g K8XQria6iiEd-a Dl ^^ 12. $'] Si D. 14. Post 
aTcX&g del. vito D^ 15. nQoaacpBQsaecog D, corr, D*. 16. 
STCEtxEv] -V del. C^, ETtEtxE D. 17. rovriatL D, comp. B. Na- 

^ovaauQOv D. 18. @a}d''\ -^ ins. D^. a'] voviir]VLcc D. ofia- 

Xm'' C. 19. a7tEdEL^o(iEV D, corr. D^ /x] om. D. o] om. A. 

In fine KXavdiov IlToXEfiaiov ^ad^rjiiatLyifjg avvrd^Eoag A, KXav- 

diov UroXEfiaLOv (iad-r]fiarLyifig avvrd^Ecog §l§Xlov y' B, KXavdCov 

IlroXE^iaLOv (lad-rnia avvragEcog y C, IlroXEfiaCov iiad-JifiarLTiav y D. 



Tdds £V£6tLV iv ta d' tfjg Iltoke^aiov fiad"r}y.attxflg 
6vvtd^£G)g' 
a\ djtb JtOLG)v d£t trjQ7]0£(ov td 7t£Ql triv 6£X7]vr]v 

5 £^£td^£LV. 

P\ 7t£Ql t&V 7t£QC0dLX&V %q6v(X)V tfjg (JfAlJvT^ff. 

y'. 7t£Ql tcbv Tcatd ^£Qog b^alcov xlv7]0£G}v tfig 6£k7]vrjg. 
d\ xavdvcjv £xd-£6Lg 7t£QL£x6vtc3v tdg (i£6ag TtaQoSovg 

tfig 6£lrivrig. 
10 £. otL xal £7tl tfig dTtXfjg v7tod'£6£C3g tfjg 0£Xr]vr]g td 

avtd g)aLv6^£va 7t0L0v6LV r] t£ xar' £XX£vtQ6- 

trjta xal r] ^car' £7tCxvxXov. 
g'. d7t6d£L^Lg tfjg 7tQG)tr]g xal aTtXfjg dvco^altag tfjg 

6£Xr]vr]g. 

16 5'. 7t£Ql tf]g dL0Qd^G)6£G)g tcbV ^£6G)V 7taQ6dG)V tfjg 

6£ki^vr]g iiriKOvg t£ xal dvcD^aUag. 
r] , 7t£Q\ tf]g £7to%f]g t&v S^akcjv tfjg 6£kr]vr]g xlvt]- 

6£G)V ^7]xovg t£ xal dvcj^aXiag. 
O"'. 7t£Ql tfjg dL0Q^G)6£G)g tG)v xatd jtXdtog ^£6g)v 
20 7taQ6dG)v tf]g^6£X7]vr]g xal tfjg £7toxf]g avtcbv. 



1. z^'] om. ABC, UtoXBficciov (la&rjfiazLii&v A D. 2. r^g] 

xdiv D. \x,cL%"r\\x,axiY.f\<i cvvxa.i,Baii\ fia&rjficcxiyiav D. Deinde 

add, Z C. 4. a'] et ceteros numeros om. D. dEi] d^ C. 

xTjQT^Gscov] -6- corr. ex q in scrib. C. 13. anodsL^Lg] corr. 

ex anodE^Lg A. xfjs (pr.)] x- corr. ex g in scrib. C. 



KAATA. nXOA. MAGHMATIKHS STNTASESiS A'. 265 

l\ il^ritpocpoQLU xal xav6vL0v trig jCQatrjg xal aTcXfjg 
dvco^akLag tfjg ^eXTJvrjg. 
La\ otL ov TtaQo. tag dLacpOQag tcav vTtod^i^eov^ aXXa 
TtaQO, tovg kiLXoyL^^ovg dLrjveyxav Tcata xhv 
"l7t7taQ%ov rj TtrjhKotrjg trjg ^sXrivLaxrjg dvco- 5 
^aUag. 

a . 'Aito TtoLcov dsL trjQrjescov td jtSQl f^v 
6sXr]vrjv s^std^SLV. 

^Ev rcS %Q0 tovtov <&vvtd^avtsg^ o6a av tLg Idoi 
^v^fiaLVOvta tcsqI tijv tov rjXLOv XLvrj6Lv^ dQxo^svoL lo 
ts xatd tijv scps^rlg dxoXovd^Lav xal roi) TtSQl trjg 6s- 
Xrjvrjg Xoyov JtQcotov rjyov^sd^a 7tQ06r]KSLV ^rj aTtXcbg 
firjd^ cog stv%sv 7tQO0LSvaL tatg tcov sig tovto tr]Q7]6scov 
XQt]6sdLV^ dXXd TtQog ^sv tdg xad^oXov %ataXriil)SLg sxsl- 
vaLg ^dXLOta TtQO^s^SLV t&v dTtodsL^scov^ o6aL ^ij 15 
liovov SK tov TtXsLOVog xQovov^ dXXd xal dit avtSov 
tG)v xatd tdg ^sXrjVLaxdg STcXsLi^SLg trjQrJ6scov Xa^pd- 
vovtaL' d^d ^ovcov yaQ tovtcov dxQL^cog dv oi toTtOL 
trjg ^sXrjvrjg svQL0xoLvto tcbv dXXcov^ o6aL ijtOL d^d 
tG)v JtQog tovg djtXavstg dctsQag TtaQodcov r) dtd tav 20 
OQydvcov TJ dLa tcbv tov rjXLOv skXsliIjscov d^scoQovvtaL^ 
TtoXv dLatlJSv6d"f}vaL dvva^svcov d^d tdg TtaQaXXd^SLg 
tf]g esXtjvrjg' TtQog ds td xatd ^SQog STtL^v^^aCvovta 
xal ditb tcbv dXXcov ijdrj trjQtjascov TtOLStad^aL tijv ijCL- 



1. XQ:fc'(pr.)] lac. 1 — 2 litt. C. 3. la'] cci B. SLacpogdg] 
-Q- e corr. C. vno&sGEcovl om. D. 5. zfig csXrjvLcc-nfig &vco- 
liccXiccg'] om. C. 7. a'] om. ABCD. 11. tg^elfig'] corr. ex 

I^T^S D^ 12. firj] corr. ex ^s in scrib. A. 13. (ir]di D. 

Btvxs D. 14. ;|jptj(;f(7ir] corr. ex xqtiglv C^D^ v,axcc- 

lri't\>SLg'\ post -rj- ras. AC (/x eras.?). 19, ogul] corr. ex o6u D*. 

22. TCQaXXdihLg A. 



266 KAATAIOT nTOAEMAIOT 

6xstl)LV. tov yag dTtoefTtj^cctog^ 6 ug)B6tr}Ksv rj acpatQa 
tfjg eslTJvrjg ajto tov TcsvtQov tfjg yf^g^ ^rj ovtog c367Csq 
Tial tov xata tbv ^(pdLaxbv xvkXov trjXixovtov ^ Sdts 
6rj^SL0v TtQog avtb koyov sxsiv tb tfjg yfjg ^sys^og^ 
6 dvdyxrj tijv dnb tov TcsvtQOv tfjg GsXrjvrjg STcPaXXofisvrjv 
svd^stav STcl td tov dcd ^s6cov t&v ^adLcov kvkXov 
^SQrj^ TtQbg rjv aC dxQL^stg jtaQodoi, Ttdvtcov voofjvtai^ 
^rjxstc firjds JtQbg al6%^6LV tfjv avtf^v yCvsed^aL Ttdv- 
tots tr} dito tLvog i7tL(pavsLag tfjg yfjg^ tovtsCtLv tfjg 

10 bilfscjg tcjv oQavtov^ STtl tb xsvtQOV tfjg ^sXt^vrjg sk- 
^akloiisvri^ TtQbg iji/ ri cpaLvo^svrj TtaQodog avtfig d^SG)- 
QSttaL^ dkXd orai/ ^sv xatd xoQvcprjv fj tov trjQOvvtog 
rj 6sX7]vrj^ tots ^ovov iiCav xal tfjv avtrjv svd^stav 
yCvsed-aL tijv dito ts tov TcsvtQOv tfjg yfjg xal tfjg 

15 bipscog tov d-scoQOvvtog STtl ro xsvtQov tf]g GsXtjvrjg xal 
tbv ^cadLaTcbv sxPaklo^svr]v ^ otav ds dnovsvsvxvta fj 
bnc30dri7tots tov xatd xoQvcpriv tOTtov, dLacpoQOvg ts 
tdg TiXCcsLg tcbv JtQOXSL^svcjv sv&sl&v d7totsXst0d-aL 
%al dLa tovto tfjv cpaLvo^svrjv itaQodov ^fi tfjv avtfjv 

20 yCvsad^aL tfj dxQL^st TtQbg dXXag %a\ dkXag d^sasLg tf}g 
bil^scjg xata^Lpa^o^Bvrjg t&v d^d tofj xsvtQOv tfjg yfjg 
dcpOQL^o^svcov dvdXoyov tatg 7trjXLx6tr]0L tcbv VTtb tfjg 
syxXCdscjg yLvo^svcjv ycjvi&v. 

dLOTtSQ 6v^psprjxs tcbv ^lv rjXLax&v sxXsCtfjscov yLvo- 



1. o] ov D. 2, (17]] -7] e corr. D^. 5. avaxrj A, corr. A*. 

T^ff] r^ff yi)? xovxioxi xov ^(pdLccyiov Slcc xov ksvxqov xfjs D, 
corr. D^. 8. yCyvicQ-ai D. 9. xovxtaxi D, comp. B. 10. 
oQmvxoiv] 6- corr. ex co Cl 12. aXX' D. ^] om. D. 13. i]] 
^v 17 D, 17 17 D^ 15. xat'] corr. ex xara D^ 20. yCyvsGd-at. D. 

xj]] xr\v C, -V del. C^ Q-icei? v.al aXXag D. 22. Scva- 

Xoycog D. nrjXiv^oxrjOiv B, m]Xiv.6xr]i6i D. 23. syv.Xri6Eoog C. 

24. Gvii^s§r}V8v D, -v del. D^ ivXiipscav A, corr. A^ iv,- 
XsCipscov yivoiisvoov] om. B. 



MA0HMATIKHS STNTASESiS A'. 267 

(isvcdv ifjtb trjg 6eXrivLaKYig vTtodQo^rjg xal i7tL7CQO0d"t]- 
^scog^ TJtig e(i7CL7ttov6a eig tov ccTto trig oifjecjg rj^cbv 
ijtl tbv riliov %G)vov Ttoiettac trjv iie%QL tfjg itaQekev- 
6ecog e7tL6oc6tr]6Lv^ fii) 7tavta%rj Tavrag ^rjte totg ^eys- 
^e6LV iirite totg %Q6voLg cct6avt(Dg ccTtoteXet^d^aL iirite 5 
7ta6LV b^OLcog^ dt' ag eLQrjxa^ev altCag^ e7tL67cotov6rjg 
trjg 6elr]vrjg ^TJte Tcatcc t&v avtcbv ^eQcbv tov rjXLOV 
(paLVO^evrig ^ eTtl dl tcbv 6eXr]VLaxG)v eTcXeCipeov iirjxett 
firjde^Cav tOLavtrjv dLacpOQav e% tcbv 7taQaXXd^ecov 
eTtaxoXovd-etv roi) yLVo^evov 7teQl trjv 6eXi]vr]v exXeL7t- 10 
tLKOv ^tdd^ovg p) 6vijL7taQala^pdvovtog tr]v tcbv bQGiV- 
tcjv b^Lv elg tr]v aCtCav rov 6v(i7tt(b^atog. cpcotL- 
io^evr] yo^Q r] 6elr]vr] 7tdvtote VTtb tfjg r]kLa%f]g 
7CQ06Xd^^e(og^ i^tecddv xara; dLa^etQOv 6%e6LV avt& 
yevr]taL^ tbv ^ev aXlov %q6vov cpaCvetaL i]pLtv okr] 15 
7te(pcotL6^evr] dLcc tb 7tav ro 7tQo6la^7t6^evov avtrjg 
r]^L6(paCQL0V a^a xal r]^tv tote 7tav 7tQ06veveLV ^ orav 
de ovtcog dLa^etQrjd^f] S6te eCg tbv tf]g 6KLdg tf]g yfjg 
^cbvov e^7te6etv tbv dvtL7teQLay6^evov del r« r]XCcp^ 
t6te yCvetaL dcp(DtL6tog dvaX6ycog tatg tfjg i^7ttcb6ecog 20 
7tr]XL7c6tr]6LV i7tL6xotov6r]g tfjg yfjg tatg tov i]XCov 7tQo6- 
Xdiiil)e6LV' evd^ev b^oCcog xatd 7tdvta td ^eQrj tfjg yfjg 



3. nccQaXvGBcog C, corr. C*. 4. rccvtccg] corr. ex tag ccvtdg D*. 

^Eysd-soL D. 5. iLrjts (alt.)] corr. ex /xrj D^ 7. ju-rjtf] corr. 
ex firids D^. Post ccvt&v del. rj C^. tov rjXCov fisgav D. 

8. q)aLVOfisvr}g'] D, (paivofisvcov ABC. 11. avv7caQaXa^§d- 

vovtog A, 6V(i7tBQLXaii^dvovtog C. oQOvtcov C. 12. cviiTtto)- 
fiatog] -og in ras. A^ 13. GsX^qvr}] -s- in ras. A. 14. tzqo- 
Xdfitpsoig C, corr. C^. "iiatd] fort. xara ti]v yiatd. 15. tov 
— cpaLvstaL] mg. D^ {v.SLfisvov add. D^). r](iLv] -l- in ras. D^ 

16. nQOcXapLTtofiEVov] -fnrofisvov e corr. D^ 17. tcqocvsvslv] 
-SL- in ras. D. 22. td] supra scr. C^. 



268 KAATAIOT nTOAEMAIOT 

ital totg fieysd^e^LV xal totg t&v di,a6td6scov XQOvoLg 
izksLTtovea (paCvstaL. 

dLa tavta drj TTQog tijv xad^o^ov sjcl^xsjI^lv t&v 
ccKQLpcjv toTtcov Tijg 6sX7]vrjg ^ aAA' ov tav cpaLvo- 
6 iisvcDv^ hfpSLkovtcov TCaQaXa^pdvsad^aL ^ sitSLdriTtsQ xal 
tb tstay^svov xal ro o^olov t&v dtdztcjv xal dvo- 
fiOLCov dvayxatov dv SLrj TtQovTConstcd^aL^ tatg ^sv aX- 
XaLg trjQy]6s6L cpa^sv ^rj dstv 6vyxQr]6%'aL tcbv sv avtaig 
tojtcjv dLa trjg otjJSCDg tcbv trjQovvtcov TcataXa^pavo- 

10 ^svcov^ ^iovaLg ds tatg tcbv sxXsLtl^scov avtfjg^ snsLdrjjtSQ 
sv avtatg ovdsv TtQog trjv tcbv tOTtcov ytatdkriipLV rj 
'o^Lg ev^i^dkXstaL' o yaQ dv t^rj^a tov dLcc ^s6cov 
tcbv ^codLCOv 6 r]hog STtsxcov s-bQL^KrjtaL xatd tbv 
fis6ov XQOVov trjg STcXsLtJjscog^ sv d) tb xr]g 6sXii]vrjg 

15 KSVtQOv VTtb Toi) tov yiXlov %atd ^rJKog dxQL^cbg oog 
svL ^dXL6ta dLa^stQsttaL^ tovtov drjXovott tb xatd 
dLd^stQOv scps^SL nal tb trjg 6sX7}vrjg xsvtQOv TtQbg 
dxQL^SLav xatd tbv avtbv ^s6ov xqovov trjg sxXsLil^scog. 

/3'. IIsqI tcbv jtSQLodixcbv xq6vcov tfjg 6sl7]vr]g, 

20 '^cp' OLCov ^sv ovv tr]Q7]6scov td tcsqI ti]V 6skr]vr]v 

ocpsCkovta xad^oXov ka^pdvs6%^aL jtQ067]KSL 6K07tstVy 

dtd tovtcov Tcatd tb tvjtcbdsg r]^tv TtQOEXtsd-sC^^co. 

1. (isyEd^EGLv^ -V del. D*, fiEysd^eCL B. 3. ^i^ nQog] -t/ tt- 
in ras. A. 5. s7C8i-8^7t£Q] -rf- in ras. A. 6. tstccyy,^vov] -y- 
in ras. A. avoixoimv] -co- corr. ex o C^ 7. Trpoi/woxstiu-d-at] 
-V- in ras. 2 litt. D^. 8. cpa^sv fiTjj corr. ex q)cc(isv C^, -(isv 
fir- renouat. D^. Sstvl -s- corr. ex rj in scrib. C. GvyxQfiGd-aL] 
-y- in ras. D^, -?)- corr. ex t C^ 9. tr]Qovvtcov] seq. ras. 2 
litt. D, 11. avtats] tavtaig D. ■aat dXrjilJLv] corr. ex Tiata.- 
IrjfiipLv AC^ 13. svQLcyiiqtaC] -?]- corr. ex sl C, ex s D. 15. 
tov tov] A, tov BCD. 19. ^'] mg. AC, om. BD. xQovov C. 
20. OLCov] 6(iOLa)v C, cccp' OLiov (ihv ovv mg. C^ 22. ttqog- 
syitsd^SLG&o) BD, sed pr. g eras. 



MA0HMATIKH2 STNTAHESiS A'. 269 

rbv ds tQOTCov^ xad'' ov zs oC TCaXatol ratg r&v aTto- 
dsc^scov STti^okalg s%Qri6avto^ ocal xad'' bv av rjiisTg 
triv tmv TCQog ta (paivoiisva ev^qxhvav vTCod^s^scov 
SidxQc6LV svxQ7]6t6tsQov Ttococ^sd^a^ TCscQa^d^sd^a dcs^- 
sXd-scv. 5 

STtsl tocvvv avco^dXcog fisv rj esXijvrj cpacvstac 
xcvov^svrj xatd ts fifixog xac Ttldtog xal ^rj l6o%QovcGig 
lirits tbv dcd fcs^cov t&v ^cjdccov xvxXov acsl dcsQ- 
loiisvri ^rjts JtQbg triv xatd tb Ttkdtog avtov TtdQodov 
ditoxad^c&ta^svri^ %G)Qcg ds tr]g s^bQS^scjg tov trjg dvcj- 10 
^alcag avtfjg d7toxata6tatcxov xqovov xatd tb dvay- 
xacov ovds tdg tcov dklGiv TtSQCodovg ka^scv ocov t 
^v ysvocto^ xatd itdvta [isvtoc td ^SQrj tov ^a)dcaxov 
td ts ^s0a xal td ^syc6ta xal td skd%c6ta dcd tcbv 
xatd ^SQog trjQ7]0sc3V (paivstac xcvov^svri %al xatd 15 
Ttdvta td ^SQrj poQScotdtrj xal votccjtdtrj xal xar 
avtbv tbv dcd ^s6cov tcov ^cjdccjv xvxXov ycvo^svrj^ 
stpfitovv scxotcjg oc Tcalacol ^ad-rj^atcxol %q6vov tcvd^ 
dc 660V TcdvTOTS rj 6sXr]vrj tb l'6ov xcvrjd-rj^stac xatd 
lir]xog cjg tovtov ^6vov trjv dvco^aXcav djtoxad-c^tdvscv 20 
dvva^svov. jtaQatcd^s^svoc drj trjQrj^scg 6skrjvcax&v 
sxlscxfjscov^ dc dg sHtco^sv actcag^ s6x67tovv^ tcg dv 
jckri^ovg ^r]VG}v dcd6ta6cg c6o%Q6vc6g ts ycvocto Ttdv- 
tots tatg tov l'6ov Ttlrjd^ovg dca6td6s6c xal c'6ovg 
xvxXovg 7tsQcs%oc xatd fifjxog r^toc olovg t} [istd tcvcov 25 

4. svxQTiGtoxBQOv] £- coiT. ex o D^, -ov mut. in av D^; 
ivxccQ7]Gt6t£Qov B, sed a eras. ; evxccQi^atoTSQOv C, corr. C^. 

noLOLfisd-a] mut. in TtoLov^sd-a D^ 8. tov] AB^D^, r&v 

BCD. v.vv.Xov'] corr. ex %vv.Xcov D^ alsC] AC, a%L BD. 

9. x6] om. D. 14. xd rs] %al rd D. 16. Ttdvra] om. BC. 
■ xat (pr.)] rs xat D. vorLardrr}] D, vorLordrr] ABC. 17. 
liscov C. yivovoyisvr] D. 20. [lovov] om. B. 21. Srf] 

ds D. 22. aCrLug] supra scr. D. 23. ysvoLxo D, corr. D^ 



270 KAATAIOT nTOAEMAIOT 

l'6(0V TtEQlCpSQELGiV. bko6%EQe6teQOV ^EV OVV 01 Eti 

TtaXaLorsQOi tbv %q6vov tovtov vnEXdii^avov £tvat] 
rj^EQav ^^7tE xal y'' dca to6ovtov yaQ Eyyi^ta icoQm 
^fjvag ^Ev ccTCotEXov^Evovg 07cy^ d7toxata0td6ELg dh\ 
5 dva)^aUag ^hv aXd'., Ttldtovg dl <?ft)3, TtEQidQOiidg 
fitJKOvg 0^a xal EtL^ o6ag xal 6 i^XLog EJtLla^pdvELl 
totg Trj TcvxXoLg iv t& TtQOELQrj^Eva) xq6vg) ^OLQag l T^y\ 
G}g trjg ditoKata^td^Ecag avtcbv itQog tovg d7tlavEtg\ 
dotEQag d^EcoQOv^Evrjg. £7cdXE6av ds tbv %q6vov tovtovl 
10 TtEQLodLzbv cjg TtQ&tov ELg iiCav d7toxatd6ta6LV dyovtcci 
£yyL6ta tdg dLa<poQdg tcbv XLvrj^ECJv. xal Xva e^ oXcjv 
rj^EQG)V avtbv €v6tri6G)vtaL^ EtQL%Xa6La6av tag ^gtpjts 

a 

y' rj^EQag zal e6%ov rj^EQav dQtd-iibv ^ p"^v^^ ov sxd- 
lE6av E^EXLy^^v' ocal td dXla de bfioLcag tQL7tXcb6avtEg 

15 ^6%ov ^rjvag ^ev %|'9', d7toxata6td6ELg ds dvco^aXLag 
^EV ^tj, 7tXdtovg ds ^jcs", 7t£QLdQ0^dg ds ^TJxovg ijJTcy 
xal EtL^ o6ag %al 6 i]XLog £7tLXa^^dv£L totg v8 xvxXoLg 
^OLQag A/3. 

i]drj ^EvtOi TtdXLV 6 "l7t7taQ%og ijXEy^EV d7t6 tE tcbv 

20 XaXdalTC&v xal tcbv xad"' iavtbv trjQy]6Ecov i^tLXoyL^o- 
[LEvog (lii i%ovta tavta dKQipag. d7todEL%vv6L ydQ^ 
dt' d)v i^id^Eto tr]Q7]6£C3v^ otL 6 TtQcbtog dQLd^^bg t&v 



3. xat'] om. D. zogov D. 4. Ss] S' D. 7. UQOSiqri- 
jLteVco] 7tQ0K£L(isv(a D et supra scr. B^. -^'*] f'^ C, F seq. ras. 1 
litt. A, Fo A^D, Sl(iolqov supra scr. D^, X§ B, sv aXXm l v^ o 
xal aXr]d-sg mg. B^. 10. TtQarov] corr. ex nQog xov B^. 12. 
avTOv rjiiSQcbv D. Gv6zri6(ovTai'\ B et supra scr. D, cvazriGovzaL 
ACD. szQiTcXaGLaGav] zQLnXcocavzsg D. 13. %at] om. D. 

^] ^ di D, yi" ^ a D^, iivQLag U Dl 14. sh,SLXLy\L6v corr. 

ex i^LXsLyiiov Dl zd aXXa 8s] zaXXa d' D. 15. ds] S' D. 

16. ^] ^ C. 19. r]Xs\y^sv corr. ex i]Xsy\^sv A^ 21. 
ano8sL%vvsL D. 



^ MA0HMATIKHS STNTAgESiS A'. 271 

'^liEQ&v^ di O0C3V Ttdvtots 6 iKXsLTttLxbg XQOvog iv 

l'60Lg ^rj6lv xal iv L60Lg %LVYi^a<5LV dvaxvxXsitaL^ ^ 
i6tLV xal stL ^gj rj^SQ&v xal fiLdg wgag L67}^SQLV7]g^ iv 
alg ^rjvag ^sv aTCaQtL^o^svovg s{}ql6ksl ^^^|f, okag ds 
dvco^aXLag d7Co%ata6td6sLg pfpoy^ ^cjdLaxovg ds zvxXovg 5 
d^Lp IsLTtovtag ^OLQag ^L' syyL6ta^ o6ag xal 6 ijhog 
SLg tovg t^LS xvxlovg IsCtisl^ TtdkLv cog trjg ditoxata- 
6td6scog (^vrwv TtQog tovg dnXavsLg d6tSQag d^scoQov- 
fisvrjg. od^sv s^bQL^KSL xal tbv ^rjvLatov ^s6ov xqovov 
iTtL^SQL^o^svov tov TtQoxsL^svov t&v rj^sQ&v TtXyjd-ovg 10 
Sig tovg ^d^lS ^rjvag rj^isQ&v 6vvay6^svov k^ Xa v rJK 
syyL6ta. iv ^sv ovv t<p to6ovtco xqovc) tdg ditb ix- 
XsLil^scog 6sXr]VLaKfig iitl skXsliI^lv aTtlcbg dvtaTtodido- 
lisvag l'6ag dLa6td6sLg dTtodsLKvvsL, cog drjXov yiyvs^d^ao 
t6 djtoKad^L^ta^d-aL f^v dvco^aXCav iK tov Ttdvtots dLa 15 
tov to6ovtov X9^^(>'^ tovg ts to6ovtovg (ifjvag jtSQL- 
sxs^&ccL Kal tatg i'6aLg Katd ^rJKog utSQtodoLg ^d^La 
l'6ag iitLka^pdvs^d^aL ^OLQag tv^ L! dKoXovQ^cog tatg 
TtQbg tbv riliov ^vt^vyCaLg. 

SL ds tLg ^ri tbv dnb iKXsCipscog ^sXrjvLaKrjg iitl 20 
SKXsLxfjLV dQLd^^bv t&v [irjvcov iitL^rjtoCr}, ^ovov ds tbv 
dicb 6vv68ov iq 7tav6sXrjvov iitl trjv o^oCav 6vt,vyCav^ 



1, EV.XsinxLV.6Q\ i- ins. A*. 2, firjaiv'] -v del. D^. yiLvt]- 

fiaeivl ■Kivi]- corr. ex jtirjort D^ ^] in ras. A, (ivqlccScov D. 

3. iaxLv'] conip. B, -v del. D*. >tat(pr.)] l^ %at D. ?rt] corr. 
ex STTj B. 4. /(tI^] },6^^ C. 9. svQLCy.SL] -SL in ras. C. 

tov] triv A, tbv' (lEV D. 11. v rj] B et e corr. D^, vr] AC. 

13. ^■nnlsLipLV D. 14. dLccctdGELg] -eig in ras. D^, supra -ct- 
ras. ccTtodELKvvsL] -SL in ras. A. driXov] corr. ex SfjXcc D^ 

yLvsG&ccL C, ysviad^ccL D. 16. tov] om. D. toaovtovg] 

taovg D. 17. rag 1'accg D, corr. D^ 18. (loiQccg] ante -q- 

ras. 1 litt. A. 21. inL^ritoT in extr. lin. A. 



272 KAATAIOT nTOAEMAIOT 

8VQ0L civ £tL ^tzova tbv d7toKata6tatLxbv tijg te avcj- 
fiaXcag xal tcov ^rjv&v aQLd^^bv Xa^hv tb ftdi/ov avt cov 
Kovvbv ^etQOV iTttaxaLdsxatov ^ o 6vvayei ^r^vag ^ev 
6va^ avcoiiakCag 8e aTtoxata^td^eig 6^,%'. ovKSti ^evtov 
5 6 JCQOTcec^evog XQ^^^^S evQi^Keto Tcal trjv Katd TtXdtog 
ditaQtCt^cov d7toKatd6ta6LV' ri yaQ dvtaitodo^ig tcov ex- 
2,eCfec3v TtQbg tdg dLa6td6eig {lovov tov te %q6vov koI 
tav xatd ^rJKog iteQLodcov ecpaCveto dG)^ov6a tdg 1^6- 
tr^tag^ ovKett de TtQbg td ^eyed-r^ xal tdg o^ototrjtag 

10 rrav i7tL6KotrJ6ecov^ dtp' cov xal tb Ttkdtog xatakait- 
pdvetaL. 

fjdri iievtOL TtQOKateLXrj^^evov tov tfjg dvco^aXCag 
d7tOKata6tatLKOv xqovov ^taQad^e^evog Ttdhv 6 "iTtTtaQXog 
diaOtd^eLg ^rjv&v b^oCag xatd 7tdvta tdg dxQag ix- 

15 keCijjeLg ix^vtcov xal totg ^eyed^e^L xal totg ;^()dvotg 
t&v i7tL6xot7]0ecov ^ iv alg ovdev iyCyveto dLatpoQOv 
7taQd triv dvco^aXCav^ cog dtd tovto xal trjv xatd 
TtXdtog 7tdQodov d^toxad^L^tauevrjv (paCveed^aL^ deCKvv6Lv 
Kal tijv tOLavtrjv 7teQCodov dTtaQtL^o^evrjv iv ^rj6lv 

20 {lev ^evv^^ 7teQL6doLg de 7tlatLKatg ,e^Ky. 

6 fiev ovv tQ67tog^ co TtQbg tdg totavtag xata- 
XrjipeLg ixQ^6avto ot 7tQb rj^&v^ toLovt6g tLg rjv. 6tL 
de ovx aTtXovg ovd' ev7t6QL6tog^ dXXd 7toXXrjg xal ov 
trjg tvxov6rjg de^^ievog i7tL6td6ecog^ ovtcog dv xatavoTJ- 

25 6aLfiev. Lva ydQ dcb^ev dxQLpcbg l'6ovg dXXrjXoLg to^bg 



1. riTTOVu t6v\ 7]ttov D. aTtoatttccatL-Kov J). 2. ccQid'- 

(i&v C. 5. 7]VQL6yi£to D. 7. TiQog Tag SiccGtdasLg] om. C, 

^ovov^ avTwv (lovov D. 10. acp'] e corr. D^. xai] om. D. 

13. ccnoyicctaatL-iiov AD, corr. A*. 15. (isysd^saLJ -sd^sci. 

renouat. D^. 16. syCvsto D. dioccpOQav C. 18. dsL-AvvaLvl 
-V del. D^. 19. fATjGt D. 20. ij^] AB^, ^irxy BCD. 

22. sxQrjaato A, corr. A^ 23. ovds C. 



MAeHMATIKHS STNTASESiS A', 273 

r&v dLa6xd6eG3v xQovovg avQL^KS^d^aL^ TtQ&rov ^ev ov- 
dev otpeXoq rov roiovrov ^yj xal rov tjXlov t6 TtaQcc 
rrjv dvco^aXLav didcpoQOv ri ^rjdsv yj ro adrb Ttoiovv- 
rog xad^ ixarsQav rcbv dca^rd^scjv. sl yaQ firi tovro 
6v^^aCvoi^ yCyvoLro ds rL^ ag s(pr]v^ itaQa rrjv dvcj^a- 5 
XCav avrov dLdq)OQOv^ ovrs avrbg s6raL sv rolg l'60Lg 
XQovoLg L6ag TtSQLdQO^dg TtsnoLrj^svog ovrs drjXovorL i] 
6sX7]vr]. sdv yaQ Xoyov svsxsv sxarsQa ^sv r&v 6vy- 
XQLvo^svcov dLa6rd6SG)v iisd"' oXovg xal rovg l'6ovg 
svLav6Covg XQ^^^^^S STtLla^^dvrj rb r]^L6v rov svLav- 10 
6Cov xQOVov^ sv ds ra ro6ovr<p STtLXSKLvrj^svog 6 rjlLog 
rvyxdvrj xard ^sv rijv TtQmrrjv dLd6ra6Lv aTtb rrjg xard 
rovg 'Ix^vag ^s6r}g TtaQodov^ xard ds rrjv dsvrsQav 
dnb rfjg xard f^v IlaQ^svov^ xard ^sv rijv TtQorsQav 
ska66ov S7tSLXrj(pG)g 6 7]XLog s6raL rov rj^LXvxlCov ^ol- 15 
Q&v d C d' syyL6ra, xard ds rr^v dsvrsQav ^st^ov 
rj^LxvxXCov ratg avratg fioCQaLg' co6rs xal rrjv ^sltjvrjv 
sv rotg L60Lg xQovoLg ^sd-' oXovg xvxlovg xard ^sv 
rijv TtQorsQav 8Ld6ra6Lv S7tSLXrjg)svaL [loCQag qos d\ 
xard ds rrjv dsvrsQav Q7td C ^' ^f^i^ ovv q)a[isv 20 
rovro TtQ&rov sxslv rdg dLa6rd6SLg JtSQL rbv t^Xlov 
6v^^s^rixbg rb rjroL oXovg avrbv xvxXovg %sqlsxslv t} 
xard ^sv rrjv srsQav r&v dLa6rd6sc3v rb djtb rov 
djtoysCov ^i^lxvxXlov STtLXa^pdvsLV., xard ds rrjv srsQav 
t6 ditb Toi) TtSQLysCov^ ?) djtb rov avrov r^ri^arog 25 
dQXs6d^aL xa^' sxarsQav twv dLa6rd6scov rj t6 i6ov 



5. yCvoLxo D. nciQa] pr. u corr. ex c in scrib. D, 8. 
Bv.ciXEQDcv D. 9. oXovg'] -X- e corr. C, oXov(s %vv.Xovq D. 

10, £7nXcc[i§dv£i CD. 12. ngmxriv] TCQOXSQav D. 14. r^v^alt.)] 
om, D. 15. in£iXT]q)(X)g] -£- ins. A\ -£l- in ras. D^, -X- corr. 
ex d D-. 16. /.'] xal Z ^ta^ D. 19. £7tT]X£L(p£Vca D. 20. 
dsLv] corr. ex cc£C D^. 22. ccvxov] corr. ex ccvxoiv D. 
Ptolemaeus, ed. Heiberg. 18 



274 KAATAIOT nTOAEMAIOT 

a7ce%SLV sxatsQCjd^ev ijtoi tov anoysCov iq tov tcsql- 
ysCov xatd ts tijv TCQOtSQav STiksL^iv tfjg stSQag dia- 
6tcjc0S(og aal xata tijv dsvtSQav trig stSQag. ovtag 
yaQ av ^ovcog rj ovdsv rj ro avtb yCyvoito didcpoQov 
5 TCaQa triv dvcj^alCav avtov xad'' sxatSQav t&v dca- 
6td6sc3v^ &6ts xal l'6ag tdg STCikaii^avo^svag yCvs^d^ac 
TCSQccpsQsCag ijtoc dXlt^kacg rj %al dXli^Xacg %al tatg 
bybakalg. 

dsvtSQOv ds rjyov^sd^a dscv xal tcsqc tovg dQo^ovg 

10 trjs ^sXt^vrjg xijv bfioCav S7cC6ta6cv Tcocsc^d^ac. tovtov 
yaQ ddcazQCtov ^svovtog svdsxo^svov jtdkcv (pav7]6stac 
t6 Tcal trjv ^ski^vrjv jtokXdxcg l'6ag TtSQccpsQsCag xatd 
^rJKog sv totg L'6ocg xQOVocg STCcka^^dvscv dvva^d^ac 
^rj Tcdvtcog xal trjg dvco^aXCag avtfjg dTCOKad^c^ta^svrjg. 

15 6vii^7]6stac ds t6 tocovtov., sdv ts xad'' sxatSQav tcjv 
dca6td6scjv djcb tov avtov %atd TCQO^d^sGcv r\ tov av- 
tov Tiatd dcpaCQs6cv dQo^ov 7Cocrj6rjtac trjv dQxijv xai 
liij S7CC tbv avtbv Katakrjyrj^ sdv ts %atd fisv trjv 
itSQav d7cb tov ^syC6tov Sqo^ov dQxo^svrj S7cl tbv 

20 ikdxc6tov dQo^iov xataktjyrj^ Tcatd ds tijv stSQav djcb 
Tov skaxC6tov dQo^ov S7cl tbv ^syc6tov^ sdv ts tb 
c'6ov d7Csxc36cv SKatsQCjd^sv d7cb tov avtov skaxC6tov 
rj ^syC6tov dQo^ov o ts tr^g stSQag dca6td6sc3g 7CQcbtog 
dQd^og xal 6 trjg stsQag s6xatog. s7ca6tov yaQ tovtcjv^ 

26 idv 6v^PaCvr], r] ovdsv Ttdkcv rj t6 avtb 7C0C7]6sc TCaQa tijv 



4. ytVotro D. 5. t&v] bis D, corr. Dl 9. d^] S' D. 

10. 6(ioLav] 6- ins. A. 11. ya^] seq. ras. 3 + 2 litt. A. 

ScdLwnQLTOv] a- in ras. A. 16. Kccrd] corr. ex yial rd D*. 17. 
noLr\67]raL] noLfjraL corr. ex TtoiBtraL D^. 18. yLaraXriyBL D. 

20. dqo^ov] om. D. 21. 8^6^10^] om. D. rov] xo D. 22. 
L6ov] L6- e corr. A^ 6ini%oi6Lv] -coo- in ras. A. 25. rf (pr.)] 
om. D. avro] bis C. 



MA0HMATIKHS STNTASESiS A'. 275 

dvco^aXtav avtrjg did^pOQOv xal did rovro rdg ^lv xard 
fiijxog STaX^^tl^ELg l'6ag dTtSQydt^eraL ^ rijv dh dvco^akcav 
ovda^&g d7ioxara6r7]6£L. ovdev aqa ov8\ rovrcov rcov 
6v^7trcj^drcov £%slv det rdg jtaQaXafi^avo^evag dia- 
6rd6eLg^ ei ^eXX7]6ov6LV avrod^ev rbv d7toxara6rarLxbv 5 
rfig dvcD^alLag xq6vov TteQLe^eLv. rovvavrCov d' dv 
ofpeCXoL^ev exXeyeLV rdg ^dkt^ra rijv dvL66rrira i^(pa- 
vC6aL dvva^evag^ edv ^rj okaL JteQLexcovraL rfjg dvG)- 
^akCag d7toxara6rd6eLg^ rovre6rLv orav ^ri ^6vov d7tb 
dLacpoQcov dQ6^cov rdg dQ^dg e%co6LV^ dkkd xal 6(p6dQa 10 
dLa(p6QG}v ri xard ^eyed^og rj xard dvva^LV^ xard ^e- 
yeS-og ^ev^ ag brav xard ^iev rr]v ereQav dLd6ra6Lv 
dTtb Tov eka%C6rov Sq^^ov dQ%r]raL xal ^ij eTtl rbv 
^eyL6rov xarakr^yr]^ xard de rrjv ereQav^ orav aTtb rov 
^eyC6rov dQ%rjraL xal fir] eTtl rbv ekd%L6rov xarakriyrj' 15 
7tkeC6rrj ydQ ovrcog e6raL rrjg xard ^rjxog e^tLk^^i^ecjg 
dLacpoQd ^rj bkcjv xvxkcov d^taQrL^o^evcov rrjg dvcj^a- 
kCag^ brav ^dkt^ra reraQrrj^^QLOv ev i] xal r^Ca fiLccg 
dvcj^akCag e^tLka^pdvrjraL^ dv6l r6re rotg 7taQd rijv 
dvcj^akCav dLacpoQOLg dvC6G)v rmv dLa6rd6ecov e6o^e- 20 
vov xard dvva^Lv de^ cjg brav xa^' exareQav ^ev 
r&v dLa6rd6ecov dTtb rov iie6ov dQ6^ov ccQ^rjraL, ^r] 
d7tb rov avrov de ^ie^ov^ dkkd xard ^ev rriv ereQav 
dTtb rov xard 7tQ66^e6Lv^ xard de rr]v ereQav dTtb rov 
xard d(paCQe6Lv' xal ovrco yaQ rb 7tkeL6rov dLoC6ov- 25 



2. a7t£Qyd6£tac D. di] d' D. 4, 7t(XQaXafi§civo(i£Vus] 

-§a- ins. in extr. lin. A*. 5. (isXXi^Govaiv'] mut. in ybiXXovaiv 
C*, pr. X del. D^ Scjtov.ataGTiyiov D. 7. ocpuXoybev BC. eyb- 
(pav7]6aL BC. 9. anoyiataatd^rig D, corr. D^ (comp.). fiovcov C. 
10. dQOiKov — 11. diacpoQcov] mg. D" {v.EC^ivov). 12. v.atci 
liBv] corr. ex iilv Y.atd D^. 16. nXELetov C. yap] y- corr. 
ex 6 in scrib. D. 23. ftsV] i^i^ A, om. D. 25. ovtcog D. 

18* 



276 KAATAIOT nTOAEMAIOT 

6lv dXlTjlcjv ai tov ^7]xovg iitov^iai ^dXi^ta ^ij aito- 
xad-L6ta^8vrjg tfjg avcD^aXCag tstaQtri^OQiOv ^sv ivbg 
Ttdkiv ri xal tQicbv 87tila^Pavo^£vc3v ^iccg dvco^aXiag 
dv6i totg Ttaqd trjv dvco^aXiav diacp^QOig^ rj^ixvxXiOV 
5 ds tBttaQ6i. did tavta dri xal tbv "iTtitaQxov oQ&^ev 
jtaQatrjQrjtiKthtata^ ag iidki6ta svo^i^sv^ xsxQrj^evov 
tfi tcbv TtaQSikrj^^svov Sig tr^v toiavtrjv S7ti6xsiljiv 
dia6td6scov sxXoyfj xal 6vyKS%QriiLSvov ^sv t<p tr^v 
6sXrivriv xatd ^sv tijv stSQav did6ta6iv ditb tov fis- 

10 yi6tov Sqo^ov TtSTtoirj^d-ai f^v dQxr^v xal ^ij STtl tbv 
iXd%i6tov xataTtSTtav^d^ai, xatd ds f^v stSQav ditb tov 
ika%i6tov Sqo^ov 7tS7tOifj6d-ai tijv dQ^rjv xal ^rj iitl 
tbv ^syi6tov xataitSTtav^d^ai^ diOQd^cb^avta ds xal tb 
TtaQO, trjv tov rjkCov dvco^aXiav ysvo^svov didcpoQOv 

15 xaCtoi ^Qaxv ov did tb d' syyi6ta svbg dcjdsxatrj^o- 
qCov xal ^rj tov avtov 7J tov tb i6ov Jtoiovvtog did- 
(poQOv trjg dvcoiiaXCag xaO'' sxatSQav tcbv dia6td6sav 
sig okovg xvxXovg ikkskoLTtsvai trjv tov rjXCov ditoxa- 
td6ta6iv, 

20 ravro: ds siTto^sv ov dia^dkkovtsg trjv jtQOXSi- 

lisvrjv iTti^oXijv tfjg t&v JtSQiodiX&v d7toxata6td6scov 
xatakTJipscjg^ dXXd 7taQC6tavtsg^ oti ^std ^sv trjg 7tQ06- 
r]xov6rjg i7ti6td6SG)g xal tov xatd tb dxokov^ov i7ti- 
Xoyi6^ov yivo^svrj xatoQd^ovv dvvatat tb TtQoxsC^svov^ 

25 sC ds tiva xal tb tv%bv t&v ixtsd^siiisvcov 6v^7ttc3- 



3. ocvco^alLag] -fia- ins. in extr. lin. A^, -g corr. ex -v D*. 

4, SvaCI supra scr, D*. zols Ttaga rr]v avcofiaXiav] om. D. 

5. di] supra scr, D*. xitaQGi AC. 6. 8v6(iL^e D. 7. sjrt- 

GKEtpLv D. 8. xat] corr. ex t in scrib. D. 10. %at] supra 
scr. D^. 12. dQOfiov] om.I). 13. rdi'] corr. ex t6 Dl «0:7«- 
Ttsnsnavad-aL B. dLogd^aiGavTa] -v- in ras. D". 15. d'] 

xhaqxov D. 18. hXbloLTchaL CD, corr. Dl 20. di] $' D. 



MA0HMATIKHS STNTAEESJ2 A'. 277 

^drcjv JtaQeXd^oL^ dtaij£v6d-ri6stat, 7tavxd7ta0LV rrig STtL- 
^Yjrov^avrjg xaraXij^Ecog^ xal ori dv67t6QL0r6g iorLV 
rotg dLOQatLK&g jtoLOv^evoLg rijv rcbv roLOvrcav rrjQrj- 
6e(Dv exXoyrjv rj TtQog rb dxQL§ieg Ttdvrcov rmv ocpeL- 
X6vrcDV avralg vitdQieLV dvra7t68o6Lg. 5 

rcbv yovv exred^eL^evcav TteQLodLX&v dnoxara^rd- 
0eG)v xard rovg vjtb rov ^lmtdQxov yeyevrj^evovg ijtc- 
XoyL6^ovg rj ^ev rcbv ^rjv&v^ ag eq^a^ev^ vyLcbg^ C3g 
lidh6ra ivfjv^ i7tLkekoyL6^evri ovdevl alG^rinp cpaC^ 
veraL dLe^ev6^evrj rrjg dXrjd^eCag^ r] 8e rr]g dvco^aXcag 10 
xal rov TtXdrovg di,Lok6ycp rLvl dLrj^aQrrj^ivrj^ G)6re xal 
rj^tv ev6vvo7trov yeyovevaL ix rcbv elg rrjv roLavrrjv 
dLdxQL^LV xard rb d7tXov6reQOv xal ev7toQL6r6reQOv 
TtaQeLXrj^^evcov i(p6dcov, dg evxl^vg d^todeC^o^ev d^a rfj 
7trjXLx6rrjrL rfjg ^eXrjvtaxrjg dvco^aXCag ^tQoexred^eL^ivoL 15 
jtQ&rov dLd rb 7tQbg rd e^rjg evxQrj6rov rd xard 
^iiQog yLv6^eva ^i6a XLViq^ara ^TJxovg re xal dvco- 
^ialCag xal TtXdrovg dxolov^cog rotg 7tQoxeL^ivoLg 
rcbv 7teQLodLXcbv XLV7J6ecov d7toxara6rarLXotg XQ6voLg 
xal rd ix rfjg d7todeLx^rj6o^ivrjg avrcbv dLOQd^co^ecog 20 
i7tL6vvay6^eva. 



2. ■iiccrccXT^y.ipscos C, corr. C^. ion D, comp. B. 4. rf] 
ins. D^ 5. ccTccTtodoaig D. 7. ysyivvrjiievovg AC, pr. v 

eras. A. 8. vytcag] C^D, vysL&g ABC. 10. diSil^svaliisvT] 

mut. in dLSipsv\6^svT] A^ rj'] corr. ex sl T)^. 12. ysyovsvccL] 
corr. ex ysyovsv Dl 15. TCQoasyid-sfisvoL D, -a- del. D^ 16. 
rd (pr.)] corr. ex rag C^, ro D. 18. dv.olovd-cog'] pr. o in ras. A. 

19. dcTCoyiccraarLKOis D, 20. ccTtodsLx^rjoofisvLg A, corr. A^. 

dLOQd^mOscog ccvrmv D. 



278 KAATAIOT nTOAEMAIOT 

y'. IleQl tcbv Tcata fiSQog b^aX&v 7Ci,V7J66G)v trig 
^sXTJvrjg. 

'Eav toCvvv tb aTCodedsLyiiivov fie6ov tov 'f}Xcov 
mvrj^a rjiiSQTJ^LOv o vd- rj l^ Ty l^ Xa syyL0ta nokka- 
6 7tXa6Ld0(o^sv STcl tag tov ivbg ^rjvbg rj^SQag ocd' la v 
ri X xal totg ysvo^svoLg jCQO^d^&^sv svbg kvtcXov uol- 
Qag rl, s%o^sVj ag sv ta svl fii^vl ^s^cjg ri 6sXr]Vf] 
XLVsttaL Kata ^ijKog uoLQag tTtd- ^ xy a 7cd ^ X v^ 
syyLGta. Tavrag STtL^SQLdavtsg SLg tag TtQOTcsL^svag 
10 tov ^rjvbg rj^sQag s%o^sv rj^SQrj^Lov ^s6ov XLvrj^a ^r]- 
xovg ^OLQag Ty T Xd vri ky X X syyL6ta. 

TtdXLv tovg a^d' xvxXovg trjg dva^aXLag TtoXXaitXa- 
6Ld6avtsg STtl tdg tov ivbg tcvkXov ^OLQag t| s%o^sv 
TtXrjd^og ^OLQcjv fi ^gwJLt. tavtag ^SQL6avtsg slg tdg 
15 yLVOfisvag rj^SQag t&v 6vd firjvcov jC,vl^ T ^d vd ]l s%o- 
^sv Kal dvcj^aXLag r]^SQr]6L0v ^s6ov Kcvrj^a fiOLQag Ly 
y vy vg Kd' Xr] Xr]. 

biLOLcog tdg J%Ky tov TtXdtovg d7tOKata6td6SLg JtoX- 
Xa7tXa6Lddavtsg sjtl tdg tov ivbg kvkXov ^oLQag r| 

1. y'] mg. AB, recisum C, om. D, yiscpdlaiov y' B^. 3. 
xov rjXLov (i^aov rjfieQ^qeLov mvr^ficc D. 4. o] om. D. ty] 

supra scr. A^ lyytffra] om. D. 5. v rf] vri D, diremit D^. 

6. ysvo^ivoLg^ -8- corr. ex l in scrib. D. y.vzXov] -v in 

ras. A^ 7. stofisv] seq. ras. 2 litt. A, supra s- ras. svi] 
s C, om. D. 8. xy] x y D. 9. TtQO-nsLfiivag] -sv- corr. ex 
7]v D. 12. 6h,%-] sh,riv.ovxa ^ D, dmx/ ins. D^, mg. 6^%' D^. 

noXvnXaGLaaavTEg D. 13. "Avv^Xovg C. 14. liQLqaiv] /t ACD. 

]i] ft C et supra scr. A\ om. AB, T^ e corr. D. 15. yivo- 
iisvag] corr. ex ysvoiisvag A. 6va] 6 seq. ras. 2 litt. D, va 
supra scr. D*. >Ip] Ji tp BC. 16. xai] s C, del. C^ 

18. ofioLoog] supra -/*- ras. A. Deinde xat add. B^. xdg] 
O supra scr. D, r D^ ^£<^xy] -y in ras. D*. 



MA0HMATIKHS STNTASESJS A'. 279 

oiy 

iloftfi/ Ttlri^o^i ^OLQ&v ft p67t. tavtag ^SQi6avt6g stg 
tag tcjv ^svvrj ^rjv&v yivo^svag rj^SQag ^ ago^ vrj vrj 
y 3c s%o^£v xal itkdtovg rj^eQrj^iov ^s6ov KLvrj^a ftot- 
Qag Ty Ty jTs Xd" ]i L^ cd'. 

Ttdhv dito tov tfjg 6sX7Jvrjg ocatd ^fJKog rj^SQrj6iOV 5 
7CLvr]^atog d(psl6vtsg to tov rjXoov ^s6ov '^}isq7j6lov 
KivriiLa s%o^sv djtoxfjg ^s6ov rj^SQ7J6iOV Kivrj^a ^OiQag 
i^ Td Tc^ Jid oc i^ vd". did ^svtoi tav scps^fjg^ ag 
s(pa^sv\ rj^iv TtaQakrjcpd-rj^oiisvcjv slg tijv totavtrjv 
S7ti6}cs^)iv sg)6d(DV [cap. YII] ro ^sv tov ^r]KOvg riiisQil- 10 
6iov Kivrjua 6xsdbv dTtaQdXlaxtov svQi6K0^sv tg5 itQo- 
KSi^svo) Kal tb tfjg d7to%fig dr}Xov6ti, tb ds tfjg dvco- 
^aXiag skattov ^oiQatg oooo Td fZg Xd'^ cjg yivs^d^ai 
ILOiQcbv Ty y vy v^ i^vd vd"^ tb ds roi) itXdtovg Ttlstov 
^OiQaig oooo rj Xd^ Trj^ cjg Kal avtb yCvs^d^at ^oiQ&v 15 
Ty Ty jTs Xd' JTrj v^ ^,^. 

Katd tavta dfi td rjy.SQrJ6ia ka^6vtsg ^sv SKd6tov 
tb slK06totstaQtov s%o^sv hQtalov ^s6ov xivrj^a firj- 
Kovg iihv iioiQG)v o Ip v^ K^ Kg Ky ]T^ Ts^ dvco^aXiag 
ds ^oiQ&v o Aj3 AO- ftd v ^d Xd' vt, A, Ttldtovg ds ^oi- 20 
QG)V o Xy d Kd d' Xp kTc A/3 A, djtoxfig ^s ^oiQcav o X 



1. jx ] fi^'^ B, iivQLadag supra add. B'. ,^(>«] -« e corr. A. 

r. p 

^VQL 6Ly §671 mg. D*. 2. aQo^ C. i^vql tg ccqo^ mg. D*. 

3. x] om. B, xf supra scr. B'. 4. Ty (alt.)] l- ins. D, t^] Lf\ D. 

8. inLLV wg ^cpccfiev D. 13, (loiQccLg] comp. ABCD. oo(pr.)] 
in ras. A; pr. et tert. o e corr. D^. ytVfC^O-at] -t- in ras. A. 14. 
[lOLQ&v] comp. ABC, (lOLQagT). 15. (lOLQULg] comp. ABC, (lOLQagD. 

o (pr. et tert.)] e corr. D*. ylyvs^Q^aL D. 17. v,ata\ xat A. 

18. sUo^xoxExaQtov'] 'k j J). mQatov D, corr. D*. 19. ftot- 
Q&v] D, comp. ABC, ut etiam in seqq. 20. l§] -§ e corr. D'. 

21. d] ins. D^ l (alt.)] seq. ras. 1 litt. D. 



280 KAATAIOT nTOAEMAIOT 

xrj Xg ]iy oc [id v^ X^ tQiaKovtdmg ds jcoLTJGavtsg ra: 
ri^£Q7]6La xal d(peX6vtsg Kvxlovg s^o^sv ^rjviaiav ^i- 
erjv s7tov6iav ^7]icovg ^sv ^olq&v Xs it, k%' i^ jls is^ 
dvco^aXiag ds ^olq&v Xa v? vij rj vs vd^ X^ itldtovg 
5 ds ^oiQcov Ag v/3 fiO" vd %rj T^ Aa, dTCoxrjg ds ^oiQ&v 
^ ]iy X Jl '^ v^ L 

TtdXiV td rj^SQr]6ia 7tolv7tXa6id0avtsg sxl tdg rov 
AlyvTttiaKov sviavtov rj^SQag t^s xal dcpsXovtsg oXovg 
xvKXovg s%o^sv sviav6iov ^s6r}v sitovSiav ^7]Kovg ^sv 

10 ^oiQ&v Qxd" xp ]ig Ty v Xp X^ dvco^aXCag ds ^oiQcbv 

^ ]iy i 7tr] ]id Ty vs, TtXdtovg ds ^OiQcbv Q^r] ^^ ^^ 

tj8 ^d xs £, dTtoxrjg ds (lOiQ&v QTcd' X^ %d xrj nd" 'Ky vs. 

s^f]g oxt coxaidsKdmg noir]6avtsg td sviav6ia did tb 

rrjg xavovoyQatpiag^ mg sopa^sv^ sv%Qr]6tov xa\ d(psX6v- 

15 rsg oXovg xvxXovg s%o^sv OKtcoxaidsxastrjQidog ^£6r]v 
£7tov6iav iir]KOvg ^sv ^OiQ&v Q^r] ^d' v^ ^ d- litf, dvco- 
liaXCag ds ^oiQ&v qv^ v^ id Xg k^ T X^ jtXdtovg ds 
fioiQCjv Qvg V d" ft-O" id" Xa A, aTtoxfig ds ^oiQcbv Qoy 
i/3 Kg Xp ^d' T A. 

20 diayQdipo^sv ovv^ &6%sq xal STtl tov r]Xi0V^ xav6- 



1. fly] II- in ras. D^ 2. yivyiXovg] x D, x D^. 4. Xcc] 

-a in ras. D^. 5. Xa\ X seq. ras. 1 litt. D. 6. Ji 7]] iiri 

BCD, corr. D. vd-] corr. ex v^ D. 7. TtoXXanXaaiccoavtsg B. 

8. xat] om. D. 10. (Liot^mv (utrumque)] comp. ABCD. 11. 
mi] QTcri BC, q- eras. C. J] (i^ BC. TtXdzovs] -g ins. in 
scrib. D. (lOLQ&v] comp. ABCD. 12. yci] %- in ras. D. 

aTio%r\g\ corr. ex hTioif\g D. \ioiQGiv] comp. ABCD. 13. 
xo] om. C. 15. byixai%aibyi.aixr\Qi8og D. 16. fifV] om. D. 

|Li'9'] seq. ras. 2 litt. A. 17. yi.oiQibv] comp. ABCD. i8] 
seq. ras. 2 litt. A. h(3] -|3 e corr. D^. 18. jLtot^mv] comp. 
ABCD. Qv^] corr. ex p^ Dl v '%]'v%' ABC. 19. ^] 
-^ e corr. D^ X^] -§ e corr. Dl 20. dLayQaipoo^sv CD^ 



MAeHMATIKHS STNTASESiS A'. 281 

vccg y inl 6tCxovg ^sv tcccXlv fif , eeXCdia de Tcad"^ exa- 
6tov €' tcbv ds 6sXtdicov ra ^sv TtQcbta TtSQis^sc tovg 
OiKSiovg XQ^ovg sjtl fisv tov TCQcbtov xavovog tag 
OTctcjxaidsTcastrjQidag^ STtl ds tov dsvtsQOv ra strj xal 
scps^flg Ttdliv tag StQag^ STtl 8s tov y' tovg ^ijvag xal 5 
sq)s^fjg TtdXiv tdg rj^SQag^ td ds XoiTtd ts66aQa tdg 
oixsiag tS)v ^oiQ&v TtaQad^s^Sig^ td ^sv dsvtSQa tdg 
tov ^TJxovg^ td ds tQita tdg rijg dvco^aUag^ td dl 
T£ra()Ta tdg tov nXdtovg^ td ds Tts^Ttta tdg trjg 
dnoifjg. xaC s6tiv i] sxd-s^ig t&v xavovCcov toiavtri' 10 



1. jLtg] [ihv C. 2. Tcov] x& C. 3. nqoixov] a B. 4. 

■ dsvxiqov] § B. 5. xovg] xdg C. 6. xscauQa] A corr. ex 

A D^. 10. cLTio%f\g\ corr. ex inoxfjg B^. 



282 



KAATAIOT nTOAEMAIOT 



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r^i Oo! 


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o o o 


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o o o 


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o o o 


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MA0HMATIKHS STNTASESiS A' 



283 





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o o o o o o 

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in o, ° " a 55 '^ 

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284 



KAATAIOT nTOAEMAIOT 



'u» 


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o< O «>i 


O «^i o 


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o.^? o 


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285 





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MAOHMATIKHS STNTAaESiS A 



287 



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289 



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Ptolemaeus, ed. Heiberg. 



19 



290 



KAATAIOT nXOAEMAIOT 



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MAGmiATlKHS STNTASESiS A'. 



291 







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19^ 



292 



KAATAIOT HTOAEMAIOT 



V 


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O «>i O 


oi O "« 


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1 

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k-sit 


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MA0HMATIKHS STNTASESiS A' 



293 



-.? 


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'Si' 2 



294 KAATAIOT nTOAEMAIOT 

s'. ''Oti xal BTtl rr}g ccTtlfjg vjtod^e^scjg rijg 0sXrj- 

vrjg tcc avta cpaLv6[isva 7Colov6lv t] ts ^car' 

ixKSVtQotTjta ;cal rj xata sitCnvxXov. 

'Ejto^svov ds tovtOLg tov dst^aL tov ts tgojtov xal 
5 tijv TtrjXLxdtrjta trjg askrjVLaocfjg avcD^alCag vvv ^sv 
TtOLrj^o^sd-a tbv Jtsgl tovtov Xoyov ag ^Lug tavtrjg 
V7taQX0v6r]g ^ fl ^ovrj Tcal jtavtsg 6xsdbv oi itqb rj^cbv 
STtL^spXrjKdtsg cpaCvovtaL^ Xsyco 8s tfi ^fara tbv sxxsC- 
^svov a7toxata6tatLxbv xqovov aTtagtL^o^svrj^ ^sta 8s 

10 tavta dsC^o^sv^ otL TtOLsttaC tLva xal dsvtSQav avco- 
^aXCav r} 6skr]vrj naQcc tag %Qbg tbv rihov a7to6td0sig 
^syCotrjV ^sv yLVO^isvrjv JtSQl tag dLxoto^ovg d^cpo- 
tSQag^ djtoxad^Lataiisvrjv ds dlg sv ta iirjVLaCG) X9^^9 
TtSQL avtdg ts tdg 6vv6dovg xal tdg Jtaveslrjvovg. 

15 Ovtcj ds tfj td^SL tr}g aTtodsC^scjg xQV^o^sd^a dLa 
t6 tavtrjv ^isv dvsv tfjg 7tQd)tr]g 6v[i7tS7tXsy^svr]g ys 
avtfi Ttdvtots ^r]da^G)g svQsd^rjvaL dvvaed^aL^ sxsCvr]v 
8s xal avsv rtjg dsvtsQag^ S7tSLdr]7tSQ djcb tcjv 6slr]VLa- 
xcbv sxXsC^sciv Xa^^dvstaL^ xad"' dg ovdsv ai^d^rjtbv 

■li) yCvstaL dLdcpoQOV sx tf]g 7taQd tbv r]kLOv av^^aivov- 
6r]g. STcl 8s tfjg TtQorjyov^svrjg d7todsL%sc3g dxoXovd^r]- 
eo^sv tatg tov d-scoQTj^atog scpbdoLg^ alg xa\ tbv 
l7t7taQxov 6qg)^sv 6vyxsxQr]fisvov. Xa^^dvovtsg yaQ 

1. f'] om. AD. 2. ^] tr]v i] D, sed r-qv del. 3. yiaTcc] 
AC, y.ccr' BD. 4. tov] to B. 6. rccvrris] y-ctl rf]g avrfiq BD. 

7. J] ins. B*D^. gxeBov] gxov C. 8. Bni^£§r]v.6r8<s D, 

corr. D*. 9. ic7tov,a6rccrLV.6v A, sed corr.; ccnov,ara6rvv.6v D. 

10. Ssvrioa C. 11. anoyiara6ra.a£LS D, corr. D^ 14. rs 

tdg] rdg rs D. Mg. rdg rs rdg ([^ (h. e. 6vv6dovg) D*. 15. 
ovrcog D. dnodsL^scog] dnodsL^sag ri]v dsvr^Qav BC. 18. dno] 
g' dno D. 19. ag] seq. ras. parua C. 21. inC] -C in ras. 2 
litt. D. ds] -s e corr. D. 23. Xa§6vrsg D. 



MA0HMATIKHS 2TNTASE^2 A'. 295 

ocul avtol XQstg sxXscipsig 6slr]VLaxccg dsi^o^sv^ o6ov ts 
t6 7tXsi6tov 8id(poQOV yivstaL %aQa trjv ^s6rjv 7Civr]0Lv 
Kal fqv Tcata t6 aTtoysiotatov STCoxrjv^ dyg tfjg toiav- 
tr]g avcoiialCag xad'' iavtrjv d^scoQOv^svrjg xal dta tfjg 
xat STtCxvxkov V7tod-s6scog aTtotsXov^svrjg^ tav ^sv 5 
avtcbv Jtdliv sGo^svov cpacvo^svcov xal dtd trjg ^car' 
sxxsvtQ6trjta vTtod-s^scogy oixsiotSQOv d' dv 7tQo0d(pd^rj- 
6o^svrjg tfjg tOiavtr]g xatd trjv ^t^iv d^cpotSQCJV tcbv 
dvc3^aliG)v tfi dsvtSQCf xal TtaQd tbv rjhov 6v^^ai- 
vov0y. oti ^isvtoi td avtd Ttdliv xal svtavd^a yCvstai 10 
(paivo^sva di sxatsQag tcbv sxxsi^svcjv vTtod-sdscov^ 
xdv iJLTi i6oi d)6iv dlXrjloig^ cjOTtSQ sitl tov rjXCov ds- 
dsCxcc^sv^ Oi XQ^^^oi tcbv d7toxata0td6scov d^(potSQCJV 
tfjg ts xatd trjv dvcj^aXCav xal tfjg TtQog tbv did ^s- 
6CJV tcbv ^codCcov xvxkov ^S(0Q0v^svrjg^ dXXd xal S67tSQ 15 
STtl tf]g 6slrivrig dvi6oi tmv Xoyov Ttdliv ^ovcov vito- 
xsi^svcjv tcbv avtcbv^ ovtcog uv xatavor]6ainsv STt 
avtf]g tf]g sxxsi^svr]g d7tXf]g dvcj^alCag tfjg 6sXr]vr]g 
7toiov^svoi tf]v s7tC6xstl)iv. STtsidf] toCvvv td%iov r] 
6slf]vr] 7toisttai tf]v TtQbg tbv did ^s6cov tcbv ^oodCcov 20 
xvxXov d7toxatd6ta6iV tf]g TtQbg tf]V v7toxsi^svr]v dvco- 
^ialCav^ sv totg l60Lg xQovoig dr]Xov6ti xatd ^sv tf]v 
xat STtCxvxkov V7t6d-s6iv ^sC^ova f] xatd tb o^oiov 
7tSQL(psQSLav 6 S7tCxvxkog dsl XLvr]^f]6staL stcI tov 6^0- 



1, Tt t6] corr. ex rd ts D*. 3. iTrojjrjV] AD^, anoxfjv 
BCD. 6. cpaivo(iBvcov] om. C, 7. otyisiotsQov'] corr. ex 

OLKSiOTrjtoc D, mg. yp. oUslotsqov. 9. t^] sv Tf] D. sni- 
6v^§aivov6r} D. 10. (isvtol to: avrcc] (ihv TOiavTa C. 12. 

Kav] post ras. 1 litt. C. 14. Tdv] Tdv C. 16. (lovov TtdXLv D. 

18. aTtXi^g'] corr. ex aTtlcbg Dl 19. snsLdi]] corr. ex stzsl D. 

TCCXLOV] A, TCCXSLOV BCD, 20, Tov] Tcbv C. 23. dllOLOv] 

corr. ex b(ioCav D^ 24. inC] supra scr. D^ 



296 KAATAIOT nTOAEMAIOT 

TisvtQov r(p ^GjdLaxa xvtcXov trjg vjtb trjg 6sXt]vr)g xccta 
tbv btiCkvkIov dTCoXa^pavo^evrjg ^ Inl ds tfig %at ix- 
xsvtQOtrita rj ^lv 6sX7]vr] trjv 6^0Lav tfj STtl roi) STti,- 
xvxXov xal STtl tov sxxsvtQOv Xivr]^rj6stai %SQL(ps- 
5 Qsiav^ 6 ds sxxsvtQog sjtl ta avta tfi 6sXr]vr] itSQl tb 
xsvtQOv tov lcodiaxov trjkixavtrjv^ r]Xcxr] ^sl^cov s6tlv 
'f] xata firjxog TtaQodog trjg xata tijv dvco^aXcaVy tovt- 

S6tLV r] yLVOllSVr] tOV O^OXSVtQOV TtSQLtpSQSLa tY]g tov 

STtLXvxXov ovtcog yaQ av ov ^6vov «r tav Xoycov^ 
10 dkkd xa\ aC tcbv %q6v(ov sxatsQag tcbv XLvr]6scov 6^ol6- 
trjtsg sv d^cpotSQaLg talg V7to%'s6s6LV 8La6co^OLVto. 

tovtcov dr] xatd tb dx^Xovd^ov avt^d^sv dvayxaCcog 
VTtoxsL^svcov s6tcD 6 ^sv 6^6xsvtQog Tc3 dLa ^b6g)v tcbv 
^G^dCcjv xvxkog 6 ABF TtSQL xsvtQov tb A xal dLa- 
15 ^istQov tr]v A/i^ 6 d£ STtCxvxXog 6 EZ itsQl xsvtQov 
tb r. vTtoxsC^d-co ds^ 6ts ^sv r]v 6 s%CxvxXog xatd tb 
A^ xal r] 6sXr]vr] xatd tb E ditbysLOV tov STtLxvxlov 
ysysvr]^svr]^ sv t<p l6g) ds xq6vg) 6 ^sv sitCxvxlog ti]v 
AF 7tSQL(pSQSLav dLsXr^Xvd-ag^ r] ds 6sXr]vr] tr]v EZj 
20 xal S7ts^svx^c36av aC EA^ FZ. xal sitsl ^sC^c^v s6tlv 
-») xatd tb o^OLOv r] AF TtsQLtpsQSLa tfjg EZ^ ditSL- 
Xr^fp^co r] BF o^oCa r^ EZ^ xal STts^svx^co rj BA. 
otL ^sv ovv sv rco 1'6g) xQ^'^^ ^^^ ^ sxxsvtQog tr]v 

1. kvkXov'] om. D. Tj]g (pr.)] corr. ex to5 D^. 3. stil- 

y,vv,lov~\ Y.vv.Xov C. 5. ^f ] 8' D. 9. xcbv\ t- e corr. D^ 

11. v7to&E6S6L D. dL(X6o}^OLVTo\ -OL- 6 corr. D. 13. Tc5] 

corr. ex t&v D. t&v] corr. ex tov A. 14. 6] om. D. 15. 
AJ] -J e corr. D. ^^] d' D. 17. yiccta t6] iTtl tov D. 

18. ysv7]}i8vr] C. iv] sv Ss D. ds] om. D. 19. dLsXrr 
^mg D, corr. D^ 20. stcl^svx^co^uv BC. at Ez/] ^' ts 

EJTJ ■nal 7] D. 21. tfjg] corr, ex ttjv C^ ccTCSLX^^tpd-co — 

22. EZ] supra scr. D. 22. tfj] tf]g BC. EZ] EZ 1 D. 

ins^svx^coi A, inL^svx&oa BC, corr. C^ 23. otl] post ras. 1 
litt. C. ^yyisvtQog D, corr. D^. trjv] trj seq. ras. C. 



MA0HMATIKHS STNTASESiS A' 



297 



vTcb A^B ycoviav tijg rcov TtaQodcov aii(poreQ(ov vtibq- 
oxfjg asxLvrjraL^ xal yeyovsv avrov r6 re xBvrQOv xal 

t6 aTtoysLov stcl rfjg 
-Bz/, cpavsQov. rov- 
rov d' ovrag s^ov- 5 
rog xsLad-co rfj TZ 
l'6rj Yj ^H^ xal ins- 
^svx^co 7] ZH^ xal 
xsvrQG) rtp H^ dta- 
6rYiiiarL ds rc3 HZ 10 
ysyQacpd^G) 6 sxxsv- 
rQog xvxlog b Z0. 
Xsyco^ orL xal 6 fi£V 
rfjg ZH TCQbg H^ 
koyog 6 avrbg s6raL ra rrig z/F itQbg FZ^ xal xara 15 
ravrrjv ds rrjv v7t6^s6LV ij ^sXijvrj ^cara rb Z 6r]^SL0v 
66raL^ rovrs6rLV b^oCa xal rj Z@ TtSQLCpSQSLa s6rai 
rfi EZ. 

l STtsl yaQ l'6r} s6rlv rj vjtb Bztr ycovCa rfi vitb 
EFZ^ 7taQccUr}X6g s6rLV rj FZ rfj ^H [Eucl. I, 28]. -20 
xaC sarLV L6rj ri FZ rfi JH' xal rj ZH ccQa rfi Fz/ 
L6ri rs s6rL xal JtaQaXXrjXog [Eucl. I, 33], xal 6 rrjg 
ZH TtQbg Hzl X6yog 6 avrbg rco rrjg ^F itQbg FZ. 




1. AJB'] corr. ex ABJ D^ ymvLccv] yoovLa seq. ras. C. 

2. xe] om. D. 6. skv.slgQ^co D. r^] tfjL corr. ex t?) A, 

tfj C^ 7. JH] in ras. A^ HzJ D. kul — 8. ZH] om. D. 

7. STtL^Evx&o} BC. 9. 8lcc6ti]^ccxl 84] yial diccGtrjfiati D. 11. 
6] om. D. 12. Z&] Z@ -Aal stcs^svx^co t] ZH s-n^s^Xrja&co 

8s 7] ZB (mut. in z/B) stil t6 D. 16. tavtriv] corr. ex 

tavtaxTiv D. 17. sotaL nsQLcpsQSLa D. 20. EFZ] ZFE D. 

i) JH tji rZ J). 21. xat (pr.)] ras. 1 litt. D. sativ] 

sGtiv Ss -Aai D, -V del. D^ i} TZ tr] JH] om. D. ZH] 
HZ J). 23. TtQog (pr.)] nQog triv D. tw] sctL to5 D. 



298 



KAATAIOT nTOAEMAIOT 



TtdlLV STtsl TTaQdXlrjlog B6tiv ii ^dF xf] HZ^ l'6ri s6tlv 
fj vTth r^B yovCa tf} vTtb ZH& [Eucl. I, 29]. vits- 
xsLto ds Kal 7] VTtb r^dB tfj vTtb EFZ l'6rj' G)6ts xal 
rj Z@ TtSQLtpSQSia ty EZ o^OLa s6tLv. sv tfp l6ca ccQa 
5 XQOVG) xad-' sxatSQav tav v7to^s6s(ov zatd tb Z 
6rj^SL0v ysyovsv rj 6sXrjvr}^ snsLdrJTtSQ avtij ^sv tr]v ts 
EZ xov STtLKvxXov xal rriv ®Z roi) sjcxsvtQov TtSQL- 
(pSQsCag b^oCag dsdsLy^svag xsxCvrjtaL.^ tb ds tov sitL- 
xvxkov xsvtQOv tijv AF^ t6 ds toi> sxxsvtQov trjv 

10 AB v7tSQ0xr}v tijg AF itQbg trjv EZ' OTtSQ sdsL dst^aL. 

otL de, xdv ofioLOL ftd- 

vov a)6LV OL l6yoL xal ^rj 

l'60L ^rjts avt ol ^rjts 6 sx- 

xsvtQog t^ bfioxsvtQC}, tb 

15 avtb TtdlLV 6v^PaCvsL, xal 
ovtcjg ri^LV s6taL dfjXov. 

diaysyQdcpd^cj yaQ Xf^Q^i^S 
sxarsQa tcov V7tod^s6scjv^ 
xal s6tco 6 ^sv o^oxsvtQog 

20 TCD dLa ^s6a)v t&v ^cjdtGJv 

xvxkog b ABF TtSQL xevtQov tb z/ xal dLd^stQov tijv 
AA^ b ds STtCxvxXog b EZ nsQl xsvxqov t6 F, i^ de 
6slrivri t6 Z, xa\ TtdUv 6 n\v sxxsvtQog xvxlog b 
HQK TtSQl xsvtQOv t6 A xal dLd^stQov ti]v 0AM, 




1. sTtsi'] corr. ex STtC A. J F] FJ D. 2. vTtsyitixo ds 
V.CU 7] vnb rjB] ccQcc D, corr. mg. D' deleto aQcc. 3. icr]] 

seq. ras. 3 litt. D. 4. Z0] RZ D. igoo' A. 6. avrrjv D. 
9. syyiivtQOv D, corr. D*. 11. ds, v.av] coiT. ex dfv A. 12. 
pj] ins. D*. 13. syv.svxQog D, corr. D-. 14. xo avvo] mut. 
in xa avxd D^ 16. r]fiLv] post ras. 1 litt. A. 22. 7J $s 

csXt^vt} xb Z] om. D. 23. csX^^vl A. 24. H@K] corr. ex 
HK9 T)\ 0AM] @A D. 



MA0HMATIKHS STNTASESJS A'. 



299 




^V ^ff ^^ "^^^ Jcjdta^fov XBvtQOv s0t(x} t6 M, t6 (5e iiT 
^rjlistov ri aeXrivyi^ Kal STtst^svid^oaav sxst ^sv av z/ FE^ 
rZ^ z/Z, sv^dds ds af ifM, KM, KA, vjtoxsia^oj 
ds 6 tijg z/F :r()6ff FjE Adyo? 
6 avT6ff T« T^g 0^ TtQog AM^ 5 
;ial xsKLvri6^co0av sv tm 1'0G} 
XQOVO) 6 ^sv STCLXvxXog tr^v 
vnh AAT yciviav xal ri 6s- 
Xrjvrj Ttdhv tijv vjtb EFZ^ 6 
ds SKXsvtQog triv vito HM0 10 
ycovCav nal r] 0sXr]vrj ndkLv 
tiiv vito ®AK. l'6rj ccQa s6tl 
dcct tovg VTtoxsi^svovg tcbv mvr]6scov Xoyovg r} fisv 
i}jto EFZ ycavia tJ vito &AK^ r] ds iyTto AAT 6vv- 
aiicpotSQaig tri ts vith HMS xal tfj vjtb &AK. 15 

tovtov ds ovtcsg s%ovtog Xsycj^ oti Ttdkiv xad-' 
ixatsQav tav v7tod-s6scDv sv t» 1'6g) XQOvip trjv i'0r]v 
nsQicpSQSLav rj 6sXrjvrj (pavrJ6staL dislrjXvd^vta^ tovts- 
6tLV otL l'6ri s6t\v i] VTtb AAZ ycovLa tfj vjtb HMK^ 
ETtSLdri xatd ^isv trjv aQxrjv tr]g dLa6td6scjg STtl t&v 20 
aTtoysCcDV ov6a rj 6sXr]vrj xatd tav A A xal MH sv- 
^SLcbv scpaCvsto^ xatd ds t6 tslog sitl tcjv Z xal K 
6ri^sCcov ov6a dta tav Z/i^ MK. 



2. fxxtt' C, corr. Cl 3. TZ, z/Z] «al TZ %u\ z/Z 

«^^ftat D. ^£] BCD^, om. AD. KM] ■ao.I KM D. KA\ 
KA C, xat KA D. 4. ^s] xb D. 6. v.EviG^coaccv C, corr. C*. 
8. A/Jr] in ras. A*. 9. tcccXlv] om. D. 10. 8h B-a-nevrQog] 
d' s-KKSvzQos D', 8s yiEVTQog D. HM@] H- e corr. D. 12. 
«WD. 14. T^] rrjv C. 16. HM@]@AK B. @AK] 

HM@ D. 19. oti] supra scr. D^ egxCv] D, supra scr. 

at D*. A^Z] AJ- renouat. A* (corr. ex AJT). 20. inC] 
cbs inC D. 21. bcpuCvExo ivd-tiav D. 23. ovca — MK] 

om. D. 



300 KAATAIOT nXOAEMAIOT 

KSLCd^co drj ixaraQa: xav ®K xal EZ nsQiq)6Q£Lcbv 
oftota Jtdhv f} BF, xal stcs^svx^co r} B^. sjtsl roC- 
vvv s6tCv, cog rj zir TtQog FZ, ri KA TtQog AM^ xal 
nsQl L6ag ycavCag t^g itQog tolg jT, A arj^sCotg aC 
5 nXsvQal dvdkoyov^ leoyaviov s6tL tb FziZ t^Cycjvov 
Tw KAM tQLycjvG)^ xal vnb tdg dvdXoyov TtXsvQccg aC 
ycovCaL l'6aL [Eucl. VI, 6]* l'6ri ccQa s6tlv rj vjtb FZA 
ycovCa trj vnb AMK. dkld xal rj VTtbB/lZ tfj vitb FZA 
l'6r] [Eucl. I, 29] dLCi tb TtaQalkriXovg sivaL tdg PZ, 
\0 BJ [Eucl. I, 27] l6Giv VTtoKSL^svcov tG)v vjtb ZFE^ 
B^r ycovLG)v' l'6rj aQa xal rj vnb ZAB ycjvCa tf] vnb 
AMK vTtoKSLtaL ds xal r] vTtb AAB tfjg v7tSQ0%fig 

tCbV XLV1/]6£G}V tfi VTtb HM& tOV SXXSVtQOV TtaQodG) 

L6rj' xal olrj aQa rj vTtb AAZ i'6rj s6tlv oXi] tfl vjtb 
15 KMH' oTtSQ TtQosxsLto dst^aL. 

g\ ^AnodsL^Lg trjg 7tQG)tr]g xal dnXfig dvco^aXCag 

tfjg 6sX7Jvr]g. 

Tavta ^isv ovv iiLS%QL to6ovtG)v r]^tv TtQotsd^sa- 

Qr]6d^G)^ jtOLr]66^sd-a ds tr]v djtodsL^LV tfjg sxKSL^svrjg 

20 6skr]VLaxf]g dvcj^aXCag STtl tfjg xat sitCxvxXov vno^s- 



2. EF] FB D. Ez^] corr. ex BTz/ D^. 3. 17 KA] ovxas 
xat 7] KA D. 4. T, A\ A xai T D. a.1 nXsvQccl avdXoyov'] 
om. D. 5. EGtiv D, corr. D^. 6. KAM] AKM D. vno] 
at V7t6 D. at] om. D. 8. yoavCa'] ycoLvCa C. Supra 

pr. vTio ras. D. rZA\ corr. ex Tz/Z B^, rZz/ hziv D. 

9. rag] corr. ex rd D^ TZ] post ras. 1 litt. D. 10. 

EzJ] %al Bz/ D. 11. BJF'] xal vno BJF D. a^a] iotlv 
ccQa D. Zz/B] Z et B in ras. D^. t^] supra scr. D^ 

12. vniyisLto D. AJB] corr. ex ABJ D^ 14. lgt} ictiv] 

yavi D. oXr}] oX- in ras. D*. 15. KMH] -H e corr. C*, 

HMKictLV 167] D. 16. s'] mg. AB, om. CD. 18. Tiqo- 
ts%^sqri6Q^(a A, corr. A^ 



MA0HMATIKHS STNTASESiS A'. 301 

^smg, Sl rjv siTtoyLEv ccttiav^ rb ^sv tcqgjtov dcp^ Sv 
sxo^av dQxaiotdt(ov iKlec^scjv tQL6i tatg ddi^tccKtcjg 
doxov6aig dvaysyQdcpd^ai ^vyxQV^^^^^^^h ^^P^^^S ^^ ^cal 
dTtb t&v iv tm vvv XQOVG) tQi0l Ttdkiv tatg vcp^ ri^cjv 
avrrav dKQi^satata tstrjQrjfisvaig- ovtog yccQ iq ts 5 
s^sta6ig ri^tv vTtaQ^si^ dt' o6ov ys ^dXi6ta dvvatbv 
^]v ^aKQov xQOf^ov^ Kal akkog cpavsQbv s6tai^ dioti rd 
ts TtaQa t^v dvco^aXiav didcpoQOv tb avtb £| d^cpots- 
Qcov tcbv dsi^scov syyi6ta dTtofi^^stai^ Kal rj tcbv ^s6g)v 
KiV7]6scjv S7tov6ia 6v^(pc3vog dsl svQsd^nj^stai tfj Katd 10 
tovg SKKSi^svovg JtSQiodiKovg ;u^dvovg Katd tijv rj^s- 
tSQav diOQd^co^iv S7ti6vvayo^svr]. JtQbg dij trjv dst^iv 
tfig 7tQcotr]g Kal cjg Kad'' avtrjv d^scjQOVfisvrjg dvco^a- 
XCag rj Kat STtiKVKkov VTtod^s^ig^ Sg scpa^sv^ JtSQisxstco 
tbv tQOJtOV tovtov. 15 

vosC6%^co yaQ sv tfj tfjg 6sX7]vrjg 6cpaCQa KVKkog 
o^oKSvtQog ts Kal sv tip avtip STtiitsdcp KsCpusvog t& 
did ^s6g}v tcbv ^mdCcjv^ TtQbg ds tovtov stSQog syKSKli- 
[isvog dvaloycog tf] jtrjliKotrjti tf]g Katd jtXdtog JtaQO- 
dov tf]g 6sl7]vr]g jtSQicpSQo^svog o^aXmg sCg td jtQo- 20 
rjyov^sva jtSQl tb KsvtQov tov did ^s6g}v t&v ^(pdCcov 
kvkIov to6ovtov^ o6ov r] Katd Jtldtog KCvr]6ig vjtSQ- 
sxsi tfjg Katd ^f]Kog. sjtl ^sv ovv tov Xo^ov tovtov 
kvkXov cpsQo^svov vjtotid-siisd^a tbv KaXov^svov sJtC- 
kvkXov o^al&g Jtdkiv sig td sjtopisva tov k66^ov dKO- 25 
Xovd^cog t^ Katd JtXdtog djtOKata6td6Si^ rjtig drjkovoti 



1. 8L7toii8v'\ corr. ex einoiiitv D. 2. i-ii\Xsiip£(ov corr. ex 

l]x^£ti/;fa)v A^. 5. yccQ] D, yccQ av ABC. 6. yi\ D, corr. ex 
Ts B, TE AC. 10. afi] om.D. 12. drj] Si D. 13. savtriv D. 
17. v.Ei^£voq\ om. D. 18. gyxfxXtft^vog] AC^D^, iyv,£v,Xi6^ivog 
BC (-G- del. B), xfTtXtfifVog D. 19. avdXoyois C. 23. rovtov 
tov io|ov D. 25. BTioyitva'] -ofisv- e corr. D*. 



302 KAATAIOT nTOAEMAIOT 

TCQbg avtbv tbv di,a ^£6g)v t&v JcjdtGjv d^ecjQov^Bvrj 
tijv xata fttjxog Tioiettai XLvrj6iv^ sjcl ds avtov tov 
imxvxXov t^v 6sXrivriv hg xata tijv aTCoysiov TtSQiqjs- 
QSiav slg ta jtQorjyov^sva rov x66^ov tijv ^std^a6Lv 
5 TCOLov^svriv axolovd^og tfj trjg dvco^aXLag dicoxataetd- 
0SL. JCQbg ^svtoL tijv vjcoxsL^svrjv dst^Lv ovdsv dv 
TCaQaTCodc^OL^sd^a urjts tfjg dtd tb TcXdtog 7CQor]yr]6s(og 
^rjts trjg Xo^co6s(og tov 6slr^vLaxov xvxkov 6v^7CaQa- 
Xa^^avo^svrjg ovdsficdg d^LoXoyov dLaipoQdg tfj xatd 

10 iirjxog TCaQodG) jCQo6yLvo^svrjg sx tfjg stcI to6ovtov 
syxXC6scog. 

d)v tOLvvv siXr]q)a^sv jcakaLcbv tQLCov sxXsLipscjv ix 
tcov iv BapvXmvL tstrjQrj^svcov^ rj ^sv TCQcbtri dvays- 
yQaTCtaL ysyovvla tm TCQcotG) stSL MaQdoxs^Tcddov xar' 

15 AlyvTCtCovg &&%" xd'' sig tijv X\ rjQl^ato ds^ (prj^Cv^ 
ixXsCTCELV iistd tijv dvatokijv ^Lccg GtQag ixavcbg TCaQ- 
sXd-ov^rjg xal H^sXsltcsv oXrj. iTCSLdij ovv 6 rjXLog tcsqI 
td s6%ata tG)V 'Ix^vcov ijv^ xal "fj vv^ coqcjv L6r]^SQL- 
v&v lP syyL6ta^ rj ^sv dQxij trjg ixksC^pscog iysvsto 

20 drjXovotL TCQb d C c3QG)v L6rj^sQLvmv tov ^s6ovvxtCoVj 
6 ds ^s6og %()(5vog, ijcsLdrJTCSQ tsXsCa r]v rj sxXsLifLg^ 
TCQb /8 /.' G)QG)v. iv 'AXs^avdQsCa ccQa^ ijcsLdrjTCSQ TCQbg 
tbv dC avtrjg ^s6rj^PQLvbv tdg coQLaCag i7C0%dg 6vvl- 
6td^sd-a^ TCQorjysttaL ds 6 Sl avtrjg iis6rj^PQLvbg tov 

1. tov] ins. D^ d^scoQovfisvriv C. 2. noLSc T>. 'aCv7]6lv~\ 
om. D. 5. TcoLOv^svrj B. 7. dicc] v.utcc D. 8. [ii^ts tfiq 

Xolco6S(oq'] supra scr. Dl 11. «^xitVfco? D. Deinde add. 

ccQxri :r>o D, : — uQxri -.r^ D^ 14. ysyovvLca D. MuqSo- 

KSVTtccdov D, corr. D*. 15. Gdad-'] e corr. D^. ■ad''] -9'' in 
ras. D^ 17. s^sXltcsv A. 18. ix^va C. 19. sysvsto] 

ysyovsv D, -v del. D^. 20, [__'] corr. ex g D*; mg. (h D. 

21. s-KXLipLg A, corr. A^ 22. § /_'] 8vo 7]^i6v D. 23. tdg] 
-dg e corr. D^. sTcoxds] mg- D'. 



MA0HMATIKHS STNTASESiZ! A'. 303 

dia BapvXcbvog ^^l6£l xal tQttc) syyL^ra ^Lag aQag 
i6YiiL£QLVYig^ 6 ^deog XQovog yiyovsv rfjg TtQOxsL^evrjg 
ixkEL^sag tiqo y xal y' cjqcov L6r]^SQLVG)v tov ^s0o- 
vvxtLov^ xad'' 7]v &Qav 6 i]XLog xata tovg sxtsd^SLiis- 
vovg rj^LV sjtLXoyL6^ovg snsixsv axQL^cbg tcov 'Ixd^vcov 5 
liOLQag xd /.' syyL6ta. 

Yj ds dsvtSQa tcbv sxXslxI^scov avaysyQaittaL ysyo- 
vvla t(p dsvtsQG) stsi tov avtov MaQdoxs^Ttddov ;<ar' 
AlyvTttCovg Sad' Lr{ sig triv Ld^'. s^sXsLTts ds^ (prj6LV, 
ccTtb v6tov daxtvlovg y avtov tov ^s6ovvxtLOV. sjtsl lo 
ovv 6 ^s6og XQ^^^^S i'^ Ba^vXcbvL (paCvstaL ysyovcjg 
xat avtb tb ^is^ovvxtLOv^ sv ^AXs^avdQsCa b(psCksL ys- 
yovsvaL nQO L! ^«^ y' ^SQOvg ^idg cjQag iroCi ^s6o- 
vvxtCov^ xad'' rjv &Qav 6 ijXLog STtstxsv dxQL^ag t&v 
'IX^vcjv fioCQag Ty L! d\ 15 

r] 8s y' tG)v sxXsCtpscov dvaysyQa%taL ysyovvla tc5 
avtGi dsvtsQ(p stSL tov MaQdoxsiiTtddov xa-r' Aiyvn- 
tCovg 0a^svG)d' ls' sig trjv tg'. r]Q^ato df, (pr]6Cv^ 
sxksCnsLV fistd tr]v dvatokr]v xal s^sXsLTtsv dit ccQxtcov 
TtXsLov tov r]^C6ovg. sjtSLdi] ovv 6 ijXLog itSQl tr]v 20 
dQxr]v r]v trjg UaQ^^svov^ tb ^sv tfjg vvxtbg ^sysd^og 
sv BafivXavL Td syyL6ta coQcbv stvyxccvsv i^rj^sQLvcbv^ 

2. yiyovtv] -v clel. D^ 3. y] mut. in r^ A*. y'] jf 

mut. in r A*, xqItov D, tgitov D^; tcqo T^nrov xal tqi&v dtQibv 
mg. A^ 5. S7tSLX^v'\ corr. ex iTi/J%ov D^ 8. Post tov del. 
dsvT^QOv D. MaQdoTiSfinddov} -do- in ras. A, -^i- corr. ex 

v Dl 9. siiXsiTtsv D, s^sXltcs D^ 10. ccvtov] tiqo D. 11. 
tpaCvstai ysyovcog'] ysyovsv cbff cpccCvstui seq. ras. 2 litt. D. 

12. ocpsiXsi] ndXiv ocpsiXsi D. 14. stcslxsv ccyiQL^cbg 6 ^XLog D. 

17. dsvtSQa] B B, E post ras. 1 litt. D. MccQdo-nsvndSov D. 

19. s^iXsLTtsv] mut. in s^sXltisv D^ 20. rjfiLOovg] corr. ex 

Q. 

ri^jLiGov A^. 21. UaQ&svov] naQvov C, ut saepius. 22. Ba§v- 
Xatvi] -L add. D*. lo] l- renouat. D*. 



i 



304 KAATAIOT nTOAEMAIOT 

ro dh i]^i,6v rilg vvxrbg s C g)QG)V' xal rj ^sv aQxri 
ccQK rfjg ixXsLtl^scog ysyovs TtQO icsvrs iidU6ra coqqov 
i6riiiiSQLVcbv rov ^s6ovvxriov dia rb ^sra rijv avaro- 
^ijv '^Qx^cii', b ds ^saog XQ^''^^? ^Qb y C g}qg)v^ sitSL- 
6 diJTCSQ 6 Ttag XQ^^^^S t^ov rrjhxovrov ^sysd^ovg rijg 
sitL^xorriCsGig rQLcbv syyL6ra coqcjv ocpsCXsL ysyovsvaL. 
sv 'Als^avdQSLcc TtdkLV aQa 6 fisaog XQ^^^S '^'^S sxksC- 
jjjscog aTtsrsXsed^rj jtQb d xal y' g)qg)v Ccrj^sQLV&v rov 
lis^ovvxrCov^ xa%^ riv coQav 6 ijXLog STtslxsv dxQL^cbg 

10 rrig IlaQd^svov ^oC^ag y d' syyL^ra. 

(pavsQbv ovv^ orL ditb ^sv rov fis^ov xQ^vov rrjg 
jtQchrrjg sxXsC-ifjscog sitl rbv rfjg dsvrsQag xsxCvrjraL 6 
i]XLog^ rovrs6rL xal rj ^sXijvrj, ^sd'' o^ovg xvxkovg ^oC- 
Qag r^d' Ts^ djtb ds rov rrjg dsvrsQag sxksCipscag ^s6ov 

15 XQ^'^^'^ ^'^^ "pov rfig rQCrrjg ^oC^ag Q^d" L dXld xal 
ri rcbv ^sra^v XQ^vcov dLd6ra6Lg dTtb ^sv rov TtQcorov 
STtl rbv SsvrsQOv rj^sQag TtSQLSXSL rvd xal cjQag l67]- 
^SQLvdg aTtX&g ^sv ovrcog d^scDQOv^LV 8vo i]^L6v, TtQbg 
ds rbv rav b^aXmv vvx^rj^sQcov S7tLXoyL6^bv dvo 

20 i]y,L6v TtsvrsxaLdsxarov^ ditb ds rov dsvrsQOv STtl rbv 
rQCrov rj^sQag qo^ xal mQag L0r]iiSQLvds aTcX&g ^sv 
itdlLV X L\ dxQL^cbg ds x Tts^itrov. xLVstraL ds ofia- 
Xcbg r] 6skr]vr]' TtQbg ydQ rbv ro6ovrov %q6vov ovdsvl 
al^d^r^ra 8loC6sl^ xdv ratg 6vvsyyvg r&v dxQL^cbv 



2. nivte] 8 BD. 4. rjQx^cci] corr. ex tjx^ccl D^ 6 — 
TtQo'] mg. A^. 8. ScTtotsXsGd-ri C. 9. snstx^v 6 rjXto? D. 

11. xov\ ins. D^ 15. X~\ ins. Dl Post v,ui del. stcbC Dl 
16. 8ia,6raGig] ante 6x ras. 1 litt. D. tcqcoxov] a. B^ nQmxov 
xov C. 17. xov] corr. ex x6 A^, xriv D. 8evxsqccv D. 18. 
Svo rjix,L6v] § [_' BD. 20. rjfiLGv] om. D, /.' BD^ nsvxs- 

"naLds-iiaxov] is D, ls" D'; a I_Ts supra scr. D^. 24. al6d'r}- 
xav D, corr. D*. 6vv\syYvg A, 6v\vsyyvg A^ 



MA0HMATIKH2 2TNTASESiS A'. 



305 



TteQMcjv Tog axoXovd'fj0rj' iv ^ev xalg rvd rjfiSQavg 
xal &QaLg i^rj^eQLvatg /3 /.' ta' avco^aXLag ^sv ^ad"' 
oXovg Tivxlovg ^oiQag i^ xf, ^ijxovg ds ^ocQag t^ va^ 
iv ds tatg qo? rniSQaig xal mQaig idrj^SQivatg x xal 
xi^TCtG) dvco^aXiag ^sv ^oiQag ^ jc?, ^yjxovg ds ^oC- 5 
Qag ^ t, syyi6ta. dfjXov oifv^ oti 
at iisv tfig Ttgatrjg dia0td6s(x)g tov 

STCiKVxXoV ^lOtQai tg TCS TtQOGtsd^Si- 

Ka6i tfi ^S6rj xiv7]0Si trjg 6sX7]vrjg 
^OiQag y xd^ at 8s tfjg dsvtSQag 10 
dia6td6scog ^otQai ^ xg dcprjQfj- 
xa6i tfig iis^rig xiV7]6scog ^OLQag 

o A^. 

tOVtCOV VTtOXSi^ivOV S6tG) 6 

tfjg 6sX7Jvrjg iTtiKvxXog 6 ABF^ ib 
xal t6 ^sv A 6r]^stov s6tco^ xad'' 
ov rjv rj 6sXrivri iv tm ^i6(p 
XQOVG) tfjg 7tQG)tr]g ixXsijfjscjg , tb 
ds 5, xad'' ov fjv iv ta ^i6G) 
XQOVG) tfjg dsvtiQag ixXsCxl^scag^ tb 20 
ds F, xad-' ov ^v iv ta ^i6c) XQOvco 
tfjg tQCtrjg ixXsC^scog. vosC^d^co ds rj tfjg 6sX7]vr]g inl 
tov iTtiXvxXov iistd^a6ig ^g ditb tov B iTtl tb A xal 
djtb Toi) A iitl To T yivofisvr]^ G)6ts tr]v ^sv AFB 
TtSQicpiQSiav, rjv ijtiXSxCvrjtai ditb tfjg 7tQG)tr]g ixXsCil^scog 25 
iiti tf]v dsvtiQav^ ^oiQcov ov6av Tg xs jtQO^tid^ivai tf] 




1. ScnoXovd^qar]] D^, ScKoXovd^i^asi ABCD. 3. olovg] -X- in 

ras. C. vcc] vd^i D. 5. fiot(>as (pr.)] om. BC. df ] 

ins. D^ iioiQug (alt.)]^ om. D. 14. rovtcov] xovtcov ovv D. 

16. sata)] v7iov.SLaQ'(o D. v.kQ''] e corr. D^ 22. asXCvT\q A. 

23. xal anb tov A] supra scr. C^. 24. F] corr. ex tQttcp C^ 

26. X?] mut. in v.8 C^ v.8 D. nQoati%-ivcii] post -i- ras. 3 litt. D. 

Ptolemaeiis, ed. Heiberg. 20 



306 KAATAIOT nTOAEMAIOT 

fie6r} ^OLQag y xd, trjv ds BAF^ rjv xsKivrjtaL aTcb 
trjg devtSQag exXsi^ljsiDg stcI trjv tQitr^v^ ^olq&v ov6av 
'qv 3C5 a(paiQSiv trjg ^s6r]g ^OiQag o AJ, ^ia tovto ds 
xal trjv fisv aito tov B stcI tb A JtaQodov iloiqcov 
5 ov6av vy Is atpaiQSlv trjg ^s6rjg tag avtag ^OiQag y 
xd, tiiv ds aitb tov A stcI tb F ^olq&v ov0av 9^ r^ 
^QO^tid^svai tri ^s6rj ^oiQag /3 ^^. oti ^sv ovv ov 
dvvatbv STtl trjg BAF 7tsQi(ps- 
QsCag tb TtsQiysiotatov slvai tov 
10 sTCiTivxXov ^ (pavsQbv SK tov atp- 
aiQstiTtriv ts avtrjv vTtaQxsiv xal 
skd66ova rj^ixvxkiov trjg ^syi6trig 
Xivy]6sG}g xata tb TCSQiysiov vtco- 
xsi^svrjg. stcsI ds Tcdvtcog STtl trjg 

15 BEF^ SiXTJtpd^CJ tb KSVtQOV tov ts 

did ^s6(DV tG)v ^ipdicov kvkXov xal 

tOV (pSQOVtOg tb KSVtQOV tOV STCiXVxXoV Xal S6tC3 t6 z/, 

xal STCs^svxd^co^av dic' avtov stcI td tcbv y sxXsi^scov 
6r]^sia svd^stai aC ^A, zlEB^ z/jT. xad^oXov toCvvv^ tva 

20 xal TCQbg tdg b^oCag dsC^sig svstcC^oIov tij^fj ^staycoyriv 
tov d^scoQijfiatog jcoico^s^a, sdv ts did trjg ;car' stcCkvxXov 
VTCod^s6scog avtdg cog vvv dsixvvco^sv sdv ts did trjg ^car' 
SKKSvtQotrjta tov z/ xsvtQOv tots svtbg kaiifiavo^svov^ 
lnCa iisv tcbv STCit.svyvv^svcov tQicbv svd^sicbv sx^alks- 

25 ^d^co STcl triv dvtixsiiisvrjv icsQicpsQSiav^ dyg svd^dds trjv 




2. rQLTrjv] supra scr, D^. 3. qv] seq. ras. 1 litt. D. 6. 
ds] XB D. 7. |[IJ] ju^ e corr. D^, fi^ BC, coit. Cl 11. rt] 
Ss D, sed eras. 14. sTTft] corr. ex 8ni C^, Bneidri D. 15. 
BET] corr. ex BV A\ FEB D. 19. ^EB'] v,al JEB xat 
seq. ras. 1 litt. D. 20. evsnipolov] mut. in evsmj^oXov Dl 

21. noim^sd-a] A, corr. ex noLoviisd^a D^, itOLTiamyLsQ^a BC. 

22. dsLKVvco^sv dtg vvv D, 24. ft/o:] corr. ex ^Lag D. 



]VIA0HMATIKHS STNTASEiiS A'. 307 

^EB avx6%^Bv s%oiiev dtSKpspkrj^svr^v sjtl tb E 6rj^stov 
aico xov B xilg dsvxs^ag sxXstil^scog ^ xa ds XoiTCa dvo 
6rj^sta XG)v sxXstiJSCjv sjtL^svyvvxco sv&sta cog ivd^dds 
r] AF^ xal aTtb xrjg ysvo^svrjg xo^rjg {)7tb xfjg sx^s^Xrj- 
lisvrjg^ olov xov E^ s7ti%svyvv0%'G)6av ^sv sjtl xa konta 5 
8vo erjfista svd^stau^ (hg svd^dds au EA^ EF^ Kad^sxoL 
ds dys6d'co6av STti xdg dTtb xcbv koiTCcbv dvo ^rj^stcov 
S7tl xb xov ^cpdiaxov xsvxqov STtt^svyvv^svag svd^stag 
STtl iLSV xriv AA r\ EZ^ sitl ds xrjv Fzl rj EH^ xal 
sxi dicb xov sxsQOv xcbv SLQrnnsvcov dvo 6rj^sicjv^ cjg 10 
ivd^dds ditb xov P, Tcdxtsxog dys^d^co STtl xrjv ditb xov 
sxsQOV avxcbv^ oiov xov A^ ijtl xrjv ysvo^svrjv vjtb xrjg 
disx^okfig TtSQi66iiv xo^rjv^ olov xb E^ im^svxd^stdav 
si^d^stav^ hg ivd^dSs i^tl xrjv AE rj F®' OTCod^sv yd^ 
dv xQrj^ch^sd^a xrj xrjg xaxayQatprjg dycoyfj^ xovg avxoi^g 15 
svQri6o^sv ixpaivovxag Xoyovg did xcbv xrjg dsi^scog 
dQid^^cbv xfjg ixXoyfjg TCQbg xb sv%Qri6xov ^6vov xaxa- 
ksiTto^svrjg. 

ijtsl xoivvv rj BA %SQi(pSQSia v7toxsivov6a idsi^d^rj 
xov did ILS6C0V xcbv tfpdCcov xvxXov ^oiQag y xd^ sVrj 20 
dv xal ri vitb B^A ycovCa TtQog x& xsvxqco avxofj 
ov6a^ oZcov fisv sl6iv aC d dQd^al tJ, xoiovxcov y xd., 
oicov de aC dvo oQd^al tI, xoiovxcov g JJCrj. w6xs xal 



1. di8yi§ccUoiisvr}v (post ras. paruam) sxofisv (post o ras. 1 
litt.) avTO&sv D. 5. oiov^ sv&stag otov D. ra Xoina] -a Xoi- 
in ras. minore D^. 6. svQ^SLaC] -stat e corr. D^. at] ij ts D. 

E^] AE C, EA-Aalri D. 9. ini (pr.)] post ras. 3 litt. D. 

(LtfV] supra scr. D^. 8i~\ ins. D^. 12. A'] e corr. D^ seq. 
ras. 1 litt. 13. th E] supra scr. D^. instsvxQ^slcav D, 

corr. D^ 14. r&] e corr. D^ 16. svqriGm^sv BC. Xoyovs] 
-ovg in ras. 2 litt. D*. 21. avtov\ om. D, tov avtov supra 
scr. D^. 22. ojmvlolov CD, corr. D*. at] om. A. 23. 
otcov] corr. ex olov D^ Svo] b B. 

20* 



308 KAATAIOT nTOAEMAIOT 

7^ ^sv STcl rfig EZ Bvd-scag ^SQCcpSQSia toiovtov g ^, 
OLCOv 6 TtsQi to ^ EZ oQd^oyGyvtov yQdcpo^svog xvxXog 
rl, a^dtii ds tj EZ sifd^sta toiovtcjv 5 5 o, olcov s6tlv 
rj ^E v7CotsCvov6a 'q^. 6^0LG)g^ STtsl 7] BA 7tsQi(psQSLa 

5 ^oiQCJV s6tiv vy Afi, strj av xal 7] ijico BEA ycovia 
TtQog tfj TtsQicpSQsCa ov6a toiovtcjv vy Af, oicov sColv 
ai dvo oQd^al t|. ra)v ds avtcbv ^v xal ii 'bno BA A 
ycjvCa g JiYJ' xal loiitii [Eucl. I, 32] aQa rj 'bito EAZ 
ycovCa tcbv avtcbv s6tiv JLt^ ^^. co6ts xal 7] ^sv S7tl 

10 rfig EZ TtSQicpSQSia roiovtcov s6tiv ]i^ ^f, Oicov 6 TtSQl 
tb AEZ OQd^oycoviov TcvxXog t|, avtrj ds rj EZ sv- 
d-sta toiovtcov iil Iri A, oicov s6tlv ij EA vjtotsCvov6a 
Q7C' xal Oicov s6tiv ccQa rj ^sv EZ s^dd^sta 5 ^ o, rj ds 
E^ ^, toiovtcov s6tai xal rj AE svd^sta l^ vs A/3. 

15 TtdXiv^ STtsi ri BAF •jtSQitpSQSia vitotsCvsi tov ^aydiaxov 
lioCQag o A£, sfrj av xal r] vjtb B^F ycovCa TtQbg t(p 
xsvtQGi tov avtov ov6a^ oHcov fisv sl6iv aC d dQd^al 
t|, toiovtcov o AJ, oZcov ds at dvo OQd^al t|, toiov- 
tcov a id. co6ts xa\ rj fisv sitl rr}g EH 7tSQi(pSQSia 

20 toiovtcov s6tlv a td, oicov 6 JtSQi t6 ^EH tQCycovov 

1. s] iazXv s D. 2. oimv] corr. ex olov D^ 3. o] 6 

ABC, om. D. 5. ^gxiv'] comp. B, -v eras. D. atrj — 6. Xe'] 
mg. D^ 6. OL(ov] corr. ex olov D*. 8. EAZ] EA^ D. 

9. S6xiv'] comp. B, -v del. D^. ETii] corr. ex vno C^ 10. 
EZ] EZ svd-siccg D. sotlv] comp. B, -v del. D^ oicov] 
corr. ex 0^01; Dl 11. ^EZ] A, E^Z BCD^, ^Z D. _12. 
oioav] corr. ex olov D^ EA] -A in ras. A\ 13. ^ 0] ^o A, 
^ o BC, I D. U. EJ] ^E Bdsix&ri D. sGzai] tctCv D, 

-V eras. ^^J ^^ I^- fu-S-frort D, corr. D^ 16. 0] seq. 
ras. 3—4 litt. D. 17] supra scr. Dl B/:ir] corr. ex BA D*. 

yoivCoc] -C- ins. A*. toj] to D, corr. D^ 17. y.svtqov D, 
corr. D*. tov avTov] supra scr. D*. ovcav D, sed -v eras. 

18. 0] in ras. D. 19. a 18] corr. ex cTi 8' D^ nsqi- 

cpSQsCag D, -g eras. 20. TQCycovov] oQ&oymviov D. 



MA0HMATIKHS STNTAgESiS A'. 309 

xvxXog Tr|, avtij ds 7^ EH svd^eta toiovrcov a it, X^ 
oiGiv i^tlv Yj ^E v7totscvov6a 'qtc. b^oiog^ ijcsl 7} 
BAF TtSQtipsQSca ^olqcjv i6tiv qv scg, sl^rj av Tcal 17 
vTtb BEF ycovCa JtQog tfj TtSQLtpsQSia ov6a toiovtcov 
"qv 3cg, oIlcsv slalv ai dvo OQQ^al t^. tcbv d^ avz&v 5 
ijv xal ri V7tb B^F ycovCa a id' xal XoiTtri [Eucl. I, 32] 
aQa r] vjtb EF^ tcov a\>tG)V ictiv q^ t/3. Sats xal 
r} ^sv iitl tf^g EH TtSQicpSQSia totovtcov iatlv Q^d' ij8, 
OLCDV 6 TtSQl tb FEH dQd^oyaviov xvxXog r|, avt^i d^ 
rj EH sv^sta toiovtcov ^ls Jva xa^ olcjv i6tlv 17 FE 10 
vnotSLvovCa qx' xal olcjv i6tlv aQa rj ^sv EH sv- 
d^sta a tj A, rj ds ZlE ^, tOLOvtcov i6tlv r] FE sv- 
d-sta a X xy. t&v ds avtG}V idsLx^rj xal r] EA sv- 
d^sta TlvsYp. 

TtdXLv^ ijtsl rj AF TtSQLCpSQSLa fiOLQ&v idsLxd^rj gg 15 
m, SLrj av xal rj vjtb AEF ycovLa TtQbg tfi TtSQLtpsQsCa 
ov6a tOLOvtcov 9g i^, oXcav sl6\v at 8vo bQ^^al t^. 
co6ts xal rj ^sv i%l tr^g F® itSQL^pSQSLa tOLOvtcov 
i6tlv gg va^ oCcov 6 TtSQl tb FE® tQCyovov r|, rj dh 
iitl trjg E& TtSQLCpsQSLa tcbv koLTtGjv [Eucl. III, 31] slg 20 
ro rj^LXvxXLOv ny %' xal al 'b7totsCvov6aL ccQa avtag 
svd^staL s6ovtaL rj ^sv F® toLOvtcov jrd' jiZg td, oIlcov 

3. fcrriv] comp. B, -v eras, D. 4. ovaai D. 6. di] 3' D. 

7. Erj] EFJ ycovia D. eaTiv'] comp. B, -v eras. D. 8. 
nsQKpsQsiccs D, -g eras. 9. 6] supra scr. D^ 10. EH] E- 
e corr. in scrib. C. xa] -a e corr. D*. 11. ^x] -x e 

corr. D^. yiai] corr. ex hol C*. 12. X] D, seq. ras. 1 litt. A, 
Xrj BC. Post JE del. idsCx^r} D^. sotlv] comp. B, mut. 
in iarl -aai D^ 13. x] supra scr. Dl Ss] om. D, ^' D*. 

15. Ante ndXiv eras. s D. 16. 17] om. A. 17. dvo] b B. 

19. Qs] corr. ex 9« D^. xQiycovov] oQd^oymviov yivyiXos D. 

Ss] d' D. 20. nsQKpsQsia] om. D. 21. jry -9-] corr. ex 

Tiy A\ nyQ- CD. 



310 KAATAIOT nTOAEMAIOT 

i6tlv r} FE v7totSLvov0a qtc^ t] de E® tCbv avtS)v 
oO* kt, vs. xccl oicjv ccQcc i6tlv rj FE svd^sta a % xy, 
toiovtcov s6tav xal 7] ^sv F® svd^sta a o rj, rj ds 
E& 6^0LG)g o vy xa. t&v ds avt&v ^v i] EA oXr^ 
6 L^ vs XP' xal lovTtri aqa i] SA totovtcov i6tiv it, /3 Ta^ 
oTcjv rj r@ idsCiQ-ri a o rj. y.aC i6tiv tb ^sv aTtb tfjg 
A® tstQciycjvov 6^ cd 1%^^ tb ds ccTtb trjg F® o^oCcjg 
a o ij, a ^vvtsd^svta %oist tb ccTtb tfjg AF tstQccycj- 
vov [Eucl. I, 47] 69a cd Ag* ^7]xst ccQa ietlv rj AF 

10 toiovtcsv i^ y vj, oicjv i6tlv r] ^sv AE svd^sta qk, 
r] ds FE tmv avtcov a % xy. s6ti ds aaC^ oicov r] tov 
ijtixvxXov did^stQog qtI^ toiovtcjv r] AF svd^sta Ttd' 
jilg id' vjtotsCvsi yccQ tr]v AF jtSQicpsQSiav (lOiQ&v 
ov6av gg va. zal oXcav ccQa i6tlv r] ^sv AF sv%-sta 

15 Tt^ ^ig id^ r] ds tov ijtiKvxXov did^stQog ^, toiov- 
tcjv s6tai xal r] ^isv ^E svd^sta ika Ty Jirj^ r] ds FE 
tcjv avtcbv ^ P V' G)6ts Tcal r] ^sv i% avtfjg TtSQiCpi- 
QSia r] FE toiovtcov g fid a^ oXcov i6tlv 6 iitCKvxlog 
t^. tcbv ds avt&v vTtoxsitai xal r] BAF TtsQicpSQSia 

20 ^ 3c?' xal oXr] ^sv ccQa r] B VE JtSQiCpSQSia ^OiQcbv 
i6tiv Qv^ T a^ r] ds vTt avtr]v svd^sta r] BE toiov- 



2. Xt'] X- ins. D^ 3. xat] om. D. 4. ^f] 8' supra 

scr. D. 6, 1^] v,a\ i] T>: o] e corr. D^. saxiv] comp. B, 

i6Ti D. 7. A&] -0 e corr. D^ 8. a] e corr. A. o] corr. 
ex -9' D. &] corr. ex cc D. ro] corr. ex tco D seq. ras. 3 

litt. 9, o9a] 69 D. X?] e corr. D^ 10. sv&sta] svd-sta 

vnotSLvovaa D, vnoxsCvovoa supra scr. B^ 12. xoiovxcov — 

15. Qy,] mg. D^ 13. ^oiq&v] om. BCD. 17. ^ih] om. D. 

18. xoiovxcov] xoiovxcov S6XLV D, -v eras. ^ fid a] s|l da D. 

OLOiv] oiov D, corr. D^ s6xlv] om. D. 19. di] 8' D. 

20. Qv — nsQLcp^QSca] bis C, corr. C^. xat] (priore loco) 
comp. ins. C. 21. T a] Ta ABCD. 8i] 8' D. 



MAeHMATIKHS ^TNTAfiESJS A' 



311 



rc3v QL^ kt, A/3, oXg)v B6r\v rj ^sv tov smxvxXov did- 
fiSTQog Qii^ 7] ds E/1 svd-sta x^cc Ty JTrj. 

si ^sv ovv 'fj BE sv^sla l'6rj riv svQTj^svrj rfj dia- 
litQG) tov STCLXVxXov^ STt' avtfjg av stvy%avsv drjlov- ■ 
6tL t6 KsvtQov avtov^ xal adto- 5 
d-sv av scpaCvsto tobv dca^stQcov 
6 kdyog' sjcsl <f sXd66G)v s6tlv 
avtrjg^ sld66cov ds Tial rj BFE 
TtSQLCpsQSLa rj^LXVxXLOv , dfjXov ^ OtL 
t6 KsvtQov tov stclkvkIov sxtbg 10 
7ts6sttaL tov BAFE t^7]^atog. 
{)7toKSL6d'a) dri tb K ^rj^istov^ 

KOI STtS^SVXd^CJ djtb tOV A XSVtQOV 

tov dLcc iis6g)v t&v ^GjdLcov kvkIov 
dLcc rov K svd-sta rj ^MKA^ C36ts 15 
t6 ^sv A 6rj^stov yCvs^d^aL tb dito- 
ysiotatov tov stclkvkXov^ t6 ds M 
t6 TCSQLysLotatov. stcsI ovv t6 vTcb 
tcjv BA Kal zfE 7CSQLS%6^svov 
OQ^oyavLOv l'6ov s6tlv tc5 vtco tav 20. 

A^ Kal AM %SQiS%O^SVG) OQd^O- 

yovLG) [Eucl. III, 36], dsdsLKtaL d' 

rj^tv^ OTt, ol^cov s6tlv tov stcl- 

KVKkov ri dLa^stQog^ tovts6tLV 

7] AKM svd-sta^ ^, tOLOVtov s6tlv rj ^sv BE sv- 25 

d^sta QL^ A^ Aj8, rj ds EA tav avtcov iXa Ty Jirjj rj 




3. BE] corr. ex KE C^ 4. kvyxave A. 7. d'] Ss D. 
8. Ante ds del. sgtl Dl ij] ins. D^ 11. Post BATE rep. 
9. 7tSQL(piQ£LCi — 10. sTtLy.vy.Xov D, corr. D*. 13. ksvxqov] e 
corr. D\ 15. K] u e corr. D^. JMKA] AK, M^ D. 16. 
yiyvsGQ-ccL D. 20. sativ] comp. B, S6ti D. 21. dM] corr. ex 
AM Dl 23. tov] 7) tov D. 24. 17] om. D. 



312 KAATAIOT nTOAEMAIOT 

de B^ oXrj drjXovotL tj^ va x, yCvatai tb V7tb tcov 
5z/ xal zlE^ tovt80tiv tb vjcb t&v AA aal ^M^ 

jtSQisxofisvov ogd^oyavLov tcov avtCbv M ^/3i^ xal 
s^rjxo6tG>v s A/3. ndXcv ds, iicsl xal tb vitb A^ 
5 'KaX AM ^sta tov dnb trjg KM jtoist ro dnb JK 
tstQaycovov [Eucl. II, 6], 17 ds KM sk tov xsv- 
tQOv ov6a tov STtLKvxXov t&v avtcbv s0tiv I, sdv td 

j , , , '"^ 

/yX rov djt' avtrjs tstgayavov TtQoed^&^sv tatg M ^Pxl^ 

s Aj3, e%o^sv t6 d^tb ^K tstQaycovov tcbv avtcbv 

^^ _ 

10 M ^gr £ A/3* xal ^tjksl dqa s&tai rj ^K sk tov xsv- 

tQOV 0V6a tOV (pSQOVtOg tbv STttXVKXoV O^OKSVtQOV 

rc3 dua ^s6cov tcbv lcodCcov kvkXov toiovtcov y^ Kal 
i^rjK06tcbv rj fA/3, olcov ietlv rj KM iK tov KSvtQov 
ov6a tov ijtLKVKXov s^7]Kovta. co6ts KaC^ oXcov i6t\v rj 

15 iK tOV KSVtQOV tOV CpSQOVtOg tbv imKVKkoV O^OKSV- 



1. x] xy BC. t6] &Qa to D. 2. tovtsGtiv] comp. B/ 

tovtsoTL D. A^'] JA C. 3. t&v ccvtoav] -&v avTcoi; in 

ras. A^. M ^§ip] BC, (i^ Btp D, ^vQiddcov (i^ §ip D^, [ivQtddtov 
li^ E^a-Ai6xi7J(ov (postea del.) tQLa-noGicov {int- supra scr. postea) 
in ras. A*, ^p^ postea add. mg. -nal e^r}-] in ras. A^. 4. 
s7t8L v.aC'] om. D. AJ] t&v AJ I); seq. ras. 1 litt. B; AJKA^ 
K del. A*, A^nx i^ ^^® lineae C. 5. v.al JM] corr. ex 

xa Tjjl D. KM] KM tstQaymvov D, tstQaymvov supra scr. B^ 
JK] tfjg JK D. 7. fi corr. ex f Dl 8. ^n] ri D, 

j^ D^ taig] om. C, taiq TiQoyiSiy^svaig D. M J^^tf] (i §ip D, 

li ^^JfJD^. 9. JK]tiig JKD. 10. M] mut. in fi^ {ivq Dl 
^r s] mut. in ^g t s D*. J K] -K supra scr. D. s-k — 12. 

■hvkIov] mg. D^ (yQ-)', ^"^ T^ov "nivtQOv et ta $La (isacov tav ^cp- 

Slcov v.v-aXov etiam in textu. 12. tm] scripsi, tov ABCD. 
^] X- e corr. D*. 13. ?]] ^ CD, corr. D^ Post ^ 

supra scr. mats ■aca D^ KM] del. D^. 14. o^cra — 15. 

TisvtQov] om. D. 



MAeHMATIKHS STNTASESiS A'. 



313 



tQov rfi '6xl)Si KVTiXov i^TJxovta^ toiovxcov serac xal 17 
ix tov TtivtQOv tov ijCLKvxXov 6 Ty EyyiGta. 

rii&G) 8ri iTtl tijg b^oCag xatayQa(prlg ano tov K 
xivtQoy add^stog i%l rrjv BE r] KNIS^ xal iTcetsvxd^ay 
rj BK. ijcel toivvv^ oX(ov iiStlv r^ ^K jj^ rj |Lt/3, toL- 5 
ovtcov ijv xal rj ^sv ^E svd^sta 
%ka Ty JTfj^ rj ds NE rj^L0si,a ov6a 
trjg BE [Eucl. III, 3] rwv avrwv 
vrj Jirj ]ig^ &6ts xal okriv tr^v 
^EN tcbv avtG)v yCvsCd-ai j^ xal 10 
s^rjxo6tG)V p Ad, xal otmv aQa rj 

ZlK V7tOtSLVOV6d i6tLV ^, tOL- 

ovtcov xal 7] ^sv z/ N s6taL QLd" 
vri vt,^ r] ds iit avtr\g 7CSQL(piQSLa 
tOLOvtcov Qorj p syyL6ta, oXcuv 15 
i6tLV 6 TtSQL tb ziNK OQd-oycb- 
vtov xvxkog r|. &6ts xal rj vno 
zIKN yavCa^ olcov ^iv sl6lv at 
dvo OQd-al r|, toLovtcjv i6tlv 
Qorj /3, OLCDv ds aC d OQd^al r|, 20 
toLOvtcov Ttd' d. xal rj ^sv ^M 
ccQa tov iiCLXvxkov JcsQLq^sQSLa 
lioLQcbv i6tLv Tcd' d^ ri ds AB^ 
tG)v koLTC&v slg tb rj^LXvxXLOv 9 vd'. tcov ds avtcov 
i6tLV rj ISlB TCSQLCpiQSLa rj^C^SLa ov6a trjg BlSlE ^ol- 25 




4. BE] EB J). 5. iaxiv] om. D. JK] JK ideLx^r] D. 

^] ins. D^ 7. ;fXa] -a e corr. Dl 12. JK] J- e corr. in 
scrib. C. 14. 8i] d' D. in'] corr. ex V7t' Dl 16. JNK] 
corr. ex JHK Dl 17. mcts — 19. t|] om. C. 19. e6tlv] 
om.D. 20. ai] in ras. 1 litt. D^, om. ABC. 21. a] (iLag D. 

23. sGXLv] comp. B, -v eras. D. 24. Xolti&v] bis D, corr. D^ 

ds] om. D, 6' J)\ 25. ^TB] EST D. 



314 



KAATAIOT nTOAEMAIOT 



Qcbv OTj Af, STtSLdrjTteQ rj BE oXrj aTtedsCx^ri ^OLQav 
QV^ T ayyiGta' xccl Ioltcyj ccqcc tj AB rov iTaxvxlov 
TCSQKpeQSLa^ 7]v a7tei%ev rj aelTJvrj tov a7toyeLOtdtov\ 
xata tbv exxeL[ievov ^e^ov %q6vov trjs devteQag ex- 
5 XeLilfecjg^ ^olqcjv eattv t/3 ;cd. b^OLcog de^ eTtel rj 'bTtb 
/d KN ycDVLa sdsLxd^r] tOLOvtcov 7t%' «, oXav slclv aCi 
^ OQd^al t|, xal loLitii s6taL rj vitb K^N ycovCa^ ^tLg\ 
vTtotSLvsL t^v dcpaLQOv^svrjv tfjg ^s6rjg xatd ^rJKog] 
jtaQodov TtsQLCpsQSLav sx tfig itaQa tijv AB tov stcl- 

10 xvxlov yLVO^svrjg dvo^akLag^ t&v XoLJt&v sCg trjv ^CavX 
dQd^rjv [Eucl. I, 32] ilolq&v o vd^. xal xatd firJKogl 
ccQa ^s6G)g STtsi%sv rj ^sXrjvrj natd tbv ^s6ov %q6vov\ 
trjg devteQag eKkeC^eog UaQd^evov ^oCQag td ftd, eiteL- 
drJTteQ dxQL^ag eTtetxe fioCQag Ty ^ie^ o6ag xal 6 ^'Atogj 

15 iv totg ^Ix^^v^L, 

TtdkLv^ d)v elkricpaiiev tQLcbv exXeCtpecov ex t&v eTtL- 
^eXs6tata rj^tv ev 'AXe^avdQeCa tetrjQrj^ievcov^ rj ^ev 
7tQd)trj yeyove tm tj' eteL 'AdQLavov xat AiyvTttCovg 
Ilavvl X elg tijv xa\ tbv de fie6ov %q6vov dxQL^cbg] 

20 e7tekoyL6d^e%a yeyovevat TtQb rj^C6ovg xal tetdQtov 
liLdg &Qag L6r]^eQLvfjg tov fie6ovvxtCov' xal e^e2,eL7tsv\ 
olrj^ xad^' r]v wQav dxQL^ag e7tet%ev 6 r]lLog tov Tav- 
Qov [loCQag Ty d' eyyL6ta. 

T] de dsvtSQa yeyove rc3 Ld'' eteL ^AdQLavov xat^ 



1. sSsLx&ri D. 2.AB]BAD. 5. tGtLv] comp. B, gW D. 6. ! 
JKN] JKH D, corr. D^. 7. XoLTtrj] XoLnr] &qcc D. 8. ccq)- 
ccLQOfiEVTiv D, corr. D^. 9. AB] -B e corr. D^, corr. ex AAB A.] 

11. o] corr. ex ov B^ 15. tx^vGLv D. 20. iTtsloyqcd- 

Hsd^cc BC. rjfiLCovg — 21. fiL&g] ^ g' J' D. 21. i^ilsLTtev] 

mut. in i'6,iXinsv D^ 22. instxsv a-KQL^&g D. 24. dsvTiQa] 
'B B. yiyovs] yiyovsv iv D, iv del. D^ 



MA0HMATIKHI; STNTASESiS A'. 315 

AiyvTtrCovg XoCcck /3' eig trjv y'^ rbv ds ^b6ov xqovov 
i7tsloyi,0d^£d-a ysyovsvac tcqo a coQag L6rj}iSQLV7Jg rov 
lis6ovv7irCov' Tcal i^sksiTtsv aii aQKrcov rb C Jc<^^ y' 
rrjg dia^srQov^ xad'^ rjv coQav sjtstxsv 6 ijXiog aKQi^cbg 
rcbv XrjXcov (loCQag xs g' syyo^ra. 5 

rj ds rQCrri rcbv sxXsCtlJSCjv ysyovsv rc3 %' srsi 
AdQtavov Tiar ACyvitrCovg 0aQ^ovd-l id'' sCg rrjv %\ 
rbv 8\ ^s6ov xQovov STtskoyi^d^sd-a ysyovsvac ^sra 
d SQag Cdrj^SQLvag rov ^saovvxrCov xal s^sXscns rb 
7]^i,6v rrjg dua^srQov dit^ ccQKrcjv^ STtsl%s ds %al xard 10 
ravtrjv rrjv &Qav 6 TJhog rcbv ^lxd^vcjv ^ooQag cd v^' 
syyi<5ra. 

^avsQOv ovv^ oru xal svravd^a xsxCvr^rat rj 6sXrjvrj 
(isd'' oXovg xvxXovg djtb ^sv tov ^s6ov xqovov rrjg 
jtQcotrjg sxXsCipscjg STtl tbv ^s6ov %q6vov tfjg dsvtsQag 15 
sxksCtl^scjg ^ o6ag xal 6 rjliog^ ^oCQag Q^a vs, ditb ds 
rov rfjg dsvrsQag STtl rbv rfjg rQCtrjg ^oC^ag Qlrj vs, 
s0tLv ds xal 6 ^sta^v XQOvog rfjg ^sv TtQarrjg dia6rd- 
6scog svLavrov ACyvTtrcaxov svbg xal rj^SQ&v Q^g xal 
Sqcov i0rj^SQLVC3V dTclcjg (isv xy C d\ dxQi^cbg ds xy 20 
C r}\ rfjg ds dsvrsQag dia6rd6scog svcavrov Ttdktv Ai- 
yvTtriaxov svbg xal rj^SQ&v qX^ xal coq&v idrj^SQtvav 



1. XoCa x^ A. ds] con: ex Slcc D^. 2. ineXoyriGd- 

fisQ^cc BC. a] A, (li&g BCD. 3. s^iXsiiiev] mut. in i^ili- 
nsv D. 4. ccKQi^&g 6 ^liog D. 6. trptTTj] /" B. yiyovsv] 

-V eras. D, yiyovs B. 7. ^ccQiiovQ-i] supra Q- adp. • • A^. 

8. ineXoyiqodiiE&cc BCD, corr. D^. 9. i^iXsins] ABC, 

i^iXsiTtsv DB^, i^iXiTts D^. 10. instxsv D, -v eras. %ccxd] 

— c , 

v.a C. 11. i8] supra scr. D. 15. nQcoxr]g] cc B. iisGov 

XQovov] om. D. dsvxsQag] s B; et similiter saepius. 16. 
iv.lsi^^stog] om. D. 17. qXt]] corr. ex qcc7\ D. 18. saxiv] 

comp. B, -V eras. D. 20. d' — 21. /_'] om. C. 



316 KAATAIOT IITOAEMAIOT 

ccTtl&s iisv By dxQL^&g dh e L!. mveitat ds Tcdkiv yj 
6sX7]vrj fie6(og ^ed'' oXovg xvxlovg ev ^iev rco evl hec 
xal Yj^eQaLg Q^g xal aQacg lerj^eQivatg xy C v' «vo- 
^akCag fiev ^OiQag ^ jca, fiTJxovg de ^oiQag Q^d^ kt, 
5 eyyiexa^ ev de rc3 evl exei xal rifiSQaLg Qkt, xal aQatg 
i6rjfieQLvaig e i! dvo^akCag ^ev ^ouQag 7td 1^^ ^YJKOvg 
de ^oiQag Q^t, W eyyc^xa. drjXov ovv^ oxi Tcal ai ^ev 
trjg jtQwxrjg diaaxdeecDg tov eTCiKvxkov ^otQai ql xd 
d(priQ^Ka6iv trjg xaxd iifjxog ^s^rjg jtaQodov fiOiQag ^ 

10 ft/3, aC de xfjg devxeQag dia6xd6e(og ^otQat utd Ag 7tQo6- 

xeQ^eixadiv tfj xaxd ^fjxog ^e6r} Ttaoodco fioiQag d xd. 

xovxcjv ovv vTtOKSi^svav s6x(o TtdXiv 6 STtiXvxXog 

xfjg 6sXr]vrjg 6 ABF.^ xal xb ^sv A 6r}^stov vno- 

xsi^d^co^ xa%'' ov riv ri 6sXr]vr] sv xw ^s6(p XQOVCo xfjg 

15 %Q(bxrig sxXsiipscog^ xb ds B xb xfjg dsvxsQag sxXsiJl^scog^ 
xb ds r xb tfjg XQixrjg^ vosi6^c3 ds C36avxc3g rj ^isxd- 
pa6ig tfjg ^sl^^vrjg cjg ditb tov A s%l tb 5, sixa sitl 
tb r yivofisvrj, C36xs xfjv ^isv AB TtSQicpsQStav ^oiQ&v 
ov6av ^ xd dcpaiQstv^ ag scpa^isv^ xfjg xaxd ^fjxog 

20 fis6r]g jtaQodov ^oiQag t, /(1/3, triv de BF ^oiQCJv ov- 
6av 7td Ag %Q06ti^evai tm ^rjxec ^otQav d xa, koiJtrjv 
de tfjv FA iioiQ&v ov6av Q^ri y TtQO^tid^evat ta ybrixei 
tdg koiTtdg ^oiQag g xd. 

oti ^ev ovv eitl tfjg AB TteQicpeQeCag tb ditoyeio- 



1. /.'] ins.^^ 3. L! nl W e corr. D^ 6. Xs] Xe D, 
supra scr. Zg v8 D^. 9. ccq^TjQT^-naGi BD. 10. TtQOGrsd^sC- 

"iiccGL BD. 11. fA^di?] corr. ex fieecp D*. 12. ^gtco ndliv 6 

ijrtxvxXog] 6 i7iLv,vv,Xoq ndXiv egto) 6 D. 13. JBF] AB D. 

14. 6BX7]vri] corr. ex osXrjvi A*. 16. -S-co ds a>6-] in ras. 4 
litt. D^. 17. a^g] postea ins. D. slra] om. C, knsixa D. 

21. TtQO^Tid-svai] post -^- ras. 2 litt. D. 22. FA] AT B. 



(loiQ&v C, sed corr. 23. tds] m ras. D^ seq. ras. 2 litt. 



MA0HMATIKHS STNTAgESiS A' 



317 



ratov slvai dst^ (pavsQov ix xov fi7]t£ sitl trjg BF sl- 

vat dvvadd^ai ^ijts stcI trjg FA dioc tb STcatsQav aif- 

tav TtQO^d^stLX^v ts sivai xal sXd66ova ri^cxvxXiOv, 

SLkri(p%-Gi ds oyLGig hg firj {jjto- 

XSi^SVOV tOVtOV tb KSVtQOV TOV 5 

t,G)8LaKov Kal tov xvxXoVy S(p' 
ov cpsQStat, 6 STiCxvxXog^ xal 
s6tco tb z/, S7tst,SV%%'Gi6(kv ts 
ait^ avtov iTtl ta tmv y ix- 
ksC^SGiv 6r^^sta svd^stai, av 10 
^EA^ z/5, z/r, xal S7tt- 
^svx^sCarjg trjg BF ijxd^co^av 
ccTtb tov E 6rj^sCov svd^stav ijtl 
^sv ta B, r ai EB, ET^ iitl 
ds tag Bzf^ z/F svd-sCag xd%'- 15 
stoi at EZ xal EH^ xal stc 
dicb tov r iTtl tijv BE xd%s- 
tog rjj^^^G) rj F®, iitsl toCvvv 
r] AB TtsQicpsQsia vnotsCvsi tov 
did ^s6(ov tcjv ^GidCcov xvxXov ^oCQag 5 itt/5, strj dv xal 20 
ri VTtb AAB ycovCa itQbg rc3 xsvtQco ov6a tov ^cadiaxov^ 
OLCOv ^sv sl6iv al d oQ^al rj, toiovtcov ^ fi/3, otGiv ds 
aC dvo OQd-al t^, toiovtov Ts xd. G>6ts xal ri ^sv iitl 
tfig EZ TtSQicpsQSia toiovtcnv i6tiv Ts xd, oicov 6 TtSQi 
tb ^EZ tQCycDvov xvxXog r|, a^ri) ds 'fj EZ sifdsta 25 




1. dEL] corr. ex dr] B\ 2. iitit' D. 4. Si] d' D. 11. 
JEA] corr. ex ^A D. JB, AF] >tal JB xal JF D. ini- 
t^vX&BCGrig D. 14. B, r] Er B, B vtal F Bv&Eiai D. EF] 
xal ET D. 15. xaq Bd] corr. ex xcc EB/i D^. z^F] yicu 
rj D. Ev&SLciig D. 22. '(i§] ^- in ras. D^. 23. dvo] 

P BD. 24. iatCv] comp. B, -v del. D^ 25. xQLYoavov] dQd^o- 
y&viov D. 



318 KAATAIOT nXOAEMAIOT 

roLOvtcjv Tg d ^P^ olcov i^tlv 7] Zl E v7totSLVOv6a 'qtc. 
dfioccog^ £7tsl t] AB TtSQLCpSQSia ^olqcov s6tLv 'qI Tca, stri 
av xal ri VTto AEB yc3VLa itQog ty TtSQLfpSQSLo, ov6a 
tOLOvtcov QL za^ 0LC3V si^lv at 8vo bQ^^al t^. tcov d' 
5 avt&v fjv xal rj v7to AAB Ts xd' XoLTtrj [Eucl. I, 32] 
ccQa rj V7tb EBA ycavCa tmv avtcbv s0tLV gd v^. &0ts 
xal r] fisv STtl trlg EZ 7tSQLcpsQSLa toLovtcov s6tlv gd 
v^j olcov 6 7tSQL tb BEZ xvxXog t^, avtij ds rj EZ 
svd^sta tOLOvtcov Ttrj tc^ l^^ olcov s6tlv r} BE VTtotsC- 

10 vov6a QK. xal olcov ccQa s6tlv rj ^sv EZ svd^sta T^ 
d /li/S, r] ds AE ^, tOLovtcov s6tlv xal r] BE svd^sta 
7ia }irj i/O-. 

7tdXLv^ S7tsl rj FEA 7tsQL(pSQSLa v7totsCvov6a sdsCxd^r^ 
tov dtd ^s6cov tcbv ^cdSCcov xvkXov ^oC^ag g jca, slr] 

15 dv xal rj V7tb AAF ycovCa TtQog ta xsvtQG) ov6a tov 
imdLaxov^ olcov [isv sl6lv at d oQd^al r|, toLovtcov s^ 
3ca, oXcov ds aC dvo OQd^al t|, tOLOvtcov t/3 ^^. co6ts 
xal rj ^sv STtl tfjg EH TtSQLCpSQSLa tOLovtcov s6tlv l^ 
|[i/3, OLCov 6 7tSQl tb AEH dQd^oycovLov xvxXog t|, 

20 avtrj ds r] EH svd^sta toLOvtcov Ty Ig Ld'^ olcov s6tlv 
7] AE v7totsCvov6a q>7c. b^oCcog^ STtsl rj ABF ^tSQLcps- 
QSLa 6vvdystaL ^olqgov QCfa vf , stri dv xal r] V7tb AEF 
ycovCa 7tQbg tfj TtSQLcpSQsCcf ov6a toLOvtcov Qgd v^, otcov 
sl6\v at dvo OQd^al t|. tcbv ds avtcbv rjv xal r] V7tb 



3. AEB] corr. ex AEH D*. 4. dvo] § BD. 5. AJB] 

A^B yoovLu D. Xovjiril v.al Xomr^ D. 8. ofmv] oi'oav iazCv D, 

BEZ] BEZ oqQ-oycoviov D. 9. fu-O-fm] om. D. nri] t} 

Tlfl C. 10. EGxlv CCQCC D. 11. QTl] idSLX^Tj ^ D. SatLv] 

comp. B, ^azcci D. 14. KvtiXov] om. D. xa] seq. ras. 2 

litt. D. 17. ota^v — Ti] mg. D. ^vq] ^ BD. 18. iatLv] 

comp. B, -V del. D^ 24. Svo] (3 BD. Si] d' postea 
ins. D. 



MA0HMATIKHS STNTASESiS A'. 319 

AAT ycovLcc i^ ^^' nal XoiTtri [Eucl. I, 32] aga y] vtio 
EFzi rav avtcbv 86tiv ^oO" Te. &0t£ xal r} ^sv stcI 
trjg EH TteQL^psQSLa toLOvtcov i6tlv Qod^ Ts^ olcov 6 
TtSQL t6 FEH tQLycovov xvxXog t|, avri) ds yj EH 
svd^sla tOLOvtcov s6tlv QLd' vd' V, OLCov s6tlv rj FE 5 
v7C0tSLV0v6a QX, xal olcov ccQa s6tlv rj ^isv EH sv- 
d^sta Ty Tg Ld'^ rj ds ^E sdsLxd^r] ^, tOLOvtcov s6taL 
xal r} FE svd^sta Ty Tg x. tcbv ds avt&v sdsLX^V ^^^ 
rj BE svd^sta xa Jirj vd'. 

TtdlLV^ STCsl rj BF 7tSQL(psQSLa ^OLQCov s6tLV Tta Ag, 10 
stri av xal rj VTtb BEF ycovta TtQog t^ 7tSQL(psQSLa 
ov6a tOLovtcov Tta Ag, olcov sl61v aC dvo OQd^al t|. 
co6ts xal rj ^sv S7tl trjg F® 7tSQL(psQSLa toLovtcov s6tlv 
Tta Agr, oXcov s6tlv 6 7tsQL tb FE® tQLycovov xvxXog 
t^y rj ds STtl tfjg E@ tcbv XoL7tG)v slg t6 rj^LXvxlLOV 15 
[Eucl. III, 31] ^rj xd. xal tcbv vtt' avtag ccQa svd^SLcov 
rj ^sv r@ s6taL tOLOVtcov orj xd A^, oXcov s6tlv ri EF 
'b7totSLvov6a QX^ rj ds E® tcbv avtcbv g v x^' xal 
OLCOv ccQa s6tlv r) FE svd^sta Ty T^ x^ tOLOvtcov xal 
rj ^sv r® s6taL rj ji x^ rj ds E® b^OLCog T p fi'0'. tav 20 
ds avtcbv ^v rj EB oXrj xa '^ vd" xal XoL7tri ccQa rj 
@B tOLOvtcov s6taL Ta ]Tg T^ olcov xal rj F® rjv r] Ji 
X. xaC s6tLv t6 iTsv ccTtb tflg 0B tstQccycovov Q^.rj Xa 



1. t^] e corr. D. 4. PEH] -K in ras. D^ TQCycovov^ 
oQQ^oymviov D. 5. iexCv (pr.)] om. D. v] seq. ras. 5 litt. D. 

6. iatCv'] om. D. 8. ds] 8' D. 10. Xs] corr. ex Ti D. 

12. 8vo'\ f BD. 14. iffrtVj om. D. xqCyoivov'] bq&o- 

ywvLov D. 17. 17 (alt.)] ins. D< 20. F®] corr_ex FE D*. 

E0] corr. ex HO D. ^ ?] e corr. D^ /X'9'] corr. ex 

^ D. 21. 8s\ 8' ins. D^ i] ^r.)] >tal i] D. 22. m] -u 
in ras. D^ ^, ol(ov'] ins. D*. 23. saxiv'] comp. B, ecxi D. 

qXi]'] -7] e corr. D^. 



320 KAATAIOT nTOAEMAIOT 

TcCj tb de aito rfig FS tcbv avtcov os t^ Tct,^ cc 6vv- 
textivta TCoiBi to ocTtb trjg BF tetQaycovov {^mc\.. I, 47] 
0Ty ]iy Xfj ' iir^KEi agu £6tlv 7} BF toiovtcav id A^ t, ovcov 
ietlv ij ^sv ^E svd^sta qtc^ 'fj ds FE b^oicjg Ty Tg x. 
5 ^6ti,v ds xat, otcoi/ 7} tov smKvxXov didfistQog ^, 
tOLOvtcjv 7] FB svd-sla o^ xd Af" VTtotsCvsi yccQ ti)v 
BF TtSQifpsQSiav iioiQcbv ov6av %d Ag* %ai oicQv ccQa 
s0tlv ii [isv Br svd^sta o^ xd Af, -^^ ^^ '^ov STtncvxXov 
did^stQog ^, toLOvtcav s6tai xal rj ^sv ^E svd^sta 

10 x^y Ag A-^, 17 ds FE tcbv avtcov 'od Td d. co6ts xal 
7] S7t' axftfjg TtSQicpSQSta rj FE toLovtcov s6tlv o/3 flg I, 
oXov 6 STtCxvxXog t^. tcbv d\ avtcbv rj FEA VTtoxst- 
tat Q^rj y' xal XoiTtfi ^sv ocQa fj EA nsQvcpsQSLa ^ol- 
Qcbv s6tLV 9£ 7? V, 17 ds tJjr' ai)tiiv svd^sta fi AE 

15 tOLOvtcov Ttfj ji fcf, OLCov s6tlv f} ^^v tov iitLxvxlov 
dLa^stQog ^, fj dh E/H sx^d^sta x^y ^<S X^- 

STtsl ovv TtdXtv f} EA TtSQLCpSQSLa skd06G)v sdsC%%"Yi 
fj^LXvxXCov^ drjXov^ otL tb xsvtQov tov sitLX^^xXov sx- 
tbg 7ts6sttaL tov EA t^il^atog. siXr^cpd^co dfj xal s6tG} 

20 tb K^ xal STtst^svxQ^G} f} A MKA^ S6ts TtdXtv tb fisv 
A 6rj^stov yCvs^d^at tb aTtoysLOtatov ^ tb ds M tb 
jtSQLysLotatov. STtsl ovv tb VTtb AA xa\ AE itSQL- 



ACD. l^ corr. ex 1% D*. 4. x] corr. ex xf D. 5. sorTtv] 
comp. B, gffrt D. 6. TB] BT D. 11. Trf^tqp^^sta] seq. 

ras. 1 litt. A, nsQLcpeQSLcci C. iGZLv] om. D. 12. de] d' ins. D^. 

13. Q^T]] corr, ex p| D^ 14. v] corr. ex tj A^ 15. 17] 
ins. D*. 16. Ez/] z/E C. 19. EA r/*7j>aro?] E cctfi-qtog D, 
EA tfi-qtog D^ 20. K'] K arifieLov D. xat] supra scr. D^ 

AMKA\ corr. ex ^KA Dl 21. A^ corr. ex z/ Dl yCyve- 
(j-O-at C. t6 ^8 M t6 neQLyeLOtcctov] mg. C^. 22. Post yjrd 
add. rcoi; C^ Trsptf^fdfifvov] corr. ex neQLsxoiiev D^ 



MA0HMATIKH2 STNTASESiS A'. 



321 



exoyisvov OQ&oycbvLOv l'0ov icxlv r& vtco tcov A/1 xal 
^M [Eucl. m, 36], didsLTixai d' ri^lv^ on, oXg3v 
66tlv rj AKM Tov iTtLKvxXov 
dLcc^BTQog QX^ tOLOvttov i^tlv r] 
^sv AE avQ-sla nrj ji l^^ rj ds 6 
E^ tG)v auT^i/ x^y Ag A-O", 'fj ds 
AA oXrj dr]Xov6tL ipX^ 7g v^^ 
yCvstaL ro vTto tcov AA zal A E^ 
tovtietLv ro V7C0 AA xal AM^ tav 

avtcbv M atd jilg l^. TcdXiv df, iitsl 10 
ro vno AAM ybsta tov ano KM 
jtOLSt tb ano trjs AK tstQccycovov 
[Eucl. II, 6], 17 d£ KM ix tov 
KSvtQov ov6a tov iTtLxvxXov [s^rj- 
xovta^ TtOLSt tb dit^ avtfjg /yx^ 15 

iav ra /y% jtQOGd^co^sv tatg TtQOXSL^ivaLg M <at8 Jig tf , 




s^o^sv tb ditb AK tstQaycovov t&v avtcbv M p^8 ^g i^' 



1. affrtV] comp. B, -v eras. D. tc5] corr. ex to C^D^. xat] 
om. D. 2. 8'] postea ins. D. 3. AKM] A- postea ins. A, 
corr. ex AKM D^. didfiEtQog xov inLv.vvlov D. 4. S6x\v 17] 
corr. ex iGtCJ)^. 5. tj] irf D, corr. Dl 6. W\ -Q' in ras. D*. 
8. yCvttoci'] yC- in ras. 3 litt. D^ 9. tovtBGtLv'] -v eras. D, 
tovts6tL B. vTto] vTtb t(bv D. AA] A/J CJ)^ corr. D^ 10. 

M] mut. in ^ fi^ D^ ndXiv d^, iTtsC] ndXLv ABC, TtdUv 8' 
knC D, TtdUv d' snsC D^; conf. p. 312, 4. 11. A^M] t&v AJ 
xat JM D. KM] tfjg KM tstgdycovov D. 14. s^T^-Kovta] deleo. 
s^r\Y.ovta — 15. jyx] mg. D^; in textu tiov ccvt&v iotiv |^, quae 
del. D^. 16. ^] -X in ras. C, y- e corr. D. Deinde add. tov 

tstQaymvov D. M] mut. in fi /Lt^ D^ l^] tg D. 17. dno] dnb 

tfjg D. tstQuymycovov A, sed corr. M] mut. in {i fi^ D^. 
d%d] corr. ex j>p^d D\ 

Ptolemaeus, ed. Heiberg. 21 



322 KAATAIOT nTOAEMAIOT 

xal ^7]KSL ccQa E0tai rj zlK ix rov kbvxqov ov6a tov 
cpSQOvrog tbv stcckvtcXov o^oksvtqov ta dia ^s6g)v 
tOLOvtov %%%" rj^ oiiov s6tlv rj KM sk tov xsvtgov 
ov6a tov stcckvkIov s^tJKOvta. &6ts KaC^ oZcov s6tlv 
5 rj ^sta^v tcov KSVtQcov tov ts dca ^s6(x)v t&v iGjdC&v 
Kal tov stclkvkXov s^r^Kovta^ totovtcov s6tai Kal rj sk 

tOV KSVtQOV tOV STtLKVKloV £ id. KaC S6tlV 6 «VTOff 

syyi6ta X6yog t& dia tcov TcaXatotsQcov SKXsCipscov 
IIIKQ& TCQO^d^sv ajcodsdsiy^svG). 

10 rjxd-cj dri TcdXiV sicl trjg avtrjg KatayQaiprjg dicb 
tov K KsvtQov Kad^stog stcI trjv /lEA r] KN^y Kal 
sjcs^svxd^co r] AK stcsI ovv^ olcov r] ^K sdsCxd-rj ^ttO* 
rj^ toiOvtc3v ijv Kal rj ^sv ZlE svd^sta %^y Ag A-O-, 17 
ds NE rj^l6sia ov6a trjg AE [Encl. III, 3] t&v av- 

15 tcjv s6tiv ^d % rjy 636ts Kal oXrjv tr^v jdEN tcbv av- 
tav %%t, IJ^ ftj, Kal OiG)v s6tlv aQa rj ^K vjcotsC- 
vov6a ^, TotovTcov Kal r] AN s6tai Qid' ^^ Asr, 'f] 
ds STC avtr]g JcsQiq)SQSia toiovtcjv Qoy it, syyi6ta^ 
oCg)v s6tlv 6 TCSQi t6 zlKN oQd^oy&viov KVKkog tJ* 

20 G)6ts Kal r] vTcb /IKN ycovCa^ oCcov ^sv Si6iv at dvo 
oQd^al t|, toiovtcov s6tlv Qoy tf, oicjv ds aC d oQd-al 
tJ, TotovrcDV s6tlv Jtg Ir] L\ Kal r] ^lv ME^ ccQa 
tov STCiKVKkov TCSQicpsQSia [LOiQcbv s6tiv 7cg Xr] X^ r] ds 



2. q)iQovtog] corr. ex nsQKpiqovtog D^. 4. ovau\ om. D. 

5. xs\ om. D. 7. f] e corr. D. 8. reS] tc5 g D. 10. 
dn6\ inC D. 11. /IEA\ AE D, J add. D< 12. ini- 

^svxd-ca B. 15. iGTLv] comp. B, om. D. x ^] x^ BCD, 

corr. D*. ccvt&v] avx&v yLVSGd-ca D. 16. vg] -g e corr. D*. 

JK] -K e corr. Dl 17. 17 (pr.)] i] fisv D. z/iV] -N e 

coiT. Dl 18. di] d' D. in'] corr. ex vn' D^ 20. mcts] in ras. D^. 

mots — 21. t^] om. C. 21. iotLv] comp. B, sctai D. 22. sGtiv] 
om. D. ^] ^ BC, corr. B. 23.1] A, /.' BCD. 



MA0HMATIKHS STNTAtS^ESiS A'. 



323 



AAS t^^v XoiTtav £Lg tb rj^LxvxlLov gy xa l. t&v ds 
avtobv £6tLV ri A^ 7t£QLCpeQ£La rj^L6£ia ov6a tijg AE 
[Eucl. III, 30] iioLQ&v JitJriX 
EyyL^ta' %al XoLTtrj aga r] AA 

7t£QL(p£Q£ia ^0LQG}V £6tLV JlL£ ^y. 5 

v7t£K£Lto dh xal r] AB okri tav 
avtcbv qI ica' xal loLitii ixQa ri 

AB 7t£QL(p£Q£La^ 7]V aTt£L%£V r\ 

6£Xr{vri tov aitoy^iotatov ;car«; 
Tov £XJC£^^£vov ^£6ov %q6vov trjg 10 

d£Vt£Qag £xX£Ltlf£COg^ ^OLQCbV £6tLV 

d^OLCjg^ £7t£l rj ^£v V7tb AKN 
ycovta d7t£d£Lx^rj tOLOvtov Ttg Xrj 
£yyL6ta^ olov aC d OQd-al t^, i^ 15 
dh V7tb KAN yCv£taL tcbv Xol- 
TCcbv [Eucl. I, 32] £Lg trjv ^iCav 
OQd^rjv y x^^ v7t£X£Lto de xal rj i}7tb 
lAAB oXrj tcbv avtcbv J ft/3, xal XoLTti} ccQa 'fj V7tb AAB 
iycjvCa^ i]tLg v7tot£Cv£L tijv dcpaLQov^£vr]v tf]g ^£6r]g xatd 20 
fir]xog 7taQ68ov tov did ^£6ov tmv ^cjdCcov xvxlov 
7t£QL(p£Q£Lav £x tf]g 7taQd tr]v AB yLvo^£vr]g tov £7tL- 
xvxkov dvG)^alCag^ ^olqcjv £6taL d x. xal xatd ^rjxog 
aQa ^£0a)g £7t£L%£v r] 6£kr]vr] xatd tbv ^£6ov %q6vov 




1. ;i] A, /_' BCD. 8i] 8' D. 3. X\ A, ^' BCD. 5. 
i6xiv'\ comp. B, -V del. D^ p] -e in ras. D^ 7. xat] 

coffTf v.aC D. aQci] om. D. 8. J!J5] corr. ex AB D^ 13. 
ind'] corr. ex inC D^. j^] ins. D^. 14. idsLxd^n D. 17. eIs] 
corr. ex ig A. 18. y] in ras. D. vTiOKSLto C. xat] seq. 

19. AJB] -JB in ras. D^ oXr}] seq. ras. 

22. AB] corr. ex z/B D. tov hTiLV.vv,Xov 



ras. 1 litt. D. 
1 — 2 litt. D. 
yivo^svriS D. 



21 



324 KAATAIOT nTOAEMAIOT 

tTjg dsvtsQag iKkeC^ecog tov Kqlov ^oiQag xd" A, inH- 
dtJTtsQ axQLpcjg iitstxBv fiOLQag xs I, 66ag xal 6 ijliog 
tcbv XrjXcov. 

t,'. UeqI tijg dLOQd'(b0ecog twv ^i6c3v TtaQodcov 
5 tfjg 6ek7Jvrjg ^TJxovg te xal avaiiakCag. 

'Eicel toCvvv iv yi\v rg devtsQa t&v Jtalaiav ix- 
XeCil^ecov aTtedeC^a^ev tijv 6el7]vriv xata tbv ^e6ov 
%q6vov iite%ov6av b^akSig xata iifjxog ^ev IlaQd-evov 
lioCQag lS ^d^ avco^aXCag de aTtb tov aitoyeCov tov 

10 iTtixvxXov ^oCQag t/3 xd, iv de tfi devteQa tcov xad^ 
rj^i&g tQicbv ixkeC^ecov b^oCcog iitixov6a ^i^ag ane- 
deCxd^rj Tiata ^rjxog ^ev tov Kqlov ^oC^ag ocd' A, avco- 
fialCag de anb tov ajtoyeCov ^oC^ag ^d Ai^, (paveQov^ 
otL xal iv ta neta^v XQ^'^^ ^^^ TtQoxei^ivcov ixkeC- 

15 il^ecov iiteXaPe ^i6cog rj 6eX7]vr] ^ied'' oXovg xvxXovg 
^7]xovg ^ev ^oCQag 6x6 /«.g, avcoiiaXCag de ^oC^ag v^ 
td. dXX^ 6 ^eta^i) XQ^''^^^? '^ov te devtiQOv etovg MaQ- 
doxe^Ttddov @cod' iri elg tijv td'' JtQb C ^^^ ?' « coQag 
L6rj^eQLvfjg tov ^e6ovvxtCov xal tov Ld'' etovg 'AdQia- 

20 vov XoCdx /3' eCg tijv y' itQb ^Lccg SQag L6rj^eQLvfjg 
tov iie6ovvxtCov neQLBxeL AlyvTttLaxd strj covd xal 
rjiiiQag oy xal c3Qag L6rj^eQLvdg ditXcbg \iev jtdXLV xy 
C y\ dxQL^cbg de xal TtQbg td biiaXd vvx^^^eQa xy 

2. insLx^D. 4. ^']om. AD. diOQ&mGtojg] om.D. tcccqo- 
dcov] v,iVTqGB(ov D. 5. r^g GBXiqvrig] diOQd^dtGscog D. 6. noc- 
Xcctcbv] TiaXccimv tQi&v D. 8. %cctcc] seq. ras. 2 litt. D. 11. 
anixovGa C. 13. Xr]] corr. ex X<5 D. 14. xat] siipra scr. D^ 
15. STtsXcc^sv D, corr. D^ 16. fii^Kovg] supra [i ras. A, 

17. 6] seq. ras. 3 litt. D. 18. a &Qag'] ijfisQccg D, del. D^ 
mg. atQag D, (iiccg wQag D^. 20. Xvdn D, corr. Dl y'] 

tQLtr}v C. 21. stSL C. 22. nccXcv] om B. 



MA0HMATIKHS STNTASEiiS A'. 325 

Xa 

y\ Ttcc^ag ds 'fj^SQag M xal ^a^tlJTty xal agag i^rj^eQi,- 
vag ^ y\ alg evQL6xo^£v e7tipaklov6ag ^ed'' olovg 
xvxXovg i7Cov6iag ex tcov TtQoexred^ec^evav ri^£Qri6tcov 
XLvrj^dtcjv xata tag TtQO trjg dL0Qd'(h6ea)g vTtod^eeeLg 
firjxovg ^lv fiOLQag 6xd jirg, dvcj^aXLag de ^OLQag v/3 5 
A«, G)g tijv ^ev tov ^r]xovg ejtov0Lav djtaQdXXaxtov^ 
ag ecpa^evy evQfj6d^aL t^ dLa tcjv exxeLiievcav triQij&ecDv 
'bcp rj^G)v 6vvax^eL0rj^ tijv dl tfig dvco^aXLag JtXeovd- 
^eLV e^rjxo6toLg l^. o&ev TtQO tfjg t&v xavovCcov ex- 
^e6ec3g evexev tfig tcbv r^iieQri^LcovJSQO^Giv dL0Q^ci6eog lo 
ta it, e^rixo6td e7tL^eQL6avteg etg tb TtQoxeC^evov t&v 
ri^eQcov TtXfjd^og td exd6tr} rjiieQa eTtL^dkkovta o o o o 
la ft? AO" dcpekovteg tov itQO tr^g dL0Qd'(D6ecjg ;(ar£fc- 
Xrjii^evov tfjg dvco^aXCag ri^eQrj^Cov ^e6ov XLVT^^iatog 
[p. 278, 16] evQO^ev [p. 279, 14] ro dLcoQd^co^evov ^ol- 15 
Q&v Ty y vy v^ l^ vd vd'.) aig dxolov^-cog xal tdg ~ 
^.OLTtdg t&v xavovCcov ejtL^vvd^e^eLg eTtoLrj^d^ed^a. 

^ rj\ IleQl tfjg ejtoxfjg tcov b^aX&v tfjg 6eX7jvr}g 
XLvr]6ecov ^rjxovg te xal dvco^aXCag. 

'''Iva de xal tdg eTto%dg avtGiv ^v^trjeco^ed^a eCg tb 20 
avtb TtQcbtov etog NaPova66dQOV xat AiyvTttCovg 
Gcod' a tr\g iie6rj^PQCag ^ iXdpo^iev tbv ivtevd^ev XQ^- 
i vov y^e%Qt tov ^e6ov tfjg devteQag ixXeCipecog tcbv 



Xa ^ 

1. M] fivQiddag Xa D. 3. 7][iEQri6i(ov] rjfiiv riyiEqr^GiaiV C. 
4. xag TtQb T^s] TT^s nQwTrjg B. 8. nXeovci^siv] -d^siv e 

corr. D^ seq. ras. 5 litt. 10. 7]fiEQT]6Lcov] 17- ins. D*. dQOficov 
StoQd-mGscog] mg. D^, in textu iti&sascog D, del. D*. 11. i^rr 
yioordg D, corr. D^ 13. dcoQQ-mascog] seq. ras. 2 — 3 litt. D. 
14. TTys ava>[iaXiag] supra scr. D^ 18. ry'] om. D. 21. 

Na^ovvaodQov D. 23. Tfjg] seq. in ras. 4 litt. B. 



326 KAATAIOT nTOAEMAIOT 

TtQcbtcov xal iyyvtBQGiv tQicbv^ ijxrig, hg 8(pa^£v, yeyovs 
t<p ^' 8t8L MaQdoKSiiTtddov nat AlyvntCovg ®g)%^ lt]' 
eCg trjv iO-' TtQO C ^««^ y' oc ^Qag L^rjnsQLvrjg tov ^is- 
OovvKtLOV 6vvdystat ds ovtog stav AlyvntLayi&v tc^ 
5 xal rj^SQ&v L^ ical wqcov ccTtXcjg X£ ^ccl dxQL^cbg syyL6ta 
Td g\ Kal TtaQaKSLVtaL tm to^ovtco XQOvg) fieO'' oXovg 
ocvxXovg s7tov6Lag ^tJKOvg fisv ^otQaL Qxy x/3, dvco^a- 
lCag 81 iLOLQaL Qy Xs' dg sdv dcpsXco^sv tcbv sv ta 
^£0G) XQOVGi tr]g dsvtsQag SKlsC^SGig sitox&v sxatSQav 

10 «qp' ixatSQag OLKsCGig, s\o^sv sig to TtQcbtov stog Na- 
Pova66dQov Jtat ACyvTttCovg ©gjO' a' trjg ^s6rj^^QCag 
i7t£xov6av ^s6G}g trjv asXyjvrjv xatd ^sv nrjxog TavQov 
^oCQag Td 3C/3, dvGi^aXCag ds dito tov ditoysCov tov 
iitLKVKkov iioCQag 6^r] fi^, djtoxrjg ds drjXovdtL ^olq&v 

15 o Af, iTtSLdriTtsQ xal 6 rjlLog slg tbv avtbv XQ^'^^^ 
dTtsdsCx^rj tcbv 'Ix^vg)v insxGiv ^ioCQag o fis. 

%•'. IIsqI trjg dLOQd-G)0SG)g tcbv xatd TtXdtog 

^£6g}v TtaQodpv tr]g 6£Xr]vr]g xal tcbv iitoxcbv 

avtcbv. 

20 Tdg ii£v ovv tov ^Tqxovg xa\ trjg dvcD^aXCag 
7t£QLodLxdg XLvrJ6£Lg xal itL tdg ijtoxdg avtcbv dta; tav 
tOLovtciv i(p6dGiv ^vv^^trj^d^^d^a^ iTtl dh tcbv xatd 
Ttkdtog 7tQ6t£Qov ^£v dLrj^aQtdvo^£v xal avtol 6vy- 



1. SYyvtiQco D. 7]tt,g] ^ti C, iytXsC^tpscov ^tig D. cpcciisv D. 
ysyovsv B. 3. y' a] ya C. 4. ovtcog C. Mg. (^ D. 6. 
g'] fg B. nciQd-ASLtai D. 7. stcovgCu D. 10. Ncc^ovva- 

Gagov D. 12. (i-^HOvg C. 13. d^] supra scr. D^ 16. ano- 
dsLx^r} C. ansxcov D. 17. d"'] om. D. 18. aslrjvr^g] 

comp. AC. tav snoxotv] tfjg snoxfig D. 21. dia ta>v] -a t- 
renouat. D^. 23. diri^aQtdvofisv] Sl- in ras. 3 litt. D^ et 

supra scr. D^. avyxQm^svoL] -vy- et -co- e corr. Dl 



MA0HMATIKH2 STNTAtEjE.^iS A'. 327 

XQG)^£V0L xara tbv "IitnaQXOv ra triv ee^TJvrjv s^axo- 
^LccxLg ^sv Tcal TCsvtrjKovrdKig syyu^ta xata^stQStv tbv 
Idiov kvkXov, dlg ds xal riinL^diag tbv tfjg ^mag ^fara- 
fLStQstv xatd t6 iv tatg dvivyiaig ^s6ov d7t60tr}iia' 
tovtcov ydQ vjtoKSL^svcov Kal trlg TCrjhKotrjtog trjg sy- 5 
KUasGig tov koi^ov kvkIov trjg asXijvrjg ot tcbv Katd 
lisQog avtrjg skXsC^sov oqol dCdovrav. Xaii^dvovrsg 
ovv dia6rd0sig SKksiTtriKag Kal ditb rov ^sys^ovg rcbv 
zard tovg ^s6ovg xQ^^^^ovg S7tL6K0t7]6scjv tdg dKQL^stg 
K,atd Ttkdtog STtl tov lo^ov kvkXov TtaQodovg d(p bito- 10 
tsQov twv 6vvd£0^cjv S7tLkoyL^6^svoL dLd ts trjg dno- 
dsdsLy^sv7]g Katd tijv dvcDiialCav dLafpoQctg djtb tcjv 
aKQL^&iv 7taQ6dc3v tdg TtSQLodLxdg dLaKQCvovtsg ovrcog 
tdg ts Kard rovg fis6ovg XQ^^^ovg rcbv skXsCiJjscov stco- 
%dg Toi) TtsQLodLKOv TtXdtovg svqC6ko^sv Kal tijv sv 15 
tco ^sta^v ;^()di/a> ^sd^' oXovg KVKXovg sitov^Cav. vvv 
ds xQrj0d^svoL %aQLs6tSQaLg s(p6doLg Kal ^rjdsvbg t&v 
7tQ6tSQOV vTtotsd^SL^svcov STtLdso^svaLg TtQbg trjv tcbv 
STtL^rjtov^svcov Katdkri^)LV tiqv ts 6l sksCvcov STtLlslo- 
yL6^svrjv tov %Xdtovg JtaQodov svqo^sv dLS^sv6^svrjv 20 
Kal dnb trjg vvv xcoQlg sksCvcov KatSLXrj^^svrjg Kal tdg 
VTtod^s^SLg avtdg tdg nsQL td ^sysd-r] Kal td djto6tri- 
fiata /Ln) ovtcog sxov6ag sXsy^avtsg dLcoQ^co^d^sd^a. 
t6 ds o^OLOV 7tS7tOL7]Ka^sv STtC ts tcbv tov Kq6vov Kal 



1. "Itcccq^ D, s^a%06idyiig'] mut. in s^atioaiovtdmg C*, 

flaxofftoaaxt? e corr. D. 3. rijg] tf] D. 7. s^nXBLipscov (-v 

corr. ex g D^) ccvtfjg D. didovai D, corr. D*. 8. rcov] corr. 
ex tovg D^ 14. rf] supra scr. D^ 17. xaQtsatsQOig C. 

18. vTiotid^sfitvoav D. 19. i7tiXsXoyi6\^ivr}v A, smXsXoyila^i- 
vr]v A^ 21. y.atsiXrj^iisvTqgl pr. -rj- corr. ex X in scrib. C. 

22. xal td] v.atd C. 23. hiOQQ^oiGd^s^^a CD, corr. D^ 24. 
ds] S' D. STti] xal inC D. twv] tov C. y.ai] v,al t&v D. 



328 KAATAIOT nXOAEMAIOT 

tov ^Eqiiov v7tod-86£(Dv KLvtj^avtag tuva t&v TtQOteQcov 
ov Ttdvv axQL^cbg eUrj^^evcov dia t6 vatsgov ddi' 
ataxtotBQaLg trjQ7]6£6L 7t£QLt£tvxr}K£vaL. 7tQ067^K£L yaQ 
totg t& ovtL (pLXaXtjd-cjg xal ^rjtrjtLK&g tfj tOLavTrj 
5 d^^cjQLu 7tQo6£Q%o^£voLg ^i} TtQog ^ovrjv trjv tcbv 7ta- 
XaLcbv v^tod^e^^cjv dtdQd^co^LV 6vyxQV^^^^ '^V ^ocLvotrjTL 

tcbV £7tl t6 ddL6taXt6t£Q0V £VQL6X0^£VC3V £(p6dc3Vy 

dXXd xal 7tQbg trjv tav IdLCJv, dv ovtcjg %co^t, ^rjdh 
al6xQhv riy£L6%-aL ^£ydXr]g tLvbg xal xl^^Cag ov6rjg trjg 

10 £7tayy£XLag^ xdv V7t dXXcov ocal ^rj ^6vov v(p' avtcbv 
trjg £7tl t6 dXQLp£6t£Q0V tVXC36L dLOQd^d^^^cog. 

tCva ^£v ovv tQ^Ttov £xa6ta tovtcov d7tod£Cxvv^£Vy 
£v totg £(p£^rig tffg ^vvtd^^cog xatd tovg oix£Covg 
t67tovg d7todG36o^£v. tQ^^lj^^^d-a dh iv tw 7taQ6vtL trjg 

15 dxoXovd^Cag £V£K£v £7tl tfjv tfjg xatd 7tldtog 7taQ6dov 
d£t^Lv^ rjtLg £X£L trjv £(podov tOLavtrjv. 

TtQcbtov ^£v ovv £Lg tijv avtrjg tf]g ^£6r]g 7taQ6dov 
dL^Qd^cj^Lv it,rjt7]6aii£v £xk£Ctl)£Lg 6£XrjVLaxdg d7tb tcbv 
ddL6tdxtc3g dvay£yQa^^£vcov ^ ^t' o6ov ^dXL6ta ivfjv 

20 7tl£C6tov XQOVov, xad'' dg td t£ ^^yid^rj t&v £7ti6xo- 
t7]6£cov L6a y£yov£ xal 7t£Ql tbv avtbv 6vvd£6^0Vj xal 
d^(pot£Qag 7]tOL dTt ccQXtcov rj djcb ^£6r]^PQCagj xal £tL 
r] 6£lr]vr] 7t£Ql t6 t6ov\ f]v d7t66Tr]^a. tovtcov di] ov- 



1. vTtod^EGScov^ mg, B, TtQOtSQOv D. 2. ccdLata-nTOTSQaig^ 
corr. ex adLa<5u%T0tSQaig D; deinde del, v,atd D^, 7. t&v'] corr, 
ex tov C^ t6] supra scr, D^. adiaGtay.totsQov D, corr, D^ 

8, ovt(og] supra scr. Dl ftrjd' D. 12, tQonov] corr. ex 

tQOTKo Dl 14, ds] d' D. 16, dsi^SLV A, triv'] ^ D, r D^. 

20. ra] corr. ex %atd D^. iisysQ^SL D, corr. D^ 21. lca'] 
g 
in ras. D^, mg. i". ysyovtv BD, corr. D^ 23. t6] tov C. 

rjv] seq. ras. 1 litt. A. a7r6()T7}|ii-a] a- in ras. A^ dij] 

yaQ I), non male; corr. D^ 



MA0HMATIKHS STNTASESiL^ A'. 329 

rcjg ixovTcov dvdyxr] t6 kbvxqov triq ^slijvrjg l'6ov 
dnixBLv Kad'' ixateQav t&v ixXeC^scxiv inl td avtd 
lieQT} tov avtov 6vvdE6^ov xal did tovto tijv dKQi^fi 
jtaQodov avtrjg olovg xatd %Xdtog KvxXovg iv rc3 
[leta^v t&v triQ7]6s(ov XQOvg) jteQtexetv. 5 

iXdpo^sv drj iCQCJtrjv ^ev eKlei^Lv trjv inl ^aQeCov 
tov TCQ^tov tstrjQrj^evriv iv Ba^vkcbvL t& TtQmtcj xal 
tQLaK06tm avtov eteL ;car' AiyvTttCovg Tvfil y' elg 
tijv d' coQag g' ^e^rjg^ xa%'' r]v dLa^acpettaL^ ott i^- 
sksLTtsv ri ^sXrivri dito votov daxtvkovg /3. 10 

dsvtSQav ds trjv tetrjQrj^evrjv iv ^AXe^avdQeCq: ta 
Q'' eteL ^AdQtavov ^car' AiyvjttCovg Ilaxcov tj' f^ff "^^^ 
Lri\ TtQo tQLcbv cjQcbv i6r}^eQLvcjv xal tQLCbV jte^Tttcov 
^Lccg wQag tov ^e6ovvxtCoVj xad'' r]v b^oCcag i^eXsLJtsv 
rj esXtjvrj t6 sxtov ^SQog trjg dLa^etQov aTtb ^e6- 15 
rj^^QCag. 

riv de xal rj ^ev xatd nldtog TtdQodog trjg 6skr]- 
vrjg TtsQl tbv xata^L^dt,ovta 6vv8s6^ov iv sxatSQCc tcbv 
ixlsCjpscDV tb yaQ tOLOvtov xal ix tcov blo^x^Q^^tSQCov 
VTtod^e^eov xatala^^dvetaL. t6 de aTto^trjna eyyL6ta 20 
l'6ov xal ^LXQfp tov ^e6ov TteQLyeLoteQOV xal tovto 
yuQ ix tcbv TtQoajtodedeLy^evcov TteQl trjg dvco^aXCag 



1. avdynri] -y- corr. ex t in scrib. C. 3. tov avrov'] corr. 
ex Tov D*. 5. XQOVG)'] corr. ex xQOvcov D. 6. Mg. a D. 

iXci§o[i D, sXd^o'^ D^ dri] corr. ex ovv D^. nq6tr]v C. 

jLtfV] ins. D*. 8. itsi ccvto^ B. AiyvntLOvg] -ovg in 

ras. D^. Tv§l] T- e corr. D^. 9. s'] om. D, Bv.t7]qD^. 

dL\a6Cicp£LtuL A, dLa\6a(p8LtaL A^. i^eXsLntv] supra -si- 

scr. L D^. 11. Mg. § D. ta] corr. ex t&v D. 13. tQL&v 
nsfintcov] tqCtov v.aL nifintov D. 14, i^iXLnsv D. 17. fiiv] 
ins. Dl 20. di] 8' D. 21. nsQLytiotsQOv] -l6- in ras. 4 

litt. I32. 



330 KAATAIOT nTOAEMAIOT 

yCvstai dfjXov. ETtud'^ ohv^ otav ajcb votov exXsiTtri 
'fj 6slr}vrj^ PoQSidtSQdv s6tiv tb xsvtQOv avtfjg tov 
dia fisacov^ tpavsQdv^ oti xal xad'' sxatsQav tcbv sx- 
XsCipscov tip l'6G) TtQOYiystto tov Katapipd^ovtog 6vv- 
5 ds6[iov tb KSVtQOv trjg esXTJvrjg. aXXa zata ^sv trjv 
7tQG)tr}v STcXsLil^LV ditslisv rj 6sX7]vrj tov djtoysCov tov 
STtLxvxXov ^oCQag q ocal s^rjKO^td td-' 6 yaQ ^s6og 
XQOvog sv BafivXGiVL ysyovsv JtQb rj^LCjQiov tov ^s6o- 
vvxtCov^ sv 'Aks^avdQsCa ds TtQb ^idg tQCtov cjQag 

10 L6ri^SQLvrig ^ xal 6 ditb tfjg STtoxrjg tfjg sitl Na^ova6- 
6dQov XQ^^^^S 6vvdysL strj 6vs xal iniSQag qx^ xal 
cjQag L6rjfiSQLvdg dnlcbg ^sv T rB, JtQbg ds td b^ald 
vvxd^rj^SQa T d\ xal d^d tovto skdttov fjv rj dxQi^rig 
TtdQodog tfig TtSQLodLxfjg Ttsvts [loCQaLg. xatd 8s trjv 

15 dsvtSQav sxksL^fLV dTtstxsv rj ^sXTJvrj tov ditoysCov tov 
STtLXvxXov ^ioCQag 6va vy' xal svd^dds ydQ 6 djtb tfjg 
STtoxfjg XQ^^^^S ^^XQf' T^ov HS60V tfjg sxksCtl^scjg 6vvdysL 
str] c3oa xal rj^SQag 6v<S xal WQag C6rj^SQLvdg dnXcbg 
lisv rj xal dvo Tts^Ttta^ dxQL^&g ds rj xal dcodsxatov^ 

20 d^d tovto ds xal r] dxQL^ijg TtdQodog TtksCov rjv tfjg 
^s6r]g [loCQaLg d vy. sv ta ^sta^v ccQa %^di^03 t&v 
dvo sxXsCjpsov TtSQLSxovtL strj AlyvTttLaxd xJs xal 



2 X mg. D. s6tLV~\ comp. B, ioTL in extr. lin. D. 3, 

(lEOcov'] (i^Goav T&v ^coSCoiv D, corr. D^. xat] corr. ex k&v D^ 

6. 1^] ins. D^. 7. q] seq. ras. 1 litt. D. £|7]xo(rra] om. D, 

II" BD^. 8. iv] iv (i£v D. yeyovs D. 9. 'AXt^uvdQiai A, 

"AUiocv^ D. 10. Nccj^ovvccGccQOv D. 12. r^] IJ BD, / AC, 

^t'supra scr. D^. 13. tovto] corr. ex rd C^. ildtta C, 

corr. C^ Tjv 17] corr. ex sfT) D^ 15. ccTtstx^v] cctislxs fisv D, 
(i4v del. D^. 17. Tfjg] Tfi6\a D. 19. rj (alt.)] corr. ex o in 
scrib. C. xat (alt.)] comp. supra scr. D^ 21. ^ vy] post 

ras. 1 litt. D, dvy AC. 22. nsQisxovTL'] -l in ras. 2 lHt. D^ 



MAeHMATIKHS STNTASESiS A'. 331 

rj^6Qag Qly %al cjQag l^iqyiSQivag Tca C y' rj ^sv dxQt- 
^Yjg Kata TtXdtog jtaQodog tijg ^skrivrig okovg TtSQLSxsc 
y.vxXovg^ ri ds TtsQLodcKrj svsXsLitsv sig olovg TcvxXovg 
tatg fl d^g)otSQcov tcov dvco^ah&v 6vvayo^svaLg ^oC- 
QaLg ^' vy. sllsLTtSL ds sk tav TtQOSxtsd^SL^svcov Tcatd 5 
tdg tov 'iTtTtaQxov vTtod^s^SLg ^s6cov jtaQodcov sv ta 
to6ovtm XQdvo) sig okag d7to7iata6td6SLg [lOLQag T «al 
s^rjK06td syyL^ta /3* TtXsLcov ccQa ysyovsv jtaQa tdg 
VTtod^s^SLg ri ^s6rj xatd TtXdtog TtaQodog s^r}xo6tOLg d: 
tavta ovv S7tL^SQL6avtsg sig to TtXrid^og t&v sx tou lo 

TtQOKSL^svov XQ^^ov (Svvayo^svcov rj^sQcbv M ^Sx^ ^7' 
yL6ta xal td sx trjg TtaQaPolrjg ysysvrj^sva o o o o ^ 
Xd' Trj 7tQo6^svtsg tm nat SKsCvag tdg vTtoQ-s^SLg TtQO- 
aTtodsdsty^svG) rj^sQrj6Cc3 ^s6(p TCLvrj^atL [p. 279, 4] 
svQo^sv [p. 279, 16] ro dLcoQ^cjfisvov ^olqcov Ty Ty JTs 15 
Xd' ]Trj V? Af, alg TtdXtv dzoXovd^cog xal tdg XoLitdg 
tS)v KavovCov STtL^vv&s^sLg STtQay^atsvdd^sd^a. 

dsdsLy^isvrig ds aTta^ tbv tQOTtov tovtov tfjg tisqlo- 
dLKfjg xatd nXdtog KLvr]6scjg s^fjg Tcal sig trjv tcov 
sitoxcbv avtfjg 6v6ta6Lv i^rjtTJ^a^sv TtdXLv dcd^ta^LV 20 



1. 7}(iSQaL D. mQUL lcriiiBQivcci D. xa C. y'] seq. 

ras. 3 litt. D. Supra ajtpt^^? >iara ras. D. 2. tfig asX^^vrig 
TtaQoSog D, post -do- ras. 1 litt. nsQisixsv D, -v del. D*. 

3. svsXltcsv D. 4. ^OLQaig awccyofiivccLg D. 5. ryl v y A. 

ds €x] corr. ex 8' sv. D. 6. tov] supra scr. D^ sv'] 

ins. D^ 8. ^] 8vo corr. ex 8voi D. yiyovs D. 10. ovv] 

iisv olv D, corr.Dl 11. M] ADB^, ^i BC, /i x^ D^. 8%^] 
8xd' CD, corr. D^. 12. ro: sv,] corr. ex zaasyi D^ ysvo- 

fisva D. o (quart.)] ins. D^ 13. ro5] ins. D^ iyisLvag] 
corr. ex iKovag C*. 14. rjpLSQT^aLcp] -co corr. ex -(ov in scrib. A, 
i]- corr. ex v D^ 15. dioQd^cofisvov CD, corr. D^ 17. stcl- 
cwd^sasLg] ult. s corr. ex l in scrib. A. 19. -nal] comp. A. 

stg] s- postea ins. A. 



332 KAATAIOT nXOAEMAIOT 

adL0td7cr(DV iKXsi^ljscov dt^o, xad'' ag toc ^lv ccXXcc ta 
avta tots JCQOtSQOv ^vvs^aivsv^ tovts6tLV td ts dito- 
6tYiiLata Tijg esXijvrjg syyi^ta l'6a syCvsto xat at siti- 
0xot7]6SLg l'6aL ts xal ritoc JtQog ccQXtovg t^ TtQbg [is0- 
5 rjfiPQLav d^cpotSQaL^ 6 ds 6vvds0^og ovxstL 6 avtbg 
dXXd 6 svavtLog. 

xal tovtcov dh tcov skXsl^scov TtQcytrj ^isv i6tLV^ fi 
xsxQrj^sd^a xal TtQog tr^v tfjg dvco^aXLag ditodsL^Lv^ 
ysvo^svr] ds tco /3' stSL MaQdoxs^Ttddov xar' AlyvTt- 

10 tCovg ®d)%' Lri' slg trjv Ld'' sv ^sv Ba^vkcbvL tov ^ls- 
aovvxtCov^ sv ds ^Als^avdQsCa TtQb L! y' ft^as (hQag 
L6r]^SQLvrjg^ xad'' r]v dLa6ag)SLtaL sxXsloLTtvla r} 6slrivri 
ditb v6tov daxtvlovg y. 

dsvtsQa ds\ fi xal "IjtJtaQxog 6vvsxQri6ato ysvo^svrj 

15 Tc5 x' stSL ^aQsCov tov [nstd Ka^fiv^rjv xar' AlyvTt- 
tCovg 'EitLCpl xri slg tijv xd'' tfjg vvxtbg 7tQosXd^ov6rjg 
L6rj^SQLvdg coQag ff y\ xad'' rjv o^oCcog s^sXsLitsv ri 
6sX7Jvrj dTtb v6tov tb tstaQtov trjg dca^stQov^ xal fjv 
6 ^s6og %^oVog sv ^sv BaPvXcbvL TtQb dvo Tts^Tttcov 

20 ^LCcg coQag L6rj^SQLvfig tov ^s6ovvxtCov ^ sitsl tb rj^L- 
vvxtLov ^v t6ts coQcbv\^l6rinsQLVG)v g /.' d' syyL^ta^ sv 
'AXs^avdQsCa ds TtQb d d' cioQag L^rj^sQLvijg tov ^s6o- 
vvxtCov. 



1. adiccGtd-Axcov D, -a- eras, 2. GvvB§uiV£v] -v eras. D. 

xovtB6tiv~\ comp. B, -V eras. D. 3. Haa ^yyLGta D. syi- 

vovxo D, i supra scr. D^ 5. ovv.ixL\ corr. ex ovv. sati D^ 

6. ccXX' D, 7. TtQmtriv D, corr, D^ 9. 3e] comp. ins, D*. 

11. ngd] -6 ins. D^ 14. '^lnnaQxog] 6 '"'ImtaQ D. ysvo- 

^sviq CD. 17. g y'] s F C, sh,iXtLntv D, 18, xitaQtov] 
d' B et seq, ras, 4 litt. D. 19. niimcov D. 20, TjfiLGo- 

vv^tiov D. 21. /.'] in ras. A. 22. 'AXsiavdQiai A. d'] 
ins. D^ 



MA0HMATIKHS STNTASESiS A'. 333 

yiyove de xal tovtcov tCov exXsiJl)£(ov ixatSQa tflg 
^skilvrjg tcsqI t6 ^syL^tov ov6iqg aTtoijrTj^a^ aXXa rj ^lv 
TtQotSQa jtSQL tbv ava^ipdt,ovta 6vv8b6^ov^ rj ds dsv- 
tsQa TtSQl tbv xatafii^dt^ovta^ hg xal svtavd-a ta l6(p 
poQSLOtsQov sivai tov dik ^s6g)v sv avtalg tb KSvtQov 5 
trjg 6sl7]vrjg. 

s6t(o drj 6 lo^bg avtfjg xvxXog b ABF tcsqX did- 
(istQov trjv AT^ Kal V7toKSi6d^co tb ^sv A 6r}^siov 6 

dva^i^d^cov 6vvds6^og , tb 
ds r 6 Tcatafiipd^cov^ tb ds 10 
B poQSidtatov TtSQag^ xal 
aTtsiXrjcpd-co^av l'6ai jtSQitps- 
Qscai d(p^ sxatSQOv t&v A^ F 
6vvde6^cov 6g TtQbg tb B /3d- 
QSiov TtSQag aC AA xal FE^ 15 
cS6ts xatd ^sv trjv jtQotsQav 
sxXsitjjiv xatd tb A sivai tb 
xsvtQOv trjg ^slrjvrjg^ xatd ds trjv /3' xatd tb E. dXXd 6 
^sv STtl trjv TtQOtsQav sxXsitpiv ditb trjg STtoxrjg XQovog 
stcjv s6tiv AiyvTttiaxcbv x^ xal rj^sQ&v i^ xal g)qg)v 20 
i6rjiLSQiVG)v aTCk&g ts zat dxQifiag Td g\ xal did tovto 
d%si%sv rj 6sXrjvrj ditb tov ditoysiov tov STtiXvxXov 
ILOiQag t/3 xdj TtkeCcov te rjv rj jteQiodixrj TtaQodog trjg 
dxQi^ovg e^rjxo6tOig vd" 6 de iitl trjv devteQav ex- 
Xeiil^iv b^oicog etcbv AlyvTttiax&v 6jie xal rj^eQcov tx^ 25 
xal coQcbv i6rj^eQivcbv aTtkcbg ^ev T i' d\ dxQificbg de 




1. s^-X£Ltp8a>v D. 7. 6 (pr.)] postea ins. D. Xo^6^ D. 11. 
B] B x6 D. 12. TtBQitpiQBioci] corr. ex nsQicpBQSLa A. 13. A, 
r] AT B, A %al r D. 17. x6 (pr.)] rov D. 18. r6] xov D. 
dU' D. 20. sGXiv] ins. Dl 21. Ante g' eras. t A. 22. 
cc7t6] om. D. 24. Si] 8' D. 26. /.'] corr. ex /. A\ /,' 8'] 
in ras. 1 litt. D^ a^QL^&g ds T 8'] mg. Dl 



334 KAATAIOT nTOAEMAIOT 

T d\ xal dca rovto aTcetxev rj ^sXTJvrj aito tov cctco- 
yeCov \tov eitixvTilov ^oiQag /3 ^d^ TtXeCcav te rjv i] 
TceQLodLxrj Ttdgodog tfjg aKQiPovg e^rj7co0totg Ty. xal 
6 [leta^v dl t&v trjQTj^ecov XQovog iteQiexcov Aiyvjt- 
5 tiaKa etrj Wltj xal rj^eQag td^ xal mQag Corj^eQLvag xy 
L^' 6vvdyeL Tcatd trjv aTtodedeLy^evrjv tov Ttldtovg 
^ie^rjv 7cCvr]6Lv ejtov^Cav ^oC^ag q^ xal e^riK06td d. 

e6t(o ovv dLa td exxeC^eva xal rj ^e6rj jtaQodog 
tov xevtQOv trjg 6eXrjvrig ejtl ^ev tfjg TtQOteQag exkeC- 

10 ^e&g xatd tb Z, eTtl de tijg devteQag xatd tb H. xal 
ijtel rj ^ev ZBH TteQLCpeQeLa ^olq&v e6tLV q^ xal 
e^rjxo6tG>v d, rj de ^Z e^rjxo6tG)v vd'^ ri de EH e^rj- 
xo6tG)v Ty^ 6vva%%"ri6etaL xal rj ^E TteQLopeQeLa ^ol- 
Qcbv ()| V. xal 6vva^(p6teQaL ^ev ccQa aC A/l^ EI 

15 tcbv XoLTt&v eL6LV eig tb rj^LXVxkLov ^olq&v Ld' I, exa- 
teQa de avtcbv^ eitel l'6aL eC^Cv^ tcbv avt&v 0" A£, o6oLg 
ij dxQLprjg jtaQodog tfig ^eX^^vrjg xatd ^ev tijv itQoteQav 
exXeLi^LV VTteXeCTteto tov dvapLpd^ovtog 6vvde6^ov^ 
xatd de trjv devteQav tov xata^L^dt,ovtog TtQorjyetto. 

20 xal oXr] ^ev ccQa rj AZ TteQLCpeQeLa ^olqcjv e6tLV t" Ad, 
XoLTtf} de rj HF ^olqS)v d" x^. ca6te xal ij jteQLodLxii 
TtaQodog tfjg 6eX7]vrjg xatd ^ev trjv jtQoteQav exXeL^LV 
vTtekeCiteto tov dva^L^d^ovtog 6vvde6^ov ^oC^aLg T Xd 



1. xal dLa'] in ras. D, ano] om. D. 2. EnvY.vv.Xov] -v.vv.- 
in ras. D^. nlEvaiv] -ei- in ras. A^. xs] 8s D. 4. hr\ 

Alyvnxiccv.d D. 6. Gvvdysi] -d- supra scr. A^. ccnodeS£i,y\(iE- 
vr]v corr. in &noSEdEL\yfiEvr}v A. 7. E^rjv.oex&v D. 11. 

ZBH] ZH D. 12. EH] E- supra scr. D^ E^rj-Aocx&v] 

comp. B. 14. ET] xal EF D. 16. Ji] om. D, S' supra 
scr. D*. etGiv] comp. B, -v del. D^ &] corr. ex o D* seq. 
ras. 1 litt. Xe] X- in ras. D^. 19. nqoriyEtxo xov ■Kccxa- 

§L§d^ovxos I). 20. fioiQ&v] om. D. iaxLv] comp. B, -v 

del. D2. 23. ;L^] i J C. 



MA0HMATIKHS STNTASESiS A'. 335 

xal a7tel%ev ccjth xov B ^oqslov TCSQatog ^otgag 67C 
Ad, xara ds tiiv dsvtSQav itQoriysito tov xatapt^dt^ov- 
xog fiocQaig O* x^ jcal a7tsl%sv roi) avtov ^oqsCov TtiQa- 
rog ^oiQag ii Xrj. 

loLTtov da, STtsidri 6 aTtb tfjg S7to%fig %Q6vog ^s%ql 5 
xov iLSdov xfig jtQotSQag ixXsiil^scog STtov^Cav 7tSQis%sc 
Ttkdtovg iioCQag 67tg t-O', tavtag sav dcpskco^sv t&v 
Tcata triv S7to%rjv tfjg 7tQ0tsQag sxXsCipscog ^olqcov 67t 
2,6 ^tQoad^svtsg avtatg sva kvkXov^ s%o^sv xal sCg tb a 
etog Na^ova66dQOv ocat^ ACyv^ttCovg ®Gi%' a tf{g 10 
lis6ri^PQCag ti^v tov TtSQiodixov TtXdtovg s7to%fiv aTtb 
xof) ^OQsCov TtSQatog ^oCQag tvd Ts. xal 7tQbg tdg 
diaxQC6sig ds tcbv 7tSQl tdg 6vv6dovg xal 7tav0sX7]vovg 
yivoiisvcov iprj(po(poQiG)v^ STtsidfi xatd tdg toiavtag 
7taQ6dovg ovdsv 7tQo6dsrjd-rj66^sd^a tfjg aTtodsi^d^rj^o- 15 
fisvrjg SsvtSQag dvco^aXCag^ sxd-rj^o^sd^a tav xatd ^s- 
Qog x^rjy,dtcov xav6viOv did tcbv yQa^^&v TtdXiv^ 
co67tSQ xal S7ti tov rjXCov^ tf^v TCQay^atsCav avrwv 
Ttoir^^d^svoi xal 6vy%Qri6d^svoL ^sv t& t&v s^rjxovta 
TtQbg td i xal d' X6yc}^ disk6vtsg ds co6avtcog xd [isv 20 
TtQbg tfp dTtoysCo) tstaQtrj^^Qta d^d ^olq&v s", td ds 
TtQbg ta 7tSQLysCco d^d ^olqcov y^ cog 7tdUv trjv tov 
xavovCov 8LayQa(pfiv o^oCav yCvs6d-aL ty S7tl rov rjXCov 



1. &nsLXBv~\ corr. ex a7tE%BLV D*. 2. Ttqoriyii D." 3. 

anEtxs D. 5. 8s'] d' D. 6. iHXeCipsoog'] t&v snXsiipscov D. 

8. OTC Xd] corr. ex 67tX d D. 10. Na^ovvacdQov D. «'] 

. nQcotrj D; similia saepe omisi. 11. anoxriv D. 12. nigatog] 

corr. ex nsqag D^ 13. yiai] xal ta? D. 15, nQ06dsr]66- 

' fisd^a D. 16. t&v] t6 t&v D, supra -d ras. et ante -&- 

ras. 1 litt. 19. evvxQri^dfisvoi D, ro5] seq, ras. 1 litt. D. 

s^^qv.ovta'] ^ D, ^ D^ 20. jta^'] om. D. Xoyco] -co e 

corr. D^ disX^ovtsg BC. ds] d' D. 23. t^] tfjg B. 



336 KAATAIOT nTOAEMAIOT 

6xixG)v ^sv fti, 6eXi8Cg)v 8e tql&v^ t&v ^ev 7CQ(x)t(X)v 
dvo 7teQLS%6vrG)v rovg ccql^^ovs t&v tijg dvco^aXLag 
^oiQcbv^ tov de tQitov tag oixeLCog ixd6tG) t^T^^atL 
TtaQaxei^Bvag 7tQ0(5^a(paiQe6eLg tijg ^ev dcpaLQB^ecog 
6 yLVO^evrjg xatd trjv ^ri(po(pOQLav iitC te tov ^7]xovg 
xal tov TtXdtovg^ otav 6 tfjg dvco^aXCag djtb roi) dTto- 
yeCov tov eitLXVKkov ^vvayd^evog dQtd^^bg ecog Q7t 
^OLQcov ?y, tfjg de ^tQO^&e^eog^ orav tdg QTt ^ioCQag 
v7teQTiC7ttri, xaC e6tLv tb xavovLOV tOLOVto' 



1. GEXLdicov] -Xi- supra scr. , -8- in ras. A. tqiobv] y B, 
y D. 4. TtqoGQ^cc^pcciQiGeig] -%•- corr. ex o D^ 6. yivo- 

(i8vr]vl), corr. D^ 6. 6] 6 ccTto D. 7. scog] corr. ex cog D^ 
8. 9} — ^oCqccs] supra scr. D^ 9. vTCSQTCiTtrTj'] -rj corr. ex 
£t D^, vneQsyinintr] B. icTiv] CD, comp. B, iozi AD^ tol- 
ovtov CD. Deinde add. in imo mg. fol. 93"^: iitEixEv 17 aelriVT] 
ta cc et£i va^ovvaGccQOv tov d'cbd' vso[i7}Vicc stg tr]v \ -/ fifff- 

7}[i§Qiav :-^ I /LiTjjtT] tavQcov y, icc x(3 ccnoysiov imti/ ^ o|7] fn^ 

ccnoxfjg | / f* A^ nXditog ^oqsC nsQ [i tvj Ts : — ?► | -^-^ | D. 



MA0HMATIKHS STNTAHE^S A'. 



337 



i\ Kavoviov tf}g TtQcotrjg xal ccTtXijg avto^aXiag 
ri]g 66X7]vr}g. 



CCQl&llO 

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Q^6£ig 

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y fi^ 


v8 




y 7] 
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y va 


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y X£ 
y oty 

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8 Xrj 


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8 vd' 
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1. t'] B, om. ACD. Y.av6viov — 2. 6£Xrivrig'\ om. D. 3. 

^Sfa(p£Qi6£ig D, nQoeQ-acpuijQ C. 4. a' §' y'] om. D. 12. 
Xa] corr. ex X D. 13. va] corr. ex v D. 31. 6X8] 6Xa D. 
35. <)X^] postea ins. D. Omnia sub uno capite codd. 

Ptolemaeus, ed. Heiberg. 22 



338 KAATAIOT nTOAEMAIOT 

ta, "OtL oi) TCaQCi tag diatpoQag tcbv V7tod'd6scovj 

akXa TCaQa tovg sjtLXoyL^iiovg dLi^veyxsv xata 

tbv "l7t7taQ%ov ri TtriXiKOtTig tY^g esXifjviaKrjg 

avcDiiaXiag. 

6 Tovtcov ovtcog dTtodsdsiy^svcjv slxotcog av tig 
S7titpritri6sis^ did jtoCav aitCav sx t&v VTtb tov 'iTtTtdg- 
%ov jtaQatsd^si^svcDv 0sXrjvia7ca)v sxXsCi^scov TtQbg trjv 
trjg toiavtrig dvco^alCag sjtC^xstl^tv ovts 6 avtbg yCvs- 
tai koyog ta v(p^ rnicav dTtodsdsty^svay ovts 6v^(pcovog 

10 6 7tQG)tog xal did trjg ;««ir' sxKsvtQOtrjta vjtod^s^scog 
dsLX^^^t^S 'Pc3 dsvtSQG) xa\ did tr^g ;«ar' STtCxvxXov vno- 
d^s^scog STttXsXoyi^iisvG). xatd ^sv ydQ tijv stQcotrjv 
dsi^LV 6vvdysL tbv Xoyov trjg sx tov xsvtQov tov sx- 
xsvtQov TtQbg f^v ^sta^v tcov xsvtQcov avtov ts xal 

15 tov dLd IIS6G3V tG)v ^codCcov xvxXov^ bv s^sL td /yQ[id 
TtQbg td txl rB syyL6ta^ d) Xoya) 6 avtog s6tLV 6 tcov 
I TtQog td g Zf, xatd ds tijv dsvtsQav 6vvdysL tbv 
X6yov tfjg sx tov xsvtQov tov dLa ^s6cov tcbv ^codCcov 
^ISXQL tOV XSVtQOV tov STtLXvxlov TtQbg ti^v sx tov 

20 xsvtQov tov STtLxvxlov^ ov s^SL td /yQX^ C ^Qog 6^^ 
i\ G) Xoyco 6 avtog s6tLv 6 t&v 5 ^Qog td d 'jig* 
TtOLSL ds t6 nXsi6tov tf^g dvco^iaXCag dLafpoQOv 6 ^sv 
tcbv I TtQbg r« g d' Xoyog ^olqcov s ^d'^ 6 ds tcbv | 



1. Lcc'] B, om. ACD. tdg\ seq. ras. 1 litt. C. 7. naqa- 
TLd-sfiivayv D. 8. Xoyog yivBzai D. 11. vnoQ^BGKog^ -g in 

ras. D*. 15. jq^S] ^- corr. ex F A\ r mut. in F/ D*. 

16. ^] Tit D. r^] Fo ABC, ToB D, d^ Dl sWv] 
Igxiv g D, corr. D^. 18. loyov'^ alt. o in ras. 2 litt. A. 20. 
^ypx^] r (>x|3 D. /_'] in ras. D^. Tiq6g\ Ttgbg xd D. <>it4^/.'] 
e corr. seq. ras. 2 litt. D. 21. 86tiv\ scxi v.aC D, yiaC del. D^ 

23. x&v (pr.)J supra scr. D-. 



MA0HMATIKHS ZTNTASESiS A'. 339 

TCQog ra d ftg ^OLQcbv d Ad, xad"' rj^ccg tov tcbv | TtQog 
ta 'e 8' Xoyov s ^olq&v syyi6ta Jtoiovvtog f^v sxxsl- 
^svrjv diatpOQdv, 

otL ^sv ovv ov TtaQa triv t&v 'b7Co%'S0SGiv d6v^- 
(pcovLaVj Sg OLOvtaC tLVsg^ rj tOLavtrj TtaQrjxoXovd-rjesv 5 
d^aQtCa^ xal rd loycp ^lxq^ nQ66^sv (pavsQov rj^tv 
ysyovsv sa tov xad"' sxatsQav avtcjv td avtd (paLvo- 
[isva 6v^^aCvsLv aTtaQaXXdxtcog, xal dt« t&v dQLd^^cov 
ds^ SL ^sX7]6aL^sv tovg S7CLXoyL6^ovg 7tOLSi6%-aL^ tbv 
avtbv dv svQOLfisv yLvo^svov loyov f| dficpotsQCJv tcbv 10 
VTtod^s^scov^ sl totg avtotg fisvtoL (paivo^svoig dxoXov- 
%tri6aLiisv scp sxatSQag xal ^r^ dLacp^QOLg, w67tSQ 6 
"l7t7taQiog. dvvatbv yaQ ovtcog s6taL ^rj t&v avtcbv 
v7totsd-SL6G}V sxXsCil^scov 7] TtaQ^ avtdg tdg trjQ7]6sLg rj 
TtaQa tovg tcov dia6td6scov S7tLkoyL6^ovg trjv d^aQtCav 15 
6v^^sPrjxsvaL. svq7]6o^sv yovv xal S7t sxsCvcov tcbv 
sxXsC^jscov tdg ^sv 6v^vyCag vyLcbg tstrjQrj^svag xal 
6v^(pcovcog ysysvrj^svag tatg vcp' rj^cov dTtodsdsiy^svaLg 
tijg ts o^aXiig xal tfig dvco^dXov XLV7J6scog v7to%^s6s6L, 
tovg ds tcbv dLa6td6scov S7tLXoyL6^ovg^ Sl cov rj TCrjh- 20 
xdtrjg Toi) koyov dsCxvvtaL^ ^rj STtL^sXcbg^ cog svl ^d- 
Xi6ta^ ysysvrjiisvovg. dsC^o^sv ds tovtcov sxdtSQOv 

aTtb t&V TtQCOtCOV tQL&V SxXsC^SCOV dQ^d^SVOL. 



1. ^(alt.)] j' D. X8'] seq. ras. 3 litt. D. rjfi&g tov x&v\ -s 

xov X- e corr. D*. 2. ftot^cov] ^i D. 10. yivofievov] om. D. 
11. gqp' STiaxeQccg ccyioXovQ-'^occi^Bv D. 12. SiacpOQOigl dicc- 

qpopcbg D. 14. v7tox8Q-£L^EVoov D. avxdg'] -xdg add. D*. 

Tag TT]-] e corr. D* seq. ras. 1 litt. 15. i7tLXoyiG\iiovg A, 

i7iLXoyi\6^ovg A*. 16. svQiGOfiev C. 18. -g xalg v-] in ras. D, 
xaig supra scr. 21. xov Xoyov] xovxcov B, xov C. bvl] e 

corr. D^. ^dXL6xa] ft- in ras. 2 litt. D^ 22. xovxov C. 



.-)£)* 



340 KAATAIOT nTOAEMAIOT 

tavtag ^hv di) tag tQstg ixXsiJpELg TtaQatsd-st^d-cci 
(pr]6LV ccTch tG)v S7C BapvX&vog diaxo^LCfd^SL^cbv cjg STcst 
tstrjQrjiiBvag^ ysyovsvac ds tY^v TCQcbtrjv ccQXOVtog 'Ad"t]- 
vr]6i 0avo6tQdtov ^rjvbg no(5si8scbvog ocal sKlsloi- 
5 Jtsvac f^v ^skrjvrjv ^Qa%v ^SQog tov xvxlov dito d^s- 
Qivrlg dvatoXrjg trjg vvxtbg XoiTtov ovtog rj^icoQiov' 
xal sti, (pri6iv, SKXsi7tov6a sdv. yCvstai toCvvv ox)tog 
6 %(>dvog xatd tb r|g' stog ditb Napova66dQov^ xat 
AlyvTttCovg ds^ mg avt 6g cprj^iv^ @d)d' xg' sig tr]v xC,' 

10 iistd s IJ GjQag xaiQixdg tov ^s6ovvxtCov ^ STtSidr^itsQ 
loiitbv r]v tr]g vvxtbg r]^iG)Qiov. dXXd tov r]XCov ovtog 
jtSQl td s^xata tov To^6tov sv Ba^vkGiVi r] tfjg vvx- 
tbg cijQa XQ^vov s6tlv Ir]' r] ydQ vv^ sOtiV i6r]^SQiVG)V 
G)QG)V id xal dvo 7ts^7ttG)v' aC Ttsvts r]Hi6v aQa G)Qai 

15 xaiQixal 6vvdyov6iv i6Y]usQivdg coQag g xal tQCa 
jts^TCta. r] dQx^ aQa tfjg sxXsCipSG)g ysyovs ^std Trj 
cjQag i6r]^SQivdg xal tQCa Tts^Jtta tfjg sv tf] xg' y,s6- 
r]nPQCag. STtsl ds ^Qa^v ^SQog STts^xid^d^r]^ 6 (isv Jtdg 
XQOvog tfjg sxXsCil^scjg ocpsCksi ysyovsvac a Ij wQag 

20 syyi6ttt^ 6 dl ^s6og 6r]Xov6ti ^std tO" y' wQag i6r]^s- 
Qivdg. sv ^AXs^avdQsCa: Tcdlcv aQa ysyovsv 6 ^s6og 
XQ6vog tfjg ixkeCtltscog ^std Trj L! cjQag i6r]^sQivdg tfjg 
iv r§ 3cg' ne6ri^PQCag. xaC i6tiv 6 dicb tfjg xatd tb 

1. 87]] ovv dsL D. TtaQCitid^ecd-ai D. 3. Ttgairriv'] a' B. 
/K mg. D. 4. UoaLdeavos D, corr. D^. 6. Xoltiov] -v 

corr. ex t C^. 8. t6] ins. D^ Na^ovaGGocQov] -aoa- in ras. A, 
Na^ovvaGccQov D. 9. ds] d'a>d' x? D, alt. -^ postea add. 

&diQ' %?'] om. D. 12. rfjg] -f]- e corr. A^ 13. iariV] 

icTL D, comp. B. qjqcov tGxiv l6ri(i£QLvd)v D. 14. Tisvtt 

^fiLGv] I U BD. 15. TQLa'] -L- ins. C^, y corr. ex Ty D. 16. 
nifmra] F D, e" D^ 17. xcct] in ras. 1 litt. D. rQia 

Ttsfinra] y D, y t" D^ 18. fiSQog] om. D. 19. moag] comp. 
AC. 22. M]] corr. ex ^ D^ 



MA0HMATIKHS STNTASESiS A'. 341 

a hog Na^ova66dQov STtoxrjg XQ^'^^? i^^X9^ "^^^ ifxo- 
xst^evov et&v AiyvTCXiax&v t^s xal yj^sq&v xs xal 
c3qS)v L6r]^SQtvcjv aitlcbg fisv Irj L\ axQi^&g dh Trj 
d'' TCQog ov xQovov STtLkoyi^o^svoL xara tag ixxst^svag 
riii&v 'b7tod's0sig tbv ^sv rjXiov svqC^xo^sv dxQip&g 5 
STCSxovta To^otov ^oiQag xrj Trj^ tr^v ds 0sXr]vrjv fis6(x)g 
fisv zlcdv^cov ^OLQag xd x^ dxQi^&g ds xrj tj, ijtst- 
drJTtSQ xal xatd trjv dvo^aXCav ditsxsi tov dnoysCov 
tov smxvxXov ^oCQag 6xt, ]iy. 

Ttdliv tijv s^rjg sxXsiipCv (prj6Lv ysyovsvai ccQxovtog 10 
'Ad^rjvrjCLv Qavo6tQdtov ExLQO(poQLcbvog ^rjvog^ xat 
AlyvTttCovg ds Qaiisvco^ xd' sCg trjv xs' s^sXsLTtsv 
df, (prj6Cv^ dno d^SQLvrjg dvatoXrjg trjg 7tQ(htr]g aQag 
TtQosXrjXvd^vCag. yCvstai drj xal ovtog 6 ;u^dvog xatcc 
tb T^g' stog dnb Na^ovaC^aQov Qa^svhd' xd' sig trjv 15 
xs' TtQb s C G)Q^v ^dXL0ta xaLQLXcbv tov ^s<5ovvxtCov. 
dXXd tov iiXCov ovtog JtsQl td s^xoita t&v ^Ldvyicov 
rj trjg vvxtbg S^a sv Ba^vX&VL ^^oVcji/ s0tlv l^' aC 
ccQa s i' xaLQLxal coQaL 7t0L0v6LV i6r]^SQLvdg d xal dvo 
Tts^Ttta. rj aQxrj ccQa tfjg sxXsCifjscog ysyovsv ^std ^ 20 
cijQag L6rj^SQLvdg xal tQCa 7ts}i7tta tfig sv tfj xd' fis6- 

1. (H mg. D. Noc§ovvaGdQov D. TTQoyisiiiEvov D. 3. 

icrjfiSQLvcbv^ comp. e corr. A^ seq. ras. 1 litt., om. BC, del. D^ 

4. TtQog dv] corr. ex noaov D^. 5. rjficbv'] corr. ex v[imv D^. 

ayiQLp&g i7ii%ovra~\ lTti%ovxa av,Qi^Gig xov D. 8. ccnixEi] 

corr, ex bIxe D^ 10. cprj6iv~\ -v del, D^ dQxovxsg D, -s- 

del. D^. 11. 'J&t^vrjGL BD. Gyivd-QOcpOQL&vog D, corr. D*. 

12. di] supra scr. B. i^eXLTtsv D, -v del. D*. 13. TtQmrrig'] 

d B. 15, Na^ovvaaaQov D, 16. fidXLata cnQobv D. (is- 

ffOHTtov C. 18. 17] corr. ex 171 A, om. BC. satL D, comp. B. 
_ 19. f /_' aQa D. otat] -a- in ras. A. dvo nifiTtta] ^ s g" D, 
§ f" D*. 20. yiyovE BD. 21. ^Qug] m- in ras. 2 litt. D«, 
-a- in ras. A. tQia niiiTtta] y' s" corr. ex y f" D. tt}?] 
corr. ex tf\ D^ 



342 KAATAIOT nTOAEMAIOT 

yili^Qiag. aAA' iTtsl 6 Ttdg ^^oi^og tfjg exXsLxl^scog g)qg)v 
tQLGiv ccvayQacpstaL^ 6 ^B6og drjkovoti ysyovs ^sta 
svvsa xal dsxatov &Qag L6rj^sQtvfjg. sv ''AXs^avdQsCa 
ccQa ofpsCXsL ysyovsvau ^ista rj d' syyL0ta &Qag L6rj^s- 
6 QLvag trjg sv tfj x8' ^s6rj^PQCag. xaC s6tL %dXLv 6 aTtb 
tcbv STioxcbv XQOvog stCbv ALyvjttLaKcbv t^s xal rj^SQ&v 
6y xal d)QG)v C^rniSQLVcbv ajtlcbg ^sv rj d\ dxQL^&g ds 
^ L! y' ^Qog ov xQovov svqC6ko^sv tbv ^sv r\kLOv 
dxQL^cbg sjtsxovta ^lSv^g^v ^oC^ag xd jilg, trjv ds 

10 6slrivr]v ns6G)g ^sv To^dtov ^oCQag xy irrj^ dxQL^cbg 
ds iioCQag xd Jirj, S7tSLdr]7tSQ xatd trjv dvcjfiaXCav dit- 
stxsv tov ditoysCov tov STtLXvxXov ^oC^ag ^J A^. 
CvvdystaL ds xal rj dLd6ta6Lg rj dnb tfjg TtQcotrjg sx- 
XsCifSG)g STtl trjv dsvtSQav ri^SQcbv qo^ xal g)qg)v Ty 

15 xal tQLcbv Tts^Tttcov L6rj^sQLVG)v^ ^OLQcbv 8s^ dg 6 rjXtog 
xs7cCvr]taL^ Qoy xrj^ tov 'IititdQxov 7toLrj0a^svov trjv 
dst^LV G)g tfjg dLa6td6SG)g ri^SQcbv ^isv ov6r]g qo^ xal 

G)QG)V L6r]^SQLVG)V Ty /.' d\ ^OLQGfV Ss QOy XSL7tOV6G)V 

tb oydoov ^sQog ^Lccg ^oC^ag. 
20 tijv ds tQCtrjv q)r}6lv ysyovsvaL aQxovtog ^Ad^rjvrj^tv 
EvdvdQov iirjvbg TIo6SLdscbvog tov 7tQOtSQov xatd 

2. iiBGog] post |w-- ras. 1 litt, A. 3. ivvsa] -0- BD. Ss-ncc- 
tov'] r BD, l" D^ iGTifiSQLvfig] ABC, corr. ex laTj^SQivdg D^. 
4. ^] 7] xat D. d'] mut. in d" D^ 6. 6] ins. A^ 7. 
6y] in ras. D^ iGrjfisQLv&v] corr. ex Td r^fiSQLvatv D^ ^ ^'] 
in fine lineae add. D^, in initio sequentis r] d' del. D^ 8. y'] 
in ras. A^ nQog ov] corr. ex noGov D^ 10. xy] -y in 

_f 
ras. D^ 11. ansL%s corr. ex S7csl%sv D^ 13. TiQcotrig] a B. 

14. dsvtSQttv] B B, Q^t] l^^v QO^ D, 15. tQLcbv ns^ntcov] 

sy D, s" tQL&v D^ 18, XsLnov6a)v] -6&v in ras. D^ 19. t6 

^ySoov] 7] D, 7j" D^, mg. yQ. tb bydoov D^ ^iQoe] ^sqsl, -sl 

in ras., D. fiL&g] a B, 20. qpTyat D. ysyovsv D, corr. D^ 

21. tov nQotsQov firivbg TIo6SLdsa>vog D. v.utd] %at C, v,ata de D, 



MAOHMATIKHS STNTASESiS A'. 343 

AlyvTCtCovg ©«O* tg' elg xriv tf'* i^sXsLJtsv ds^ (prjaiv^ 
oXr] ccQ^a^EVT] aTth d-SQovav dvatokcov d aqcbv TtagsX- 
rjlvd^vL&v. yCvstat, dij xal ovtog 6 XQ6vog xata tb 
rJJ' stog djtb Napova^daQov ©«O" cg' slg t^v tj' jr^o 
/3 C ftaAt^ra coq&v tov ^s^ovvxtCov. dXXa tov r\kiov 5 
ovtog JtSQi td dvo ^SQrj tov To|otov sv Ba^vXcbvi r] 
tfjg vvxtbg S^a %q6v(ov sdtlv Irj syyiata' at ccQa ^ 
C G)Qai xaiQiTcal 7toiov6iv i6rj^sQivdg coQag y. S6ts 
r] dQxri tfjg sxXsiilfSCjg ysyovsv ^std -9- SQag iOrj^SQivdg 
tfjg iv tf} tg' ^s6r]fiPQiag. dXXa sitsidfj oXrj s^sXsiTtsv^ 10 
6 fisv Ttag XQ6vog syyi6ta ysyovsv g)qg)v d i^rj^SQi- 
v&v, 6 ds ^isdog XQ^^^S Srjlov6ti ^std Td wQag trjg 
^s6rj^^Qiag' sv 'Aks^avdQsCa ccQa 6 ^s6og XQ^^^^S ^^? 
ixXsCil^scjg ocpSiXsi ysyovsvai ^std T sxtov coQag i6rj^s- 
Qivdg tfjg iv tfi ig' ^s6rj^PQCag. %aC i6tiv 6 dnb tcbv 15 
ijtox&v ^(Joi^off it&v AlyvTttiaKcbv r|g xa\ rjiiSQ&v Ts 
xal aQav i6rj^SQiVG)v ditX&g ^sv Ttdkiv T g', dxQi^&g 
ds d" C y'' ^Qog ov xq6vov svqC^xo^isv tbv fisv ijXiov 
iitixovta dxQiPcbg To^btov ^oCQag tj A, tijv ds 6sX7J- 
vrjv ^i6cjg ^sv Aidv^ov ^oC^ag tj %d^ dxQi^cbg ds i% 20 
3c^, 8id t6 xatd tijv dvcofiaXCav dnixsiv tov djtoysCov 
tov ijtixvxXov iLoCQag Q7ta i^. 6vvdystai ds xal 7] 



1. ts'] corr. ex ly J)\ i^dUnsv D, -v del. Dl 2. 

ocQ^afiivri] om. D. d cb^coi/] corr. ex dcoQiov D^. 3. ^tj] 

di D. 4. Na^ovvaGccQov D. ig'] corr. ex x' D^ 6. sv] 
ndUv iv D. 7. iatc D, comp. B. ^ [_' ccqcc D. 9. sx- 

Xii};scog A. yiyovs D. -9'] corr. ex p D^. lo7\iLSQivdq] 

om. D. 10. &XV D. i^iUnsv D. ll^ysyovs D, corr. Dl 

14. r syitov coQaq] ig D, Tg" D^ 17. T <;'] corr. ex Z? D^. 

18. nQog ov] corr. ex nooov D^. 19. to|otov dv,QL^cbg D. 

20. xa] -o: postea ins. D, supra scr. x. 21. tou] dnb 

tov D. 



344 KAATAIOT nTOAEMAIOT 

KTcb tTJs dsvteQag btcI tijv tQLtrjv enXsi^Lv dLcc6ta6Lg 

rillEQGiV fl£V QO^ Xal L07]^£QLVG)V G)QG)V /3, ^OLQ&V dh 

Q0£ ^d^ tov ^lTtTtccQxov tcccXlv vTtod-^^evov Kal tavtrjv 
f^v 8Ld6ta6LV rj^£QG)V ^ev qo^ xal mQag a rB, ^olqcov 

5 d£ Q0£ ^. €paLV£taL OVV £V tOtg tCOV 8La6td6£G)V £7CL- 

XoyL^iiotg dL£j{j£v6y,£vog ijcl ^£v t&v rjn^Qcbv g' t£ xal 
y' [HLag SQag t6r]fi£QLvf}g^ iicl dh tcbv ^olq&v tQL6l 
:c£^7CtoLg £yyL6ta xad'' £xat£Qav ^Lccg ^OLQag^ diC£Q ov 
tijv tv%ov6av £v tfj TCrjXLxdtrjtL tov loyov dLacpcovCav 

10 d7C£Qyd6a6%'aL dvvataL. 

fistapi^^o^^d-a dii xal £7cl tdg v6t£Qov ixt^d-^L- 
liivag avtip tQ£Lg ixX£Ltfj£Lgj dg (pr}6Lv iv 'Ale^avdQ^LCc. 
X^trjQfi^d-aL. tovtcov d£ trjv TCQcotrjv q)rj6lv y^yovivac 
t& v8' £t£L tr\g d£vtiQag xatd KdlLiCTCov tceqloSov 

15 ;«aT' AlyvTCtLOvg M£6oQri tg', xaQ^ r]v riQ^aro ^£V ix- 
X£L7C£LV ri 6£Xr]vri tcqo rj^LCOQLOv tf]g dvatoXrjg^ £6%atov 
d^ dvETcXr^Q^d^r] tQLtr^g ooQag ^i6r]g. 6 ^i6og ccQa 
XQOvog yiyov£v S^ag ^hv d£vtiQag dQ^o^ivr^g^ tcqo s 

dh G)QG)V XaLQLXCbV tOV ^£60VVXtL0V^ TCQO t060VtG)V Ss 

20 xal L6r]^£QLVG)v^ i7C£Ldii]7C£Q 6 i]XLog 7C£qI td t£k£vt ata 



1. dsvtSQag] dsvr^Qag s^XsLipscog D. sy.XsiipLv'] om. D. dc- 
dcraeig] corr. ex diaGxaGsig D. 2. oiQCbv l6r\usQiv&v D. 3. 
^lnndQxov] ''Imt- e corr, D^ 4. mQag] ojqo^v D. r^] l^ A, 
I^ BCD, mg. a r" D^ 5. rj] yial 7] D. 6. 8isipsvo\fiEvog A, 
dLStpsv\6[iivog A^. s'] g coZ D. 7. y'] ron D; mg. «htc* 

Tf y,al tQLtoj D^. 8. jrsftTrroi?] e D, s" D^ ^iag] a B. 

9. 7triXiv.6tr]Lti, D. 12. avta tQSig] avtav D. (priOiv] $ D, 
^ add. D^ 13. tstrjQf^oQ^ai] corr. ex tr\QSt6%-ai D^ tprioiv'] 
comp. D, ex parte renouat. 14. hsi] U,' D, U'** D*. KdX- 
XiTtTcovD. 16. ■aat'] 'AatdD. (is60Qi B. 16. r] fiico q lov] corr. 
ex l_ mQug D^. s^xatov'] -6- e corr. D^. 17. tQitr]g\ corr. 
ex / D^ 19. TtQo] TtQog BC. 20. tsXsvtat C. 



MA0HMAT1KHS STNTASESiS A'. 345 

i]v rrjg IlaQd^evov. S<3ts ^eta t, coQag L6rjii£Qtvag trjg 
iv tfj tg' ii£0if]^PQLag iv 'AXs^avdQSLa yayovev 6 ^s6og 
XQOvog trjg iTcXsLTpscog. E6ti 8e 6 ditb t&v xatd tb 
TCQ&tov £tog Na^ova66dQOv i7to%c)v XQOvog itav Al- 
yvTttLaxav (p^<S ical r}^£Qav tjii xal cjqcjv i6riii£QLVG)v 5 
aTtkcbg ^hv J, dxQL^cjg ds g /.'* xad^' bv xQ^vov Ttdhv 
£VQL0xo^£v tbv ^£v ijhov ijtixovta dxQLfi&g UaQd^ivov 
liOLQag xg g, triv Se 6£Xr]vriv ^i^cjg ^sv 'Ixd^vcjv ^ol- 
Qag xfiy dxQiPcbg ds ^OLQag x^ ^, dLa tb xatd tr^v 
dvco^aXLav ditixsiv tov ditoy^Lov tov imxvxXov ^oLQag 10 
t xal £^Yjxo6td Ty. 

trjv ds i^fjg ixX^LipLV (prj^L y^yovivai toj v£' £t£c 
trjg avtrjg 7t£QL6dov ^car' AiyvTttCovg M^xslq 0"^ rJQ^ato 
de trjg vvxtbg 7tQO£k^ov0cbv coQmv £ xal tQLtrj^ioQLOV 
xal i^iX£L7t£v oXr}. yiyov£v ccQa rj ii£v dQX^i trig ix- 15 
X£Lil)£cog ii£td Td xal y' SQag i6rj^£QLvdg tfjg iv tf] 
ivdtf} ^^rj^^QLag^ i7t£Ldr]7t£Q TtdkLV 6 riXLog 7t£QL td 
£6xata rjv t&v ^Ix^vcov^ 6 de ybi6og XQ^"^^^ ^£td Ty 
xal y' coQag i6ri^£QLvdg dta t6 tijv 6£Xr]vriv oXrjv ix- 
X£XoL%ivaL. xaC i6tLV 6 d7tb tcbv iTtox^iv ^ixQi' '^ov- 20 



2. T^] xr] A, T^ A*, xfiv D. is'] coit. ex comp. xat D^ 
iiSGTni^qius'] ji D, '^ add. Dl 3. scxiv D, -v eras.; 

comp. B. di'\ dh %aC D. 4. eto?] t, D, U'° Dl lx&v\ 

corr. ex x&v A^, comp. D, Ix D^. 5. x\i&\ xjig D, supra <s 

ras. ajQ&v^ corr. ex 7](isQ(bv D. 6. /_'] e corr. D^ 10. 
fiOLQag ?] bis D, extr. et initio pag. 11. s^-qY.oaxd] |" D. 

12. qprjfft.] cpr^Giv B; 9 D, ^ postea add. Ta] x&l corr. ex 
Tc6 AD. vs''\ e corr. D^; v8' Ideler Hist. Unters. iib. d. 

astron. Beobacht. d. Alten p. 216 sq., qui deinde p. 346, 13 avxm 
deleri uult. IVfi] e corr. D^. 13. Me%Cq B. 14. tcqog- 

sX^-oveSiv D. xQix7]yiOQCov'] r D, mg. yQ. xqlxti^oqCov D*. 16. 
Lo] renouat. D^ yiaC] om. D. 17. svccxrj'] -S- BD. snsiSr} D, 
corr. D^ 19. yiaC] supra scr. D^ 



346 KAATAIOT nTOAEMAIOT 

tov XQ^^^^S fVwi/ Aiyv7ttLaK€bv (p^^ xal t]^SQcjv Qvrj 
xal g)qG}V l61]^£qlvS)v djtX&g ta xat dTCQL^&g syyLOta 
Ty y'' TtQog ov xqovov codavtcog evql6ko^£v tbv ^lv 
i]lLOv dxQL^&g £7t£xovta tcov 'Ix^vcov ^OLQag xi tj, triv 
5 d£ 6£krivYiv ^£6G}g ^£v XriXcbv ^oiQav d J, dxQL^cjg dh 
TlaQd^ivov ^OLQag >c? 7g, £7t£Ld7]7t£Q xatd tr]v dvco^a- 
kCav d7t£ix£v tov d7toy£LOV ^OLQag Qd" xrj. 6vvdy£taL 
dl xal 7} dTtb trig 7tQ(x)trjg ixlELipEcog i^tl trjv d£vtiQav 
dLd6ta6Lg rj^£Qcbv Qorj xal d)QG)v L6rj^£QLVC3V ^ /.' y\ 
10 ^OLQ&v dh QTt Td^ tov ^I%7tdQxov 7tOLri6a^ivov tr]v 
d£L^LV Sg tflg dLa6td6£G)g tavtrjg ri^£Qcbv ^£v ov6r]g 

QOrj Xal G)QCbV g L6r]^£QLVCbV^ 110LQG)V d£ QTt X. 

tr]v d£ tQLtr]v (pr]6lv £xk£LipLv y£yovivaL tm avrc» 
v£' £t£L tfjg d£vtiQag 7t£QL68ov xat Alyv^ttCovg Ms- 

15 60Qr] Ej r]Qi,ato d£ tr]g vvxtbg ^tQO^Xd-ov^Gfv g)QG)V i 
ro xal i^il£L7t£v oXr]. xal tbv ^i6ov d£ trjg ixX£Cip£G)g 
XQOvov (pr]6l y£yovivaL 7t£Ql mQag ybdXL6ta r] xal 
tQLtr^^oQLov^ tovti6tLv ^£td /3 tQCtov SQag xaLQLxdg 
Toi) ^£6ovvxtCov. dXXd tov r]XCov ovtog 7t£Ql td ^i6a 

20 tf]g UaQd^ivov iv AX£^avdQ£C(x r] tfjg vvxtbg ooQa XQO- 
VG)v £6tlv Ld xal dvo 7ti^7ttG)v' at dvo tQCtov ccQa 
c)QaL xaLQLxal 7t0L0v6LV L6r]^£QLvdg £yyL6ta dvo ti- 
taQtov. co6t£ yiyov£v 6 ^i6og XQ^^^^S ^£td td 8' 

1. Ir&v] U D, U D^ 5. iioiQav] corr. ex (lOiQ&v D^. 7. 

ansLXSv'] -v del. D^ 9. Qorj] fisv Qor] D. 14. hsi] t:, D, 

*' add. D*. MsGOQi B. 15. TCQosX&ovarjg ooQoig D. 16. j*] 

H ABCD, T~^ A\ s^slsLTCsv'] mut. in sisXinsv D\ 17. 

cpTjaCv B, comp. D. %al TQitrjfiOQLOv] r D, yQ. xal tQixriyiOQiOv 

mg. D*. 18. tovtsativ] comp. BD. tQitov] r B, r D. 

21. sativ] comp. BD. 8vo TcsfiTttcov] ^ ss D, ^ s" s" D^ 

tQitov aQu] yccQ D, y' aQU D^. 22. dvo tstaQtov] ^ j^" D. 

23. |Lt£ra] |Li D, ut saepe; /xa D^ •» 



MA0HMATIKHS STNTASESiS A'. 347 

wgag i6r]^SQLvag rijg £v rfj e' ^£0r]^PQtag. xac i^xiv 
TtdXiv 6 aTtb r&v STtox&v ^ixQi rovrov XQOVog ircjv 
AiyvTirLaKGiv cp^t, xal rj^eQcbv rXd Tcal Sq&v i6ri^£Qt- 
v&v ccTtlobg ii£v id d\ axQi^Cbg ds Ty i' d'' TtQog ov 
XQOVOV £VQi6X0^£V TOV ^£V ijXiOV £7t£xovra aKQi^cbg 5 
UaQd^Evov ^ioiQag Tf tj3, rriv 6} oeXtjvtjv n£6cjg ^£v 
^IX^vov fioiQag T xd^ axQi^&g dl ^oiQag i£ Ty^ £7t£i- 
d7Jit£Q xara rrjv dvco^aXtav a7t£iX£ rov djtoy£iov rov 
£7tiKvxlov ^OiQag 6^1%' -O*. 6vvdy£rai dl xal r] d7to 
rfjg d£vr£Qag £xX£iifj£C3g £7tl rijv rQirrjv did6ra0ig rj^£- 10 
QG)v ^£v Qo? Tcal dvo 7t£^7trcov ^idg wQag t6r]ii£Qivflg^ 
^oiQcbv d£ Q^rj v£^ rov 'l7t7tdQxov TtdUv v^tod^E^dvov 
xal ravrrjv rrjv did6ra6iv rj^sQcbv qo? xal ^iag rQi- 
xov &Qag i6ri(i£Qivrjg, ^otQcov dh Q^^rj Xy. xal ivd^dds 
ccQa (paiV£rai di£tlj£v6^£vog £7tl ^£v rcov fioiQcbv g' xal 15 
y £yyi6ra fiiccg ^oiQag^ i^tl d£ rcov rj^SQ&v rjiii6£i xal 
rQirco xal dExdrco £yyi6ra fivdg S^ag i^rj^EQivfjg^ d xal 
avrd dvvarai diacpoQav di^ioloyov 7t£Ql rbv rfjg h^to- 
^£6£G)g koyov d7t£Qyd6a6d'ai. 



1. ffi] rfi D, xfii D^. £6xiv] comp. B, -v del. D^ 3. 
Aiyvnxiuyi.mv] corr. ex ai^^ D^. xXdl -18 e corr. D^. 5. itn- 
i%ovxa B. 6. 6£Xi]VT]v'] (£) D, ut saepe; ([ D^ 7. ccnQL^mg] 
bis D, corr. D*. 9. [lOLQag] seq. ras. 1 — 2 litt. C. 10. dsv- 
riQccg] F B, p D. XQLxrjv] y' B, y D. 11. xat] corr. ex 

xa D^. dvo ne^nrcov] § f" D, corr. mg. D^. 12. vs] supra 
scr. A^; v-d- A, -'9' del. ndlLv] ndXiv r} A. 13. Qog] (ihv 
Q0<; D. (iL&s XQLXOV mQug] ayoQCOv D, cc y" db^^D^. 15. 

lioLQmv] (i C, (L C^. 5'] ABCD, supra scr. u C^ et fxrcD D^ 
16. y'] ADC^, y' |3 BC, co supra scr. C^, xqlxo) supra scr. D^ 
£yyL6xcc fiL&g] e corr. A^. 7]fi£Qa)v] {jLSQcbv C. r](iL6£L] yial 
t^ D, [_' D^. ■nai] om. D. 17. xqlxo}] T D. y,al ^«xaroj] 

post d£- ras. 2 litt. A, tp^' D; supra scr. l§ A^ et i^" C, i r" t" 
cbff £v rL6l avr lyQ^ D*. fiL&g] a supra scr. D, fiL&g D^. 



348 KAATA. nTOA. MA0HMATIKH2 2TNTAHESiS A'. 

yiyovev ovv yi^lv vit oipLV t6 rs rfjg JtQOxsi^evrjs 
dia(pG)vCag ahLOV^ ocal on d^aQQOvvrsg av sn iiaXXov 
^vyxQTiOaiiiisd^a tc3 Ka%'' ri^g anodsdsLyiisvG) koycj rfig 
avaiiakCag snl rcbv 6v^vyiG)v rijg asXTJvrjg zal avrtov 
5 rovrcjv rd3v ixXsLtjjscjv 6v^(p6vcov ^dXL6ra ralg ri^sri- 
Qaig vxod'i0s6LV svQsd-SL^cjv. 



1. r](iiv D. 3. GvvxQrjGUL^ed^cc D, corr. D*. 4. GsX^^VTjg] 
Qy D, d Dl 6. vTco&saeai D, corr. D^ In fine: KXocv8lov 
IItoX8(icclov fiad^rjiiaTfKris GvvTcc^Ecog z^ AC {KXccSiov C), KXav- 
diov IlToXsfiaiov (iaQ'r][iaTLy.f]g GvvTa^soog ^l§Xlov J B, KXavdCov 
IlToXEfiaLOv (laO^jjfiaTLyimv J D. 



E'. 

Tdds ^v£6tiv iv rcl e' rav tov Ilxoke^aCov ^ad^rj- 
liattxcjv' 
a' , TtSQi zat a0KSvfig a^tQoXd^ov OQydvov. 
/3'. TtBQl tfjg TCQog triv diTcXfjv dvco^aUav tfjg 6£X7]V7]g 5 

VTtod^S^ECjg. 

y'. 7C£qI tf]g Jtr^XLXotYjtog tfjg itaQa tbv tjXlov dvco- 

^aXcag tfjg ^sXt^vrjg. 
d'. 7t£Ql roi) kdyov tfjg mx^vtQOtrjtog tov ^^Xrjvta- 

xov xvxXov. 10 

e'. it£Ql tfjg 7tQO0v£v0£G)g tofj tfjg 0£Xrjvr]g iitiXvxXov. 
g'. Jtag dtd tcjv yQa^ficov ditb tav %£Qio8Lxmv xi- 

vr]6£C3v r] dxQi^r]g tf]g 6£kr]vr]g itdQodog ka^- 

pdv£tai. 
^'. itQay^at£ia xavovog tfjg xad^oXov 6£kr]Viaxff]g dvco- 15 

[laXiag. 
7]'. xavoviov tfjg xad^okov 6£kr]Viaxf]g dvcj^akiag. 
^'. 7t£Qi tf]g xad^oXov 6£lr]Viaxf]g ipr]cpoq)OQiag. 
i'. ort ^r]d£v d^ioXoyov yiv£tai did(poQOv iv tatg 

^v^vyiaig TtaQa tbv £XX£vtQov tf]g 6£lr]vr]g 20 

xvxkov. 



1. E'] om. ABCD. 2. tmv — iiaQ-THLaTiv.cbv\ rrjg UtoXe- 

liULOv (icc^7]fiatLv,7]g Gvvtd^8(og B, om. D. 4. a'] et numeros 

ceteros om. D. 6. vTtod-sGscog] om. D. 9. ivyievtQotrjtog D. 

11. Supra GsX^^vrig scr. ([ D. 12. y.iv^aeoav] snox&v D. 

15. ccvoniaXiag^ av D. 17. yiavoviov — avcofiaXLag] om. D. 



350 KAATAIOT nTOAEMAIOT 

la'. tcsqI r&v tfjg 6el7^v7jg jtaQaXM^scav. 

L^\ tcsqI Kata6}csvrjg OQydvov jtaQaXXaxtixov. 

Ly\ aTCodsL^ig tcov tfjg askTjvrjg d7Co6tri^dt(ov. 

Ld\ TtSQL tfjg TCTjXLKdtrjtog tcov sv tatg ^v^vyLaLg <paL- 
5 vo^svov dLapLStQCJv rikCov xal 6sXrjvrjg Tcal 6xLag. 

Ls\ tcsqI tov rjhaxov dno^trj^atog xal tcav 6vva7C0- 

dsLXvv^svcjv avtm. 

Lg\ tcsqI ^sysd^cjv rjXLOV xal 6sXrjvrjg xal yrjg. 

Lt,'. 7CSQL t(5v xatd ^s'Qog %aQaXld^sc3v riXCov xal 
10 6sXr]vrjg. 

Lri'. xavhv naQalkaxtLx6g. 

Ld''. tcsqX tfjg tcov TCaQaXXd^scov dcaxQL^scjg. 

a. HsqX xata6xsvf\g d6tQoXdpov dQydvov. 

"Evsxsv [isv dij tc5v TCQog tbv tjXlov 6v^vyLcav 6vv- 
15 odLXcov ts xal 7Cav6sXrjVLaxc5v xal tcov jcar' avtdg 
dTCotsXov^svcov sxksLipscov s^aQxov6av svql6xo^sv trjv 
sxtsd^SL^svrjv STcl tfjg TCQCotrjg xal aTcXfjg dvco^aXCag 
vTCod^s^LV^ xdv ax>tb [lovov ovtcog rjfitv Xa^^dvrjtaL^ 
TCQog ^svtOL tdg xatd ^SQog stcI tcov dkXcov TCQbg tbv 
20 rikcov 6%ri[iatL6^G)v TCaQodovg ovxst' dv avtdQxrj tLg 



1. TtSQL — 2. TCKQalXayiTL-KOv] om. D. 5. dLcc^Ji D. oxtag] 
a- postea ins. A. 7. avrw] avt&v C. 8. nsQL — yfig] om. D. 
11. TtaQaXla-KTLyidg] pr. % corr. ex X D. Post indicem add, 
'EfinsdoyiXfjg dinXdaLOv ansxsLv xriv (J anh xfig yfig sSo^a^sv, 
OL ds icnb xmv (la&rjfiaXL-n&v Sckql^sgxsqov snL^dXXovxsg {snL- 
^aXov'' J)) dy.xcoy.aLdsTianXdaLOV : — (: — om. CD) 'EQaxood^ivrjg 
xbv tiXlov ansxsLv axadLcov anb xfjg yfjg fivQLaScov x v.al onxd-ALg 
^vQLoav : r>o ( : oo om. C) xi]v Ss asX^^vrjv dcnsxsLV xfig yf]g (ivQLa- 
dcov s^doinq-Kovxa oHTcb axadLoov BCD^ 13. «'] om. AD, 

mg. B. nsQi] nsQL xf^g C. Post oQydvov add. s A. 14. 
a mg. D^. av^vyLmv] xfjg asXrivrig av^vyiwv D. 18. Xayir- 

pdvsxaL D, corr. D^ 20. naQodov D, corr. D^ ovnixL BC. 



MA0HMATIKHS STNTAgEiiS E'. 351 

avtrjv evQOL dta rb xal dsvtsgav^ g)s sg)a[isv^ xata- 
Xa^pdvsdd^ac tfjg osXi/lvrjg ava^alCav jtaQa tag TtQog 
tbv yiXlov d7C06td6sLg dTtozad-L^ta^svrjv ^sv slg trjv 
7CQ(btriv jcat d^tpotsQag tdg ^vt.vyCag^ ^syC6trjv ds 
yLvo^evrjv xat d^q)OtsQag tdg dLxoto^ovg. xatrjvsx- 5 
d-rj^sv ds sCg triv tOLavtrjv S7tL6ta6Cv ts xal 7tC6tiv 
dito ts tcov V7tb Toi) 'l7t7tdQXOv tstrjQrj^svcjv xal dva- 
ysyQa^^svcov trjg asXrjvrjg TCaQodcov xal djtb t&v rj^tv 
avtotg SLlrj^^svcov dLa tov 7tQbg td tOLavta rj^tv xa- 
ta6xsva0^svtog OQydvov^ TtSQLSxovtog ds tbv tQo^tov 10 
tovtov. 

dvo yccQ KvxXovg Xa^ovtsg dxQLPcbg tstOQVsv^svovg 
tstQaycovovg tatg STtLcpavsCaLg xal 6v^^stQ0vg ^sv rco 
^sysd^SL^ ^tavtaxod^sv ds L6ovg xal b^oCovg dXXt^Xotg^ 
6vvrjQ^66a^sv xatd dLd^istQOV 7tQbg OQd-dg ycovCag i7tl 15 
tcbv avtcbv STtLcpavsLcov^ co6ts tbv ^sv stSQOV avtcov 
vost6%-aL tbv dLa ^s6cov tmv ^codCcov^ tbv d' stSQOv 
tbv dLcc tcov 7t6Xcov avtov ts xal tov L6rj^sQLvov yL- 
v^^isvov ^s6rj^PQLv6v' scp ov Xa^6vtsg dTtb trjg tov 
tstQaycbvov 7tkBVQdg td tovg tov d^d ^s6cov tav ^c)dCcov 20 
xvTcXov Jc6Xovg dcpoQC^ovta 6rj^SLa xal s^7toXC6avtsg d^- 
(p6tSQa xvXLvdQCoLg s^sxov6lv 7tQ6g ts trjv sxtbg xal trjv 
svtbg STtLCpdvsLav xatd ^sv tcbv sxtbg svs7toXC6aiisv dXkov 



2. TCQog — 5. cciicpoxiQctg] in lac. complurium linn. ins. A^ 

3. 0.7106X0.6 iig] O.7C0V,OXa6xd6tl(S B. O7l0V.O%^i6XOliiv7]v] -L6XO- 

e corr. A^. 7. xcbv'] -c5- in ras. A, supra scr. D^ vtio] 

om. D. 9. yioxo6v,Eo6Q'Bvxoq D. 12. Xo^^dvovxsg C. 13. 
i7ti(povsiaig] ^tSQLcpsQsCaig D. 14. 8' i'6ovg corr. ex ds^ovg D*. 

16. xov] corr. ex x6 D^. 18. xov] xcbv B. noXoiv] -X- 

corr. ex d A. 20. xd] supra scr. D*. xov] supra scr. D^ 

21, ifi7coXi6ovxsg] -Xi- in ras. D, tj supra scr. D^, s^TcodC^ovxsg 
BC, corr. B^C*. 22. s^^xov^l D. 23. x&v] xr\v D. sv- 
S7toXi6a^sv] -Xi- in ras. D^, tj supra scr. D^. 



352 KAATAIOT nTOAEMAIOT 

xvkIov ccTCto^Evov Tcavxa^oQ^Ev ccKQi^&g rfi xoiXri avtov 
eTiKpavHa rij? %vQtrig t&v ^vvrjQ^o^^avcov dvo xvxXayv 
xal dvvd^evov TtSQLdyB^d-ai %atd ^fJKog tcsqI tovg el- 
Qrj^avovg TCoXovg tov dtd ^£6g)v tobv ^cidicjv^ xatd ds 
6 tcbv ivtbg b^iOLcag dkXov xvxXov ivsTCoU^a^sv aTCto- 
fievov ^ev xal avtbv Ttavtaxod^ev aKQLpag tfj xvQtfi 
avtov imcpaveLg^ tfjg xoCXrig t&v dvo xvxlcov^ iCBQLa- 
yo^evov de b^OLCjg xatd ^rjxog TteQl tovg avtovg ico- 
Xovg tGi e%Gi\fev. ^ceXovteg 8\ tovtov te tbv ivtbg 

10 xvxXov xal etu tbv dvtl tov did ^edcDv tCbv ^cjdLcjv 
yevo^ievov eig tdg vicoxeL^evag tf^g jteQL^etQov fiOLQag 
t|, xal o6a ive8e%eto tovtcov ^eQrj^ vcprjQ^66a^ev dxQL- 
^cbg eteQov Xeictbv xvxXl6xov dndg e%ovta xatd dcd- 
lietQOv i^e%ov6ag vjtb tbv ivtbg t&v dvo xvxXcyv^ 

15 OTCog dvvrjtac 7taQa(peQe6d'aL xatd tb avtb ixeCvG) i%L- 
Tcedov mg itQbg exdteQOv tcbv ixxet^evcjv itoXov evexev 
tf]g xatd TtXdtog 7taQatrjQ7]6ecDg. tovtcnv 8* ovtcig ye- 
vofievcov d7to6t7]6avteg iitl tov dc' d^cpotEQCjv tcbv 
TtoXcjv voovpiivov xvxXov dcp exateQOv tS)v tov t,(p- 

20 dLaxov TtoXcov trjv ^eta^v dedeLy^ivrjv iteQLtpiQeLav 
t&v dvo TtoXcov tov te dt« ^i6cov tcbv t^codCcov xal 
tov L6rjfieQLVov td yevo^eva Tti^ata xatd dLdfietQov 
TtdXLV dXXrjXoLg ivejtoXC^a^ev xat avtd TtQbg tbv 



2. avv7]Q(i06\(iev(ov A, 6vvr}Q(io\6{isvcov A\ SLQ(io6(isv(mf D, 
r)Q(io6(isv(ov D^ 5. rmvl rriv D. svsnoXL6a(isv\ AB^C^ 

ivs7co8L6cc(itv BCD, ivsnoX7]6a(isv D^. anx6(isvov^ -(isvov 

add. A^. 6. (i,sv ■aaX a-bxov^ om. A. 'navta%6%'tv'\ nav- 

add. mg. A^ Y,vQTfi corr. in y.vQxfjL A. 9. tw] corr. ex 

raiv C^ 10. t6v] t&v C. 11. yLv6(isvov CD. 14. rdv] 

e corr. D^, t&v C. 16. ms] corr. ex 6 D. iynsL^jLsvcov D. 

17. 8'] 8s D. 23. ivsnoXL6a(isv] -XC- in ras. D^, -It]- supra 
scr. D^ ivs7todL6aasv BC. 



MAeHMATIKHS STNTASESiS E'. 353 

o^Oiov iia6riiL^Qivov rcov iv &QXV '^'^S ^vvtd^ecog vTto- 
dsdeLy^evmv TCQog tag trjg ^sta^v t&v tQOTtiKcbv tov 
^sCrj^PQivov TCBQicpsQsCag trjQ7]6SLg^ S6ts tovtov jcara 
tijv avtijv %^s6iv sksCvco nataOtad^svtog j tovts6tiv 
OQd^ov ts TtQog tb tov oQC^ovtog sjcCjtsdov %al y.ata to 5 
OLTCStov s^aQ^a tov 7t6kov trjg VTtoKSL^svrjg OLKr]6scog xal 

StL TtaQallriloV tlp tOV CpV^SL ^Sdrj^PQLVOV STtLTtsdCi}, 

trjv tcbv svtbg kvkXcov JtSQLaycoy^v a7totsksL6%^aL jtSQl 
tovg tov L6ri(isQLVov TtoXovg ait avatoXcbv snl dv0^ocg 
dxoXovd^cog tfj tcbv oXcov TtQcotr] cpoQa. 10 

tovtov dij tbv tQo^tov Ka%L0tavtsg tb oQyavov^ 
ojtoodxLg '^TtSQ yrjv d^a (paCvs^xtai rjdvvavto 6 ts 
7]lLog xal rj 6sXr]vr]^ tbv ^sv s^cod^sv tcbv d^tQoXd^cov 
KvxXov xad^C^ta^sv sjtl tijv Tcat ixsCvrjv tijv S^av 
svQL6xo^svr]v syyL6ta tov r]lCov yiOiQav Tcal JtSQirjyoy^sv 15 
tbv did tcbv TtoXcov Kvxkov^ OTtcog tf]g xatd tr]v r]XiaKi]v 
^OLQav t&v xvxkcov to^r]g TtQbg tbv rjliov aKQi^&g 
tQS7to^svr]g 6Kid^co6iv avtovg d^a ol kvxXol d^g)6tSQ0L 
o ts dLcc (IS6C0V tG)v ^GodCcov xal 6 dLa tcbv jt6Xcov av- 
rov, r] idvTtSQ d6ti]Q f] 6 dLOTttsv^^isvog, oitcog tov 20 
svbg tcbv 6(p&aX(icbv TtaQatsd^svtog tf] stSQcc tcbv Ttksv- 
Qcbv tov Tcad^s^ta^isvov s^cod^sv tcvkXov VTtb ti]v -bTto- 
xsL(isvr]v avtov xatd tbv did (is6cov tcbv ^codCcov tcv- 
TiXov (lOiQav xal dtd tfjg ditsvavtCov xal JtaQaXXrjlov 
Tov xvxXov TtlsvQdg co67tSQ xsxoXkr](isvog dficpotSQaig 25 

1. Tc5v] ro5t D. avvd^scos D, corr. D^ ccnodsdsiyiia- 
Vioi D. 5. xafc] supra scr. D^ 7. naqaXlrilovg D, corr. D*. 

9. avaToXa>v\ -ar- e corr. C. 16. Kvy.Xov] corr. ex ■nviiXcav C. 

rrig] corr. ex rs D^. 18. ayiid^ovoiv C. avtovg] A, avrovg 
BCD. 20. ri idvnsQ] idv dh 6 I>, 6 del. D^, t) idvnsQ d6tr]Q 
rj mg. D^. 22. yad-LGta^isvov B. vno] inC D. 23. trov] 

BDA^, ToTA, riov C. 24. dnsvavttov] -vav- ins. A^ 25. tov 
'nvY.Xov] om. D, Tc5 supra scr. D^. yisy.oXXrj^iivaig D, sed corr. 

Ptolemaeus, ed. Heiberg. 23 



354 KAATAIOT nTOAEMAIOT 

ttvtmv tatg STa^paveCaLg 6 a<5rriQ iv t(p Sl' avtav ijti- 
Ttedcj dtOTitevrjtai. tbv de etegov xal ivtbg tcov d6tQ0- 
Xd^cov TcvxXov 7taQe(peQ0^ev TCQbg tijv ^eXijvrjv ij xal 
TtQog aXXo ti tcov ^r^tov^evcjv^ OTtcjg a^a ty roi) ijXtov 
6 7] xal akkov tov vTtoxei^evov diO7ttev0et xal rj 6eX7]vr} 
TJ xal dXXo tt tcjv ^rjtov^evcov dta tcbv xata tbv vcprjQ- 
^o6fievov xvxXtefxov oTtcbv d^cpoteQcov dtoTttevrjtat. 

ovtcog yaQ^ Ttotov te xatd ^ijxog iTte%et tov dta 
^e6cov tcbv ^cjdtcjv t^ij^a^ iittytyvco^xo^ev ix tr^g xatd 

10 triv tov iGodvva^ovvtog avta xvxkov dtatQe6tv yt- 
vo^evr^g tov ivtbg xvxXov to^Tjgj xal 7t66ag avtov 
^otQag d(pe0trixev rjtot TtQbg ccQxtovg i) TtQbg ^e^r^i- 
^Qtav cog ijtl tov dtd tCbv Ttokov avtov xvxkov^ dtd 
te tfjg ai^tov tov ivtbg d^tQold^ov dtatQe^eag xal 

15 trig evQt6xo^evrjg dta6td6ec3g ditb fie6rjg tfjg vjteQ yr}v 
ojtfjg tov V7t avtbv TtaQayo^evov xvxXt0xov iitl f^v 
lie6riv yQa^^ijv tov dtd ^e6(ov t&v t^codtcav xvxXov. 

/3'. IleQl trjg TtQbg tijv dt7tkr]v dvo^aXtav trjg 
6eXrjvrjg v^tod-e^ecjg. 
20 ^ATtkSig [lev ovv ytvo^ivrjg tfig totavtrjg 7taQatrjQr]- 
^ecog aC tfjg 6ek7]vrjg 7tQbg tbv 7]hov dta6td6etg, ex te 

2. Si07tTSvr}tai] -o- e corr. A*. de^ d' D. 3. Ttccga- 

cp^QOfisv BD. 4. tcov ^rjtovfisvoiv] corr. ex tb ^ritovfisvov D^ 

6. Tc5v ^ritovfievcav^ corr. ex tb 'Qr^tovfisvov D^ tav (alt.)] 
-mv e corr. D, v.at cc tov] supra scr. D^ 7. y.vnXLCyiov] -Xi- 
e corr. D^ ijTiOTttsvritav B. 9. iTnyLyvmGKOfiav] A, ini- 

yivm6y,o(isv BC, S7csyivoo6yio(isv D. 10. i^odvvafiovvtog] ante 
3 ras. 1 litt. D. avto C. diaiQS6iv] v.ata trjv 8iaCQS6iv D. 

14. cc6tQold§ov] a6tQold§ov v,vv.Xov D. 18. p'] mg. ABC, 
om. D. nsQL — 19. vno%-s6sa)q] hic om. D, qui %vv.Xov lin. 17 
et anXmg lin. 20 coniungit {v.v\v.Xov a\ diremit D^ {v.vvXov \ a); 
nsQt — vno^sesoiq mg. superiore D* et addito x,/ |3 mg. ex- 
teriore D^. 20. tfig] supra scr. D^. 



MA0HMATIKHS LTNTA^ESiS E'. 355 

G)v 6 "iTtTtaQXog ccvayeyQaipsv ^ %al i^ (bv rj^stg irrj- 
Qov^sv^ TtOTS ^ev 0v^(pc3voi Kateka^^dvovto totg xata 
tiiv exKSL^svrjv viiod^e^iv STtiloyi^^oig^ Jtote de dtd- 
(pcovoL %al dtdcpoQOL^ Ttote ^ev oXiyui^ %ot\ ^\ TtolXm. 
TtXeiovog d' rjatv xal TteQceQyoteQag tf}g e7ti6td6eG)g 5 
Katd t6 Gvvexeg ycvouevrjg TteQi tr^v td^iv tfjg tot- 
avtrjg dvo^aXtag xatela^^avo^ed-a, ort TteQt ^ev tag 
6vv6dovg aiel xal tdg jtav^elrjvovg i) ovdev ai^d^r^tbv 
dta^aQtdvetat rj ^Qa^v^ xal o6ov dv ai naQakkd^etg 
tr]g 6eXr]vrjg dvvatvto itotetv dtdtpOQOV^ TtSQt de tdg lo 
dtxoto^ovg diKporeQag eldxt6tov ^sv r] ovdev dia^aQ- 
tdvetat trjg 6eXrjvrjg xatd tb ditoyetov ij TtSQiyetov 
Tov eTttxvicXov tvy%avov6rig ^ 7tket6tov d\ otav JteQl 
tovg fie6ovg dQo^ovg ov6a 7tXet6tov xal tb itaQa f^v 
TtQcotrjv dvG}^akiav dtd(poQov notfj^ xat ott dcpatQe- 15 
tfnrig ^ev ov6rjg trjg 7tQd)trjg dvay^aXiag ev OTtoteQa 
t&v dtxoto^cov ett eld66cov 6 toTtog avtfjg evQi6xetat 
wv ex tf^g TtQCJtr^g d(patQe6scjg STttXoyt^o^evov ^ 7tQ06- 
"^d^sttxflg ds stt TtXsicjv C36avrcjg xal dvaXoycjg ta ^s- 
ysd^st tfjg TtQCDtr^g 7tQ06^a(patQs6S(og ^ cog dtd tavtrjv 20 
tfjv td^tv fjdrj 6vvoQav rj^dg^ ott xal tbv STtixvxXov 
tfjg 6sXrjvr]g STtl sxxsvtQOV xvxXov (psQs6^at VTtoXrjjttsov 
ditoysLOtatov ^isv ytvo^svov JtsQt tdg 6vv6dovg xal 



1. 6] om. C. 2. fisv] -Ev renouat. C. 3. Ss] corr. ex 
^ev D^ 4. SidcpoQoi] Sidcpcovoi D. 6. yLvo(i8vr]g] om. D. 7. 
avconaXtag] ccvco^iaXLag ytvo^isvrjg D. Hic mg. nsQi p. 354, 18 
— 19 vTtod-sGscag D {rcQog] sig). 9. dtafiaQTavsi, D , corr. D*. 

^Qaxvg BC, corr. C^. 10. dvvaLzo D, corr. D^. 12. ano- 
yaLov D, corr. D^. 14. SQOfiovg ovoa] corr. ex dQOfiovaa C*. 

15. 7C0LSL CD. 19. TtXslov BC, corr. C^ aaavToag] -co- 

e corr. D. 20. nQoad^acpaiQ^ascog] -at- in ras. D. 22. iti- 
^svTQOv] corr. ex tisvtqov D. vnoXi^nTsov] post r} ras. 1 

litt. D. 

23* 



356 KAATAIOT nTOAEMAlOT 

rocg jtavdeXnjvovg^ TtSQtysLOtccrov ds JtSQL dfi(porsQag 
rag dixordiiovg. Gv^Paovoi S' av rb roiovrov rr^g jtQCJtrjg 
vTtod^s^scjg roiavrriv riva rr^v dt,6Qd'(X)6Lv Xa^pavov6rjg. 
vosiOd^G) yaQ 6 ^£v d^oKSvrQog rm dcd ^b6g)v r&v 
5 ^CDdtcDV xvxlog iv ra ko^m rrjg 6elrjvrig eitiTtBdco itQori- 
yov^evog^ S^jteQ xal jtQoreQov^ eve%ev rov jtXdrovg 
jteQl rovg rov did ^e6cov r&v t^codCcov 7t6lovg ro6ov- 
rov^ O0G) v7ieQe%eL rf^g xard iifjxog mvrj^ecog r] xard 
Ttldrog^ rj de eelrjvrj rbv xaXoviievov iTtUvxlov ite- 

10 QieQ%o^evYi TtdUv mg xard rrjv dit^yeiov avrov TteQi- 
(peQeiav eig rd TtQorjyov^eva rijv ^erdpa6iv 7toiov[ievrj 
dxoXovd^cjg rfi rfjg TtQcorrjg dvcofiakiag d%o%ara0rd6ei. 
ev dri rovrG) ra Ao|« eTtiitedco dvo xivrjeeig evavrCag 
dkXfjlaig vjtond^efied^a b^aXdg xal TteQi ro rov did 

15 ^e^cov rG)v ^mdCcov otevrQOv d^KporeQag^ (bv ^Cav fiev 
rf^v JteQidyov6av rb rov emxvxlov icevrQOV eCg rd 
e3t6^eva rcov ^gjSCcjv dxoXovd^cog rfj xard nkdrog xi- 
vfj6£i^ ^Cav de rrjv 7teQidyov6av rb xevrQOv xal rb 
d7t6yeiov rov ev t« «vt» eitiTtedco Xa^^avoiievov ex- 

20 TtevrQOV KvxXov^ e(p ov Jtdvrore rb xevrQov e6rai rov 
ejtixvxXov^ 7teQidyov6av de eCg rd TtQorjyov^eva rcbv 
iGjdCcav xal ro6ovrov^ 0603 v7teQe%ei rfig xard TtXdrog 
xivfi6eG)g diTtXcjd^et^a r] d7to%f\^ rovre^nv f\ v7teQ0%f\ rf\g 
xard ^rjxog 6eXr\viaxf\g ^e6r\g xivr\6ecog TCQbg rr\v f\Xia- 

25 xfjv. co6re ev rr\ ^ia r\^eQa X6yov evexev rb ^ev rov 

1. rag] om. D. nccvGsXijvovg^ 7tciv([ D. neQLoysLOTcc- 
xov A. TtBQL^ v.ccz' D. 2. Gvfi^ccLvsL D, corr. D^. xoiovr.o D, 
corr. D^. 5. rc5] rcot corr. ex %& A. Ttfforjyovfiavrjg B, 7. 
^codLoav'] ^coSlcov v.vv.Xov D. 8. o6ov D. 17] i'] B. 10. xara] 
y.ccxcc xd C. 15. v.svxqov a^cpoxs-'] in ras. D. 16. xov] -v 

eras. A. 19. avxm] avxov BC, corr. C^. Xafi^avofisvov] 

-ov in ras. D. 23. 17 (alt.)] supra scr. D^. 25. moxs] -s in 
ras. 2—3 litt. D^ 



( 



MA0HMATIKHS 2TNTASESiS E'. 357 

ajtLXVK^ov TtdvxQov XLvov^svov Tccg rov TcXdtovg ^ocQag 
ly Ld eyyLdra sig ra STtd^eva rG)v ^ipdLCov STtl rov Slcc 
fi£6(ov rcbv t^codCcav cpaCvscd^aL TCaQCjdevxbg rag rov fti^- 
xovg fioCQag Ty Ta dLa rb oXov rbv Xo^bv xvxXov avd"- 
v7to(psQeLV sig ra jtQorjyov^sva ra rTJg vTtSQOxrjg 5 
s^rixo6ra rqCa^ ro df a7t6ysLOV rov sxxsvrQOv dvrLJts- 
QLaysOd^aL TtdlLV slg rd TtQorjyov^sva ^oCQag Td '9', 
o6aLg v7tSQS%ov6Lv aC dtTtka^Covsg rfjg aTtoxfjg ^otQac 
xd xy rdg rov nldrovg fioCQag Ty lS. ovrc^g ydQ sk 
rfig d^cporsQcov rcbv klv7J6scjv dvrLTtSQLaycoyfjg nsQl rb 10 
xsvrQov^ cjg scpa^sv^ rov Slcc ^s6cav rcbv ^codCcav yc- 
vo^svrjg rj dto: rov xsvrQOv rov STtLXVxXov rfjg dLa rov 
xsvrQov rov sxxsvrQov %Qo6a7to6rri6sraL rr^v ^vvrLd^s- 
^svrjv sx rs rav Ty lS xal rav Td d^ fioLQcbv TtSQLcps- 
QSLav dLTtXfjv yLVO^svrjv r&v ditb rfjg dTtoxfjg fioLQcbv 15 
ij3 Td L! syyL6ra. xal d^d rovro dlg iv rm ^£6C3 ^r^- 
vLaCca XQOvco rbv sxxsvrQov 6 STtCxvxlog 7tSQLslsv6srai 
rfjg TtQbg rb dTtoysLov rov sxxsvrQOv voov^svr^g d^toxa- 
ra6rd6scDg sv ralg ^s6cjg d-scjQOv^svacg 6vv6doLg rs 
xal 7tav6skrivoLg v7torL^s^svrjg d^torsXst^d^aL. 20 

Lva ds piakkov rj^tv V7t otf^LV ysvi^raL rd rfjg v7to- 
%^s6SG)g^ vosC6^G) TtdXLV 6 sv r<p Ao|«l rfjg 6sX7]vrjg 
STtLTtsda tg5 dLd ^s^ov r&v ^ojdCcov bpLoxsvrQog xvxkog 



1. rag] post ras. paruam D. 6. s^7]yio6xa\ ^a" D. xqlo] 

corr. ex xQixa C^, T B, y' D. 7. /tiot^as] -oC- e corr. in 

scrib. A. 8. 8niXu6CovBq\ -sg e corr. D^ anoxfjg] -no- in 

ras. A. 9. td] -d e corr. in scrib. D. ovxco D. 12. Eni- 

yivyiXov — 13. v,bvxqov xov~\ om. BC. 15. 8inXfiv\ St- in 

(h 
ras. D. ano] om. D. 16. /_'] corr. ex ^ Dl /ti mg. A. 

17. IhK D, '''' add. Dl 22. voeCa^coL D. 



358 



KAATAIOT nTOAEMAIOT 




6 ABr/1 tcsqI TtivtQov xo E xal did^stQov t^v AEF^ 
V3tox6t6d^(o ds a^a ;c«ra t6 A 6rj^£iov to ts aTtoysiov 
tov ixxBvtQov Tcal t6 XSVtQOV 
tov STCiTcvxXov xal t6 pdgsiov 
5 TtSQag xal rj aQxrj tov KQiov 
xal 6 ^s6og ^liog. iv toCvvv 
T§ r}^£Qrj6i(x TtaQodco t6 ^lsv okov 
sjtiTtsdov cpriiii xivsi0d-ai sig ta 
TtQoriyov^sva hg ccTtb tov A snl 

10 t6 z/ TtsQi t6 E xsvtQov s^rj- 
xo6ta y syyi^ta^ G)6ts t6 A 
fioQSiov TtSQag yCvsdd^ai xata tag 
t&v 'Ixd^vmv iioCQag xd' v^, t&v ds dvo VTtsvavtCcov 
Xivrj0s(x)v vTtb tfjg b^oCag tfi EA sv^sCag TtSQi t6 E 

15 Ttdkiv tov did iis6(x)v tcbv ^codCcov xivtQov o^aXcog 
aTtotsXov^ivcov inl tfjg r]^SQr]6Cag G)6avtcog cprj^l itaQ- 
odov trjv fisv did tov xivtQOv tov ixxivtQov b^oCav 
tfi EA %SQia%%^Si6av b^aX&g slg td jtQorjyov^sva t&v 
^(pdCov cjg iiti trjv E^ tb ^sv djtoysiov tov ixxiv- 

20 tQov (piQSiv iTti t6 z/ xal yQdcpsiv jisqI t6 Z xivtQOv 
tbv AH sxxsvtQOV, trjv ds A/i %SQi(piQSiav itoislv 
^OiQCov Ta %^j tr]v ds 8id tov xivtQOV Toi) ijtixvxlov 
nsQl t6 E JtdXiv b^al&g 7tSQiax%Si6av sCg td sjto^sva 
tcbv t,(pdCci)v cog tijv EB (piQSiv ^sv ijtl t6 H tb xiv- 

25 tQOV tov STtiXvxkov^ trjv ds AB %SQi(piQSiav %oislv 



1. AEF] seq. ras. 3 litt. D. 3. b-a-abviqov] h D, ^hK'' D*. 

yihxQov'] om. D, K*** supra scr. D^, item lin. 10. 10. 8^,7]- 

-A06td\ s|a D, g||a D^. 15. v.BvtQOv] %"! D, " add. Dl 21. 

Tov] AD, t6 BC. eWD, ?xh*'*' Dl 22. iioiq&v'] ^ D, ^' D^ 
et similiter saepe. 24. TtsQKpsQSiv D. v.tvrQovi -vxqov in 

mg. transit A\ y, D, K'"' D^ 25. xov] -v in ras. 2 litt. A^ 



MA0HMATIKHS STNTASESiS E'. 359 

lioLQcav Ty td, &0xe t6 H xsvtqov rov iTtixvTclov aTCo 
^sv tov A ^OQsCov TCSQarog a7t8%ov (paivsad^aL rag Ty 
id ^OLQag rov TtXdrovg^ cctio dl rrig dQ%rig rov Kqlov 
rdg Ty Td ^OLQag tov ^rixovg dtd rb rb A ^oquov TtSQag 
sv ro6ovr<p ysyovsvau xard rdg rcjv 'Ixd^vcov ^OLQag 5 
xd- vt,^ djtb ds rov z/ ditoysLOv roi) sxxsvtQOv rdg 6vv- 
ayo^svag 6vva^q)orsQ(ov rfjg rs AA xal AB TtSQL(ps- 
QSLobv 7cd Tcy ^OLQag^ al sl6lv 8L7tka6L0vsg rcjv rfig 
rj^SQri^Lag ^sdrjg dTtoxfjg. ovrcjg ovv^ snsLdri <3vva^- 
(porsQttL 7] XE did rov B xal rj dta rov A XLvrj^Lg sv 10 
ra ri^L6sL rov ^s6ov ^rjVLaLOV xqovov rrjv ^Cav dno- 
xard0ra6LV TtOLOvvraL TtQog dXXt^Xag^ dfjlov, orL sv r^ 
6' rov avrov XQ^'^^'^ '^^^ ^''^^ *'^ "^^ ri^CcsL xal rs- 
raQrip ndvrog dLa^srQ7]0ov0LV dXXrikag^ rovrsarLV sv 
ratg ^s0C3g ^scDQOv^svaLg dLxoro^oLg^ rb ds dLa rfjg 15 
EB xsvrQOV rov STtLXvxkov dLa^srQfjOav rb d^d rfjg 
EA dnoysLOv rov sxxsvrQov xard rb TtSQCysLov avrov 
ysvrj^sraL. 

cpavsQOv ds, orL xal rovrcov ovrcjg syjovrcov itaQd 
(isv avrbv rbv sxxsvrQov^ rovrs6rLV rf^v dvo^OLorr^ra 20 
rfjg AB nsQLCpsQsCag TtQog rrjv z/ii/, ovdsv s6raL dLa- 
€poQOv TtaQd rrjv o^alrjv xCvr}6LV rfjg EB sv^sCag 

1. id] mg. add. A^ 4. m] corr. ex lS B^ (loigag] 

om, D. t6] om. C. A'] corr. ex TtQ&Tov D. 5. Post 

xoaovxcp del. ovtan D. 6. ^v.v.svtQov] fxK ^i " add. D^ 8. 
SinXccGLovBs ta>v] -vsg t&v e corr. A, dLnXdoLOv iatcov C. 9. 
iTiELdrf] corr. ex stieC D^ Gwcc^cpotBQaL] ABD, avvaficpotSQu 
CD^. 13. ttL iv tm rjfiLGSL] corr. ex hrj b asL D^ supra scr. 
v.aL iXL iv Tc5 r}iiLGtL Kal S'^ D^. TStdQtoj]'^' B, Tj D, j" D*. 

14. tovtsGTLv] supra scr. D^, i D, tovA' D^ 15. ds] A, 

[om. BCD, -naL 8Ld tovto supra scr. D*. 16. nsvtQov] corr. ex 

yisvtQov B*. 17. tov] corr. ex t6 Dl ixK D, ** add. Dl 19. 

KaloTLl). 20. fy.;4 D, "'^ add. D-. TovTtGrit'] comp. B, -j/ del. D^ 



360 



KAATAIOT nTOAEMAIOT 



ov rrjv z/i/ tov ixxEVTQOv 7tEQL(p8Q£tav, aXXa xy\v z/5 
xov dia 1186G3V XG)v t,€pdL(ov b^alCbg 7C6Qi£Q%o^svrjg dia 

Xb flYj Jt£Qi xb Z TiivXQOV XOV £KX£VXQOVy 7t£Qi ds xb 

E TCOiEiGd^ai xriv jtSQiaycoyi^v^ itaQa d£ ^ovrjv xr]v xax 
5 avxbv xbv iTCiKvxXov yivo^ivrjv diacpoQCiv ix xov %£- 
Qiy£i6x£Q0v avxbv yiv6^£vov av^£iv ahl xb itaQa xijv 
dv(D^aXiav didcpoQOv i^ l'6ov xaxd xs d(paiQ£6iv xal 
jtQbcd-E^iv xr]g dTtoXa^pavovdrjg avxbv JtQbg xfj 6ip£i 
ycoviag iv xaVg 7t£Qiy£iOX£Qaig %-£6£0iv ^£i^ovog dito- 
10 x£kov^£vr}g. 

ovdlv ^£v ovv £0xai JiaQa xrjv TtQCJxrjv vn6%'£0iv 
xa^^Xov didipoQOVj orav xaxd xb A d%6y£iov fj xb 

XEVXQOV XOV iltiXVxXoV^ yiVO^EVOV XOV XOiOVXOV TtEQl 

xdg fi£0Ci)g ^ECjQov^ivag 6vv6dovg 
15 xal 7tav6£Xr]vovg. 

idv yaQ yQd^co^EV 7t£Ql xb A 

xbv MN iTtixvxXov^ 6 xrjg AE TtQbg 

xrjv AM X6yog 6 avxbg yCvsxai x^ 

did XG)v ixXEitl^Ecav dTtodEdsiy^ivip, 
20 xb dh 7tX£i6xov E6xai didcpoQov^ 

oxav xaxd xb H xov ixxivxQOv 

7t£Qiy£i6xaxov 6rj^£tov 6 i^tlxvxXog 

Ttoirjxai, xrjv 7tdQodoVy dyg 6 yQa^ 

1. ov] D (supra est ras.), ov ydq ABC. ^v.v.ivxqov^ corr. 

ex £x Dl 2. nEQisqxoybhrii] -s del. Cl 3. fxK I^, ^ add. D*. 

5. xov] supra scr. D*. ytrofi^vTjv] corr. ex t mg. D^ efc 

supra scr. D^ 6. yivoiiEvov] corr. ex /^ D^ et D^. 8. ngo- 
d^eciv A. 9. 7tsQiy8L0tiQ«Ls] post alt. q ras. 1 litt. A. d^iGSGi, D. 

11. ^atai] corr. ex iGnv D*. TtuQa] nsQL D^. 12. ^] seq. 
ras. 1 litt. D. 15. nav(l D, "' add. D^ 16. A] cbrr. ex 

nQ&TovY). 17. rdi'] corr. exro C^ AE^EAJ). 18. ytVfrat] 
BCraL D, mg. yQ. ytVfraiD^ 20. hx(o B. 23. Trot^rort] DA*, 
noLEuaL ABC. 




MA0HMATIKH2 STNTASESiS E'. 361 

q}6^Evog dta tcov ^^ O 6rj^£LC0v. OTteQ JtdXiv (Sv^i- 
^atvsL xata tag ^£6cjg d^ecoQOv^evag dcxoto^ovg' 
^SL^cov ydQ 6 trjg ISIH ^Qog tijv HE Xoyog yCyvetat 
TcdvTcov tcjv xatcc tdg iiXkag d^e^eLg ^vvayo^evcov^ 
eneLdriTteQ L6rjg del xal trjg avtf^g ovdrjg tfjg ^H ix 5 
tov KevtQOv tov eTCLXvxXov rj EH ex tov xevtQOV tfig 
yfig 7ta6cbv tcbv dklcov enl tbv exxevtQov iitL^evyvv- 
^evcov iatlv iXd66cov. 

y'. neQL trjg 7trjXLx6ti^tog trjg TtaQa tbv rjXLOv 

dvcoiiaXCag trjg 0eX7]vrjg. 10 

"Iva dij d-ea^d^^ed^a^ jtrjXCxov yCvetaL ro TtXet^tov 
TtaQa trjv dvco^akCav dLdcpoQov^ otav xatd tb TteQL- 
yeL6tatov rov ixxevtQOv (peQ6^evog 6 inCxvxkog tvy- 
xdvT}^ 7taQetrjQfJ6a^ev tdg tOLavtag t(bv JtQbg tbv tjXlov 
dLOTttevo^evcov tfjg 6ekfjvr]g dLa6td6ecov^ iv alg oX te 15 
8q6iilol avtfjg ^e60L eyyL6ta itvy^avov t6te yaQ rj 
7tXeC6trj dLafpoQa yCvetaL tfjg dvco^akCag' xal t] 7tQbg 
tbv r]kLOV avtfjg d^to^r] ^e6cog ka^^avo^evr] tetaQtr]- 
^6qlov eyyL6ta iTtoCeL^ orf xal 6 iTtCxvxlog 7teQL tb 
7teQLyeL6tatov iyCveto tov ixxevtQOv^ xal etL iv alg 20 
tovtcov v7taQx6vtcov ovds 7taQ7]kXa66ev tL xatd ^rjxog 
f] 6el7]vr]. tovt oov yaQ 6v^PaLv6vtcov xal tfjg cpaLvo- 
^evrjg iv tfj dL07ttev6eL xatd ^fjxog d7to6td6ecog trjg 
avtrjg yLVO^evrjg tfj dxQLpet ka^^dvoLto dv d6cpakcbg xal 

3. HEI corr. ex NE B-C^. yivsruL D. 4. ndvzav] 

mg. D^ 5. alsC D. 8. sXdtrwv D. 9. y'] mg. ABCD. 

TtSQL — 10. asXi^vrjg] mg. inf. D. 10. ccvcofiaXiag] |3^ dv(o- 
fjLaXCag D. 11. ^r]] corr. ex ds D^ 12. Post rd del. nsQt 

x6 D^ 13. SV.V.SVXQOV] corr. ex «x D^. 16. STvy%avov] corr, 
ex xvyxavov A^ 19. s^yiGza D. 20. sysvszo D. sv.}^" D, 
sv add. D^. 21. naQijXaGsv D, -v del. D^. 24. Xufi^dvoizoj 
-voi- e corr. D^ (t in ras. 5 litt.). 



362 . KAATAIOT nTOAEMAIOT 

ri ^r}tov^8vr] dtccg)OQcc rfjg devrsQag avco^aXiag. ix t&v 
TOLOvtav toivvv trjQ7]6ec3v TtoLOv^evoi tijv eTtLOxeijjLV ev- 
Qc6K0^ev^ otav Tcata t6 TCeQLyeiotatov fj 6 eTCLXvxlog^ 
triv 7iXeL0tr]v dLacpOQav tfjg avco^aXCag yLVO^evrjv TCQog 
5 ^ev tijv ^eorjv TtccQodov ^olqcjv t, xal rS eyyL^ta^ TCQog 
de tijv TCQfhtrjv dvcj^aUav ^olqg)V /3 xal r^. 

vicodeCy^atog yccQ evexev^ %va enX ynag r) ^vo trj- 
Qr^6ec3v V7C o^jlv rjfLtv rj tOLavtrj dLaxQL^Lg yevrjtai, 
diKtTCtevea^ev rdv te tiXlov xal trjv eeXT^vrjv ta /3' 

10 etec ^Avtc3vCvov xat AlyvTCtCovg ^a^evcod' xe' fietd 
^ev trjv dvatokijv tijv tov rjlCov^ tcqo icevte d^e xa\ d' 
G)QG)v L6rj^eQLVG)v tfjg iie6ri^^QCag. tov yaQ rjlCov 
dLOTCtevo^evov xatd 'TdQoxoov (^LoCQag Trj L' y' ^(^\ ft£<?- 
ovQavov6rig To^otov iioCQag d' rj ^eXtjvi^ ecpaCveto 

15 e%exov6a UxoqtcCov fioCQag d- r§, xal dxQL^&g de to0- 
avt ag eTcetxev^ eTcecdij jceQL td TCQata ^eQrj tov Uxoq- 
TcCov iv Ake^avdQeCa d C coQav eyyc^ta dicexovGa iCQog 
dv(3^dg tov ^e6r]^PQLVov xatd firjxog ovd^ev aL6&r]tbv 
7taQaXXd6CeL. xaC e6TLv 6 djcb tcbv eTCox^^v tav xatd 

20 t6 «' etog Na^ova^OaQov ^exQL tfjg trjQ7]6ecog XQOVog 
etcbv ACyvTCtLaxcbv OTce xal rj^eQ&v 6y xal g)Q&v L0r]- 

2. Supra zr]Qri6Ecov add. irE D*. 3, ^] ijv ABCD, -v 

eras. D. 4. yLvofievTjv^ -v e corr. D. 5. (iolq&v ^ v,a.l r^^ 
ft f JJi in ras. maiore D. r^'] A\ Ih ABC. 6. nQcotriv] Tcqco- 
renouat. D^, supra scr. o: D*. r'^'] 11 BC et in ras. D, t^ A. 
8. 7}] supra scr. D*. 9. to5 ^' ftft] BCD*, rc5 l^ bzsv A, 

Twt (seq. ras. 1 litt.) Sh' D. 11. nivzs'] f BD. 12. ydg] 

fort. di]. 13. /.'] corr. ex b' Dl 15. i"*] Fb A\ in ras. D^, 

Jo ABC, di^ mg. D-. zogccvzcc B. 16. (isqj] zov] -t] z- in 
ras. 3 litt. D. 17. 'a] s C. [_'] corr. ex b' D^, ut saepius. 
18. (i£ar]v^QLVov D. ftijxo?] corr. ex fi-^Kovg C^ 19. nuQ- 
aXd66ti D. 20. ^zos] corr. ex b' D*. Na^ovaaaQov D, 

V supra add. D-. 



MA0HMAT1KHS IlTNTASESii; E'. 363 

li£Qtvcbv aTtX&g rs xal dxQi^&g iij /_' d^' Tcgbg bv X9^~ 
vov tbv 7]Xiov €vql6xo^£v ^£6G)g ^£v £Tt£%ovxa ^TSqo- 
j(,6ov ^OLQag Tg xf, aKQL^obg d£ fiOLQag Trj v^ xad^hg 
xal £v r(p aGtQold^G) 6 LCDitt £V£to. Tcal yj 6£X7]vrj dh 
xc^t' £X£Lvrjv tijv cjQav ix tfjg TtQcotrjg vTtod^ia^cog £v- 5 
Qi6x£taL £7t£%ov6a ii£6G}g xatd ^rjzog ^hv ZJxoQTtLOv 
ILOLQag L^ 3C, G)g t£taQtrj{iOQiov tvy%dv£LV ^yyL^ta trjv 
fi£0rjv d7to%riv tov rjXLOV, dvoiiakCag d' dnb tov dito- 
y£LOV tov £7tLXvxXov ^oiQag Tt^ tO-, 7t£Q\ ag TtdlLv ro 
7tl£L6tov yLV£taL dLd(poQov tfig dvcj^aXLag. iXd^acov lo 
aQa 7] dxQL^rjg TtdQodog £y£V£to tr]g o^akfig y,OLQaLg 
^ r§ dvtl £ tcbv xatd tijv 7tQG)tr]v dvco^alLav. 

TtdkLV^ Lva xal £x t&v VTtb tov 'l7t7tdQ%ov t£trjQrj- 
liivcDv tOLOvtG)v TtaQodcav cpav£Qbv rj^tv tb £7tl tmv 
6^0LG)v dLd(poQov y£V7]taL^ 7taQa%^ri66^£^a xal tovtcov 15 
fiLav, rjv g)rj6L t£tr]Qrjx£vaL tc5 v' £t£L tfjg tQLtrjg xatd 
KdkL7t7tov 7t£QL6dov ^ittr' AiyvTttCovg 'E^tLCpl tg' rov 
diuoCQOv tfjg 7tQG)tr]g mQag ^taQ^Xrjlvd-^tog. dQ6^og 
^£v ovv^ (prj6Cv^ rjv 6^a\ tov dh rjXCov dL07tt£vo^£vov 
xatd Aiovtog ^oCQag rj i' l^' i] 6£X7]vr] £(paCv£to iiti- 20 
%ov6a TavQOv ^oCQag l^ y\ xal dxQL^&g d£ £7t£L%£v 
£yyL6ta tdg avtdg. yCv£taL ccQa r] ^£ta^v tov r]lC(yv xal 
tfjg 6£Xr]vr]g dxQL^S^g d-^coQOv^ivr] dLd6ta6Lg ^olqS)v Tt^ i£. 
dXXd tov r]XCov ovtog Tt£Qi td itQcbta ^iQr] tov Aiov- 
tog iv 'Podw, 07tov r] t7]Qr]6Lg iyiv^to^ 7] tfjg rj^iQag 25 



3. tg — (lOLQccgj ins. loco 1 litt. D^. 7. mg] mars C. 8. 
S'] d8 D. 12. rS] u ABC, Fb renouat. Dl 13. xov] f A, 
om. D, T supra scr. D*. 16. v'] v ABCD^, v' D, va' Ideler 
Hist. Unters. p. 217, v3 Halma. 17. KdXXnmov D. 'Enicp'^ D, 
corr. D^ 19. oiia'] dua ABCD. 20. tj /.'] h^ D. i^'] 
i (3' AC, ip' B, i^ D. 23. T7)?] r- in ras. D^ 



364 KAATAIOT nTOAEMAIOT 

Sqk xq6vg)v i6rlv it, y' ' ai tiqo rfjg ^s6r}^PQiag aQa 
f y' d)QaL xaLQLxal 7Colov6lv L6rj^£QLvag g g'* a6TS ys- 
yovsvaL ti)v riqQr}6LV tcqo g g' caQcbv L6r}^SQLVC3v rr}g 
sv rri Lg' ^s^rj^^QLag ^s6ovQavov6rig TavQOv ^OLQag d'\ 
5 6vvdysraL roCvvv xal svravd-a 6 aTcb r&v s%o%&iv s%\ 
rijv rr]Qrj6LV XQOVog srCbv ACyvTtrLax&v %l%' xal rjfiSQCJV 
nd Kal cjQav L6rj^SQLvcov aTtk&g ^sv L^L!y\ dxQL^&g 
ds L^lJd'' TtQOg ov xq6vov svql6ko^sv rbv tjXlov xard 
rdg rj^srsQag vTCod^s^SLg^ STCSLdyJTCSQ 6 avr6g s6rLv ^s6- 

10 rjfipQLvbg dLa 'P6dov xal ^Als^avdQsCag^ ^s6c3g ^sv 
s%s%ovra Aiovrog \iOLQag T xj, aKQL^cbg ds ^OLQag rj Ky 
xal Ti)v 6sX7]vrjv ds ^s6CDg xard ^rjxog ^sv s%s%ov6av 
TavQov iioLQag 8 xf, hg syyvg sivaL %dXLv rrjv ^s6r]v 
d%oxriv rsraQrriiioQLOVy dvoj^aXLag d' d%b rov d%oysCov 

15 rov s%lxvkXov ^oCQag 6v^ ^^, %Qbg alg %dXLV syyL6ra 
yCvsraL rb %XsL6rov didcpoQov rfjg %aQd rbv s%CxvkXov 
dvco^aXCag. 6vvdysraL ccQa rj dLd6ra6Lg rj d%b rfjg 
^s6rjg 6sXi]vr]g s%l rbv dKQL^f] r]XL0v ^olqcov 9y vs. 
srsrr]Qr]ro ds r] d%b rfjg dKQL^ovg s%l rbv dKQL^'^ ^olqcov 

20 jrg t£* %ksCovag ccQa s%slxsv rj 6slr]vr] aKQL^cbg ^sg)- 
Qov^svr] rf]g 6^alf]g %aQ6dov ^oCQag %dhv l r^ dvrl 
s rcbv xard rf]v %Qd)rr]v v^^d^s^Lv. (pavsQbv ds ys- 
yovsvy OTL Kal rwv dvo rovrcov rr]Q7]6scov %sqI rdg 
dsvrsQag dLXor6^ovg ysysvr]^svc3v r] ^sv Kad-' r]^ag 



1. xQov(ov~\ %- in ras. A. iatCv] -v del. D^, comp. B. 5. 
roLvvvl ovv D. Post xat del. o C^. 9. fffTiv] comp. B, -v 
del. D*, iGtiv 6 A. 14. tstaQtrjfioQCov] ante alt. q ras. 1 

litt. D. d'] Si BD. 15. syyiGtayLGta D, sed corr. 19. 
ayiQi^ovg'^ ScnQL^ovg 6sXi]vr}g B; ^ add. mg. A\ supra scr. C. 
ini tbv a%Qi§fj'\ om. D, ([ inl tbv dtiQi^Ti ^ mg. D^ civ,Qi^f\\ 
a-HQi^fj riliov B, ^ supra scr. A^C. 21. r'*] lo ABCD*, 

rj D. 22. F] bis C, sed corr. 



MA0HMATIKHS STNTASEiiS E'. 365 

iXX£C7tov6a evQsd^rj trjg xatcc tijv TCQchtrjv ccvcj^aXcav 
diaTCQL^scog dv6l ^OLQaig xal difiOLQco^ rj ds xata tbv 
''ImtaQxov V7tSQpdXXov6a tatg avtatg^ ineLdii nal olov 
t6 TCaQdc tijv dvcj^aliav xad"' rj^dg y^ev dcpaLQStLTcbv 
itvyyave,^ Tcatd de tbv "ImtaQxov TtQo^d^EtLxov. xal 

i^ dklcOV 8e TtXudvCOV tOLOVtCOV trjQ7]6£C0V £7ttd ILOl- 

Qcbv xal ri £yyL6ta £vql6ko^£v t6 7tk£t6tov 7taQd tijv 
dvco^aXLav dLacpoQOv^ otav 6 i^tLKvxXog xatd t6 7t£QL- 
y^Lotatov fi t^fj^a tov ixxivtQov. 



d'. II£qI tov Xoyov trjg ixKEvtQotr^tog tov 10 
eeXrjVLaxov xvkXov. 

Tovtov ovv ovtcog ^xovtog £6tco 6 £XK£vtQog tr}g 
0£X^vrjg KVKlog b ABF 7t£Ql xivtQOv tb A xal did- 
^£tQov tijv A^r^ icp^ ^g v^toxELC&co t6 xivtQov tov 
dLd ^i^cov t&v ^codLcov t6 E, co6t£ tb ^£v A yLV£6%ai 15 
t6 d7toy£L6tatov tov ixxivtQov 0rj^£tov, t6 df F t6 
7t£QLy£L6tatov. xivtQG) ds t(p r y£yQd(pd-co 6 i^tiKvxlog 
trjg 6£Xrivrig 6 ZH@^ Kal rjxd-co icpaTtto^ivrj avtov ri 
E®B, Kal i7t£l£vi^(ii r\ r@. 

i7t£L toCvvv Katd trjv icpa7tto^ivrjv tov iitLKVKkov 20 
tfjg 6£Xr^vrjg yLvo^ivi^g t6 7tX£t6tov trjg dvco^aXCag 



1. evXbCtcovgo. D, corr. D-. rju^^-S"?] D. 2. dnioiqcp] 

i^D, FBD*. 4. acpccLQBxr]v.6v K. 5. xovl om. D. "'Inaqxov D . 

6. knxcc fioi(>c5'v] ^ jj/ B, fioiQav ^ D. 7. r'?] Fb D et corr. 
ex lo A, lo BC. 9. ^] 7} A, rjv D. 10. 8'] mg. ABC, 

y 

om. D, S ccQ mg. D^ nsQL — 11. xvhXovI hoc loco mg. D* 
et mg. superiore D. 13. 'hevxqov] K C. 15. ^coditov 

%vv.Xov D. yCvBcQ^ai] vnov,BL6%^ai D. 16. anoysioxaxov^ a- 

in ras. A. F] in ras. D. 17. 6 £-] in ras. A. 18. ZH&] 
Z0 D. 19. E@S] E@ D. 



366 



KAATAIOT nTOAEMAIOT 




didcpooov 6vvC6raxaiy tovto d' sdsLX^V ^vvayo^svov 
^OLQ&v l rB, etr} av xa\ rj vtco FE® yavCa TtQog tm 
KSVtQG) ot)^?^ tov dta 

^E6C0V t&V ^(pdCcJV^ OLCJV 

5 ^sv £l6lv ai d OQd-al t|, 
toLovtcov 5 ft, OLCov 6' aC 

P OQd-al t|, tOLOVtCOV L£X. 

xal 7] ^ev ccQa STtl r^g 

r0 TtSQLCpSQSLa tOLOVtCDV 
10 S6tlv LS %, OiCJV 6 TtSQL 

t6 FE® dQd-oycjvLOv %v- 
xlog t|, y} d' vit avtijv 
sv&sia '^ r@ toiovtov Ig 
syyi6ta^ olcjv s6tlv rj FE 

15 VTtotsCvov6a Q7C. C36ts xaC^ 
oXov rj ^sv r& sx tov 
xsvtQov Tov STtLKvxXov sSsCxd-rj s Ts^ rj ds EA rj ccTto 
tov xsvtQov tov dia ^s6cov tcbv ^codCcov inl t6 aTto- 
ysiov tov sxxsvtQov |, rotovTcov s6tai xal rj EF rj 

20 djtb tov avtov xsvtQov STtl t6 itSQCysiov tov sxxsv- 
tQov Xd' xfi. xal olr} ^ilv ccQa ri AF did^stQog tcbv aiftcov 
s6tai qd" x/3, rj ds /lA sx tov xsvtQov tov sxxsvtQOv 
ft'9' ^id^ r\ df E/i iista^v tcbv xsvtQcov tov ts did ^s- 
6cov tcbv ^G)dCcov xa\ tov sxxsvtQov T id". xal dsdsixtao 

25 rjfiiv xal 6 V7tb tf}g ixxsvtQotrjtog TtSQiSxo^svog Xoyog. 

1. S'] de D. Gvvayoiitvovl -ov (o) corr. ex j' in scrib. A, 
-svov supra scr. D-. 2. r^^ In ABCD. yoovLo] x&v D. 

3. v.ivxqco] comp. seq. ras. D, ^ add. D^ 4. Post ^(pdCcov 
add. TiviivKXov D, v.v- del. Dl 7. §] dvo C. 8. r)'] in ras. A. 

10. iaxLv] comp. B, -v del. T)\ 17. EA] laD. r) (Ali.)] 
ins. Dl 22. q¥] Q- e corr. D*. 24. T t^] corr. ex ^ A\ 
i inter duas ras. D. 



MA0HMATIKHS LTNTASEiiS E'. 367 

b\ IIsqI rfjg 7tQ06vsv6£(x)g roi) rfjg aeXTJvrjg 
£7tLxvxXov. 
"Evsxsv ^sv ovv tG)v TCSQi xs xag Gv^vyCag xal sxl 
tcsqI xovg 8i%ox6^ovg xfjg es^TJvrjg airnLaxL^novg (pai- 
vo^svcDv ^sxQo xo6ovxG)v av xvg sjCL^dXoL xatg x&v 5 
sxxsL^svcov avxfig xvkXcov V7Co%^s0s6lv^ sk ds xCbv xaxa 
ILSQog tcsqX xag ^rjvosLdstg xal d^q)LXVQxovg dno^xd- 
6SLg d-scoQov^svcjv jcagodcov, xad'' dg ^dXL6xa ^sxa^v 
yivsxaL xov xs djcoysLOv xal xov TCSQLysCov xov sx- 
xsvxQOv 6 STCLKvxXog^ IdLov XL jcsqI xfjV XOV STCLXVXXOV 10 
7Cq66vsv6lv STcl xfig 6sXijvrjg svql6xo^sv 6v^pspr^x6g. 
sjcsLdij yaQ sv xl xal xb avxb xad-6Xov x&v stclxvxXcjv 
vjcoxst^d^aL dst 6rj^stov^ TCQbg 6 Tcdvxoxs xdg xcov sv 
avxotg XLVov^svcov d7Coxaxa6xd6SLg dvayxat6v s6xlv 
d7CoxsXst6d-aL^ xovxo ds xakov^sv djc6ysLov 6^aX6v^ 15 
d(p' o\) xal xdg dQ%dg xcbv xf]g xaxd xbv stclxvxXov 
XLV7]6scog dQLd-^&v vcpL^xd^sd-a^ Sg stcI xf^g TCQOXSCfis- 
vrjg xaxayQa(prig xb Z, xal d(poQL^sxaL xb xolovxo 6rj- 
listov xaxd xrjv sjcl xav djcoysCov xal x&v TCSQcysCcov 
xcbv sxxsvxQcov To4) STCLXVxXov d^s^LV VTcb xfjg dLa Tcdv- 20 
xcov xcbv xsvxQCov sx^aXlo^svrig svdsCag^ cog xfjg z/EF^ 
STcl asv xcbv dkXcov VTCod^s^soov 7Ca6cbv djcX&g ovdsv 



1. f'] mg, D^ TtQovsvGscog D. 3. Tf] om. D. 4. 6f- 
X'^vr}g'] post -s- ras. 2 litt. A. 5. Post fiEXQi- del. rav D^. 

inL^dXXoLBCD, corr. D^ 6. syyiSLiiEVcovD, corr. D^ ccvtijg] 
a- et -X- in ras. D^, supra scr. avxfig D*. -kv-kXov C. vno- 
&E68aL, -L in ras. 2 litt., D*. 7. (irjvosLSiig C. 9. yivsxai] 
corr. ex xsLvsxaL D^. s-nyisvxQov] -q- supra scr. D^. 10. xl\ 
corr. ex yaQ D^. 12. rt] corr. ex x6 D. snLyiv-iiXoov] corr. 
ex vnoyiv-KXcov C^. 13. dst] corr. ex 8si6 D^ 15. Supra 

oiiaXov add. fiaXXov D*. 17. ccQLd^fi&v] corr. ex ccql&ijlov D". 

vcpL^xdiis&a] mut. in vcpiGxmfisd-a D*. 21. z/EF] supra J 

add. a D, del. D^ 



368 KAATAIOT nTOAEMAIOT 

OQCj^sv £x r&v (paivo^ivcov dvTLJilTCzov Td3 Tcal xara rag 
ccXXag rcov £7tcxvxX(Dv TtaQodovg rrjv dia rov jtQOTcec- 
Hevov aTtoysiov tov iTtiTcvxXov dtd^erQov^ rovre6rcv ri)i/ 
ZFH^ r^v avrijv d^iaiv aiel 6vvrrjQ£tv rfi rb xsvtqov 
5 avrov o^aXcbg 7t£QLayovar} £vd-£iay cog ivd^dd^ rfi EF^ xal 
v£v£Lv, 07t£Q ccv TLg xal dxoXovd-ov rjy7]6aLro^ Jtdvtore 
TtQog rb xivrQov rfjg Tt^QLaycjyrjg^ TtQbg d) xal iv rotg 
L6oLg XQOvocg l6aL ycovCaL rrig 6^aXrjg XLV7]6£Cjg dito- 
Xa^^dvovraL^ iitl df rrjg 6£Xr]vrig ivL6raraL rd cpaLvo- 

10 n£va ra xal iv ralg \i£ra\v rcov A xal F jtaQodoLg 
rov iTtLKvxXov rrjv ZH dLd^£rQOv ^ij TtQbg ro E xiv- 
rQov rfjg 7t£QLayc3yfjg v£V£lv xal rrjv avrijv rfi EV 
^iOLv dLa6d)^£LV. £vql0xo^£v yaQ TtQbg ev ^iv rt xal 
rb a\)rb 6r]^£L0v rcov iTtl rrjg AF dca^irQOv rijv ixx£L- 

15 ^ivrjv 7tQ66v£v6LV aUl 6vvrr]Qov^ivrjv^ ovr£ ^ivroL JtQbg 
ro E xivTQOv rov d^d fLi^cov rcov Jcjdtcoi/ ovr£ 7tQbg rb A 
rov ixxivrQov^ dkXd TtQbg ro rr^v l'6r}v rfi AE ^£ra^v 
rcov xivrQCJv dTtijov rov E cog TtQbg rb %£QLy£Lov rov 
ixxivrQOv. xal orL rovd-' ovrcog £%£l^ dsL^o^^v Ttdhv 

20 d7tb Ttl^Lovcov rrjQri6£cov ixd^i^^voL dvo rdg ^d- 
kL0ta ro 7tQox£L^£vov i^cpavL6aL dvr^a^ivag^ rovti^rcv 
xad^' dg r£ i^tCxvxkog 7t£Ql rdg ^ii^ag d7to6rd6£Lg 
f]v xal r] 6£kr]vr] %8qI ro d7t6y£Lov r] ro 7t£QLy£Lov rov 



1. xai] in ras. D^, oiri. C. 2. Supra TiuQodovq scr. (ov D, 
del. D*. 3. xovxiotiv] comp. B, -v del. D^ 4. ZFif] corr. 

ex ZK TH A\ ZHT rj B, ZHT ri C, Z 7} FH C^ -FH in 
ras. D*. asL BD. 10. Post to5 del. [ir] %al ^rj Dl 11. 
iTtL^KVTiXov] s- ins. A. (ii^] fw] D', Jit] D^. 14. AF] corr. 

ex ABF D^. 15. asi D. 16. E yisvxQOv] corr. ex fx- 

V.EVXQOV D^. 17. JE] corr. ex z/ E D^ 20. i^^sfisvoL] 

corr. ex iyid-SLfiivcav D*. 21. xovxsgxl B, xovxsoxlvxlv D, -vxlv 
del. D«. 23. x6 (alt.)] om. D. 



MA0HMATIKHS STNTASESJ2 E'. 369 

iTtMvxXov ^ dca rb tceqI xag roiavrag TtaQodovg rriv 
^XeC^riqv diacpoQav Cv^^aLVStv rCbv ixxei^svcjv jtQ06- 
vev6sov. 

dvaygdcpsi, roCvvv 6 "IitTtaQiog sv ^Podq) rsrr^Qr]- 
xsvau did r&v ogydvcov toi/ rs iqXLOv %al rr^v ^sXrjvrjv 5 
ra Qc,^' srsL dito rrjg ^^Xs^dvdQov rsXsvrrjg icar 
AlyvTtrCovg QaQ^ovd"! ua' wQag p' dQxo^svrjg TcaC (prj^tv^ 
ort rov rjXCov dLOTtrsvo^svov xard TavQOv ^oCQag f 
Ijd' t6 rrjg esXtjvrjg xsvtqov icpaCvsro S7ts%ov 'Ix^vcov 
lioCQag xd rB, i7tsi%sv 8s dxQLp&g xd y''ri\ xard 10 
rbv SKXsC^svov ccQa xqovov d7tsl%sv rj dxQL^rig 6s2,7]vrj 
rov dxQL^ovg r]XCov slg rd STto^sva ^oCQag rly ^p 
€yyL6ra. dXHl iTtsidrj dsvrsQag cjQag dQxo^ivrjg yiyovsv 
^ rrJQrj^tg^ jtQb Ttivrs ds hQcbv syyt^ra xaiQLx&v rr}g 
iv rfj La' ^s^r^^^QCag^ avr aL 6' iTtoCovv iv ^Podfp rors 15 
lcriiiSQLvdg G)Qag s rB syyL6ra^ 6vvdysraL 6 djtb rijg 
ijtoxrjg rj^G)v ^sxql rrjg rr]Q7]6scog %^oVog srcbv ACyvTt- 
rLaxcbv pc xal rj^SQ&v 6l^ xal coQcbv C^rj^SQLV&v 
aTtkSyg ^sv TtdXtv Trj y\ dxQL^cbg ds Ti] ^ovcov slg ov 
XQOVov svqC0xo^sv rbv ^sv o^aVov rjhov sjtixovra rov 20 
TavQOv ^oCQag g Jid^ rbv d' dxQL^rj ^oC^ag t, Jis^ 
rr]v 8s 6^akr]v 6skr]vr]v xard ^fjxog ^sv i7tixov6av 
XG)v ^Ix^vcov ^oCQag x^ Ty, dvoaaXCag d' d7tb rov 



4. 'P6dco\ "P- e corr. C. 6. ^9^ fVet] p9| seq. ras. 1 litt. D, 

^ i* D*. 7. ^aqiiov^l lal -l i- corr. ex N A. ^'] ^ D, 

-^ add. D2. 10. r^'] corr. ex 4 A, Jo BC, Tb D, uJ' D^. 

i7tu%Bv\ -V del. D*. 13. d£vtiQa?\B' B. 14. nivxs] s BD. 

15. T^] corr. ex Tfj A*. d'] di t). inoCovv'] iTtsl ovv C. 

16. r^] corr. ex l^ A, iS BC, Fb corr. ex tp D^. 18. ^] 
-'9' in ras. D^ Post aiQcbv ras. 1 litt. C. 19. iiev] ft D, 
ft D^ y'] supra scr. D^ iiovcov'} mut. in }i6vov D^ 

Ptolemaeus, ed. Heiberg. 24 



370 



KAATAIOT nTOAEMAIOT 



HE60V aicoysCov xov iiaxvxXov [lOiQag Qjts A, &0ts 

xal rriv xYig o^aXfjg ^sXt^vrjg aito rov axQLpovg r^XLOV 

did6ra6LV 6vvdya6%'ai ^oiQcbv rid xrj. 

rovrav ovv vjtoKeL^svcjv sGra 6 sxxsvrQog rrjg 
5 6sl7]vrjg xvxXog b ABF tcsqI xsvxqov ro z/ xal didiis- 

rQOV rijv A^F^ 

i(p ijg sdra) rb tcsv- 

rQOv rov dtd ^s- 

6g}v r&v t,(p8i(ov 
10 xvkXov t6 Ey xal 

xsvrQG) ra B ys- 

yQdcpd^G) 6 STtC- 

xvK^og rrjg ^sXt]- 

V7]g 6 ZHS^ TtsQi- 
15 aysad^cD d' 6 ^sv 

STtCxvTclog rrjv sig 

rd STto^sva rcbv 

t,G)dCc3v xCvrj^iv cjg 

djto rov B STtl t6 ^, rj ds 6sX7]vrj ri]v xard rbv STtC- 
20 xvxXov G)g ditb rov Z snl t6 H xal t6 0, xal iics- 

isvxd-G)6av 7] rs ziB xal r] E@BZ. 

ijtsl roCvvv iv ra ^s6g) firjViaCG) xqovg) dvo jtsQi- 

sxovrai d7tox.ara6rd6sig rov iitixvKkov TtQbg rbv sxksv- 

rQOv^ xard ds rr]v ixxsi^svr]v d^s^iv dnsixsv r] ^s6r] 
25 6sX7]vr] rov ^s6ov r]Uov ^ioCQag rCs A/3, idv diitka- 

6id6avrsg Tavrag dg^sXco^sv xvxXov^ s^o^sv rr]v djtb 

Tov aTtoysCov rov ixxsvrQov ysysvr]^svr]v djtoxr^v rors 




1. iiiaov'] corr. ex iiiaovg D^. iniyiv-iiXov] 8ni- e corr. D^ 
X] in ras. D. 21. xat 17] BD, v,aC AC. 22. (irjVLaCo)] -la- 
corr. ex n in scr. A. 24. ^HXftftfVTjv] h- e corr. D. hioiv] 
ri]Qriat.v D. 



MAeHMATIKHS STNTASESiS E'. 371 

tov BTCLKvxXov sIq tcc eTto^sva llOLQCbV 'oocc d' &6t6 
xal rj vjcb AEB yovCa tcDV XoiTtGiv sCg tccg d ogd^ag 
ietai, ^oLQcov mj vg. ^xd^cs d'^ xdd^stog djtb tov A 
STtl tiiv EB ii ^K. STtsl ovv i^ '^Ttb ^EB ycovLa^ 
OLcov ^sv SL6LV at d OQd^al t|, tOLOvtcjv sdtlv TCri vg^ 5 
OLCjv (f aC dvo OQd-al t|, toLOvtcov Qot, Vj3, str] av 
xal rj ^sv STtl tfjg JK ^SQLcpsQSLa tOLOvtcjv Qot r/S, 
o^Lcov s6tiv 6 TtSQl rb zlEK oQd^oycovLOv xvxXog r|, rj d' 
STtl tfjg EK tcov koLTtcbv [Eucl. III, 31] slg tb rifiLXvxXLOv 
/3 rj. nal t&v vTt^ avtdg ccQa svd^SL&v ri ^sv /d K s^tat 10 
tOLovtcov QLd' vO*, OLCov s6tIv rj JE dLa^stQog qx^ 
rj ds EK tcbv avtcbv /3 Ld. xal olcov s6tlv ccQa rj ^sv 
^E ^sta^v t&v xsvxQCOv ~l Ld"^ rj ds z/5 sx tov 
xsvtQov tov ixKsvtQOv fiO' jH^, tOLOvxcov xal r} ^sv zfK 
s6xaL 7 Ld" TtdUv syyL6ta, rj ds EK b^OLCog o t/3. 15 
xal STtsl tb aTtb trjg zfK XsLcpd-sv [Eucl. I, 47] i)7tb 
tov djcb tYig AB itoLSt tb d%b tf\g BK^ s^o^sv xal 
tijv fisv BK tcbv avtcbv ^ Ag, tijv ds BE olrjv ]i7J 
Jirj. TtdXLV^ STCsl r] ^sv tfjg b^aXfjg 0sXrivrig djcb tov 

1. ^OLQ&v] D, comp. B, (lOLQag AC. oocc] -o- in ras. 2 
litt. A. 3. d] corr. ex A D^. 4. EBJ EzJ A. 5. fWi;] 
comp. B, -V del. D^. vg] corr. ex v v.ai D^ 6. dvol § BD. 

roiovToov — 8. t|] mg. D. 6. r^] renouat. D. 8. ottov] 
-oov supra scr. D. fcrtV] om. D. 9. rjfii-KvyiXLOv §] &B D, 
c>' B D*. 10. avtdg] corr. ex avzrig D. 11. z/E] corr. ex 
d^E D^ 12. 78] -d e corr. D^. 13. JE] corr. ex AE Dl 

r i-O-] e corr. D^ JB] BJ D. 14. y.8VTQ0v] y.ivtQOv 

ov6a D. 15. rl^] e corr. D^. EK] EK ndliv D. 16. 
inBi] corr. ex nsQi D^ AK XsicpQ-ev] corr. ex azXr]q)d-4v 

D^ {-T]- corr. ex ei in scrib.). vno tov anb ttJ?] vnb tfjg D, 
anb tov anb tfig D^. 17. z/B] BJ D. Post noLst del. t6 
anb tfjg BJ noiSL D^ 18. (iev] om. C. BK] corr. ex 

KB J). Se] bis extr. et init. pag. A. EE] EB D. jZ^] 
om. B. 19. insl rj] corr. ex inl sC D^. 

24* 



372 KAATAIOT nTOAEMAIOT 

dxQLpovg 7]Xlov dLcc0rcc6ig ^olq&v tjv nd lcfj^ rj ds rijg 
aKQi^ovg rcbv sk trig trjQ7]66G)g ^olq&v tly /li/3, Sets 
d(paiQ£tv tb JtaQa f^v dvco^aXiav avtrjg didcpOQOV 
^OLQag o JLtg, d^scaQsttac d' rj b^aXri jtaQodog tr^g 

5 6sX7]vr]g stcI tfjg EB svdsCag^ V7to7csi6%'03 7] 6sX7]V7]^ 
STtSidr] TtSQi tb jtSQiysiov r]v tov smxvxkov^ Tcatd tb 
H 6r]^siov^ xal S7ti^svx^Si6c3v t7]g ts EH xal tTJg BH 
xdd-stog ditb tov B tjx^g) S7tl tr]v EH sx^Xr]%-si6av 
i] BA. STtsi ovv 7] vTtb BEA yovCa 7tsQis%si tb 

10 TtaQa tr]v dvo^alCav trjg 6slr]vr]g did(poQov^ str] av^ 
Oiov ^sv Si6iv aC d oQd^al rj, toiovtov o jilg, oZov 
d' aC dijo oQd^ai t|, toiovtoiv d A/3' &6ts %al 7] ^sv 
ijtl tf]g BA svd^sCag TtSQicpSQSta toiovtcov s6tlv d X^^ 
oXcnv 6 TtsQi tb EBA oQd^oycSviOv xvxXog rj, r] ds 

15 7)71 avtr]v svd^sta r] BA toiOTJtcov a Ag', otcov s6tiv 
7] EB v7totsCvov6a ^. co6t£ xaC^ oCcov s6tlv r] ^sv 
BE svd^sta ]irj ^, i] ds BH ix tov xsvtQOv tov STti- 
XTjxkov s Ts^ toiovtcov s6tai xal r] BA svd^sta o kd'. 
xal oicov s6tiv aQa r] BH sx tov xsvtQOv tov S7ti- 

20 xvkXov QKy toiovtcov Kal r] (isv BA svd^sta s6tai td 
v/3, i] d' S7t avtr]g TtsQicpsQSia toiovtcov id td, otW 



3. avTJJg] corr. ex avt&v D^. 4. d'] di D. 5. f5rt] 

inl To C, corr. C*. 6. insLdi]'] -r\ corr. ex i A*. TTf^t- 

yfto C. 7. xf\q Tf] corr. ex tcov D^ EH xat tt)?] in ras. 2 
litt. D^. 8. xa-d-STog anh xov\ in ras. minore D*. B] ^f\xa 
in ras. D^. 9. f] (pr.)] ins. C^ BA\ corr. ex J5z/ D^ EE^] 
corr. ex BE D*. ycovta] om. D lac. 3 litt. relicta. 11. 

o ft?] corr. ex o^ g D*. 12. 8v6\ b B. lf\ corr. ex A^ A, 
e corr. D*. &ax£ — 13. BA\ in ras. D. 14. EjByf] "Wea B. 

6q&oymviov\ corr. ex oqd-Siv Dl 8b\ 8' I>. 16. EB] 

BE D. 17. 8s BU\ 8' D. 18. o 7^\ ^ C. 19. aga 

iaxiv B. i} BH iv,] renouat. D^. 20. Supra qx ras. D. 

BA\ corr. ex BA D. 



MA0HMATIKHS STNTASESiS E'. 373 

i0tlv 6 tcsqI t6 BHA oQd^oy^viov ocvxXos t|. co6ts 
xal rj ^sv vTib BHA ycovia toiovtcov ecftlv id td^ 
oicjv sl6lv at p OQd-al rj, XoLTtri [EucL I, 32] ds yj 
4)710 EBH tCbv fiEv avtcbv i/3 ftjS, oXcov d' at d dQd^al 
t|, toiovtcov g 3ca' to6ovtcov aga e^tat ^olqcjv {] H® 6 
tov iitLKvxXov TtSQLCpeQSca tijv aTto t^? aslTJvrjg i%l 
t6 aKQL^sg itSQCysLOv 7tSQLS%ov6a dLcc^taGLV, aXX 
ijtSLdii tov iisCov aTtoysLov aitstxsv r] 6sX7Jvr} xatct tbv 
Xq6vov tfjg triQYiijscDg ^OLQag Qjts A, drjXov^ ott Tcal t6 
TtSQLysLOV t6 fis0ov TtQorjysttaL trjg asXrjvrjg^ tovteatLV 10 
tov H erj^SLOv. s0tc3 drj t6 M, xal dLT^xd^G) r] BMN^ 
Tcal ccTtb tov E xdd^stog iit avtr^v rjx^ca rj ElSl. ijtsl 
tOLvvv r} ^sv ®H %SQL(peQeLa ideCx^ri ^olqcjv g %a^ 
rj de HM VTtoxsLtaL tcbv dnb tov itsQLysCov ^olq&v s A, 
m6ts oXriv trjv 0M ^vvdysdd^aL ^olq&v Td va, s'Cr} dv 15 
ocal r] 'bitb EBlSl ycovCa^ oXcov [lev el^Lv aC d oQxf^al t|, 
tOLOvtcov Td vd^ olcov d' ai dvo oQd^al t|, tOLOvtcov 
Tcy fi/3. &6te xal r] ^ev iitl tfjg E^ jteQLipeQeLa toiov- 
tcov i6tlv xy ft/3, olcov 6 TteQl t6 BElSl oQd^oyavLOv 
xvxXog T^, avti] 8e r] ES svd^sta toLOvtcov %d A-O", 20 
oXcov i6t\v r] BE v7totsCvov6a qx. %al oXcov i6tlv 
ccQa r] BE svd^sta ]irj ]irj^ tOLOVtcov s6taL Tcal r] ES 



a 



2. yoivCa] I^ D, ut saepius. i8 (alt.)] corr. ex lcc D^. 3. 
'^^Svo BC. 4. §'1 mut. in 8i D^. ^ 5. g] corr. ex tg D. 

17] postea ins. A. 9. xo] corr. ex tov D. 10. tovtiaxiv'\ 
comp. B, -V del. Dl 11. -rd] seq. ras. 1 litt. D. 12. E] 
supra scr. C^ xa-^-fTog] v.dQ-sto- in ras. minore D^ 13. 
©ff] supra scr. D, renouat. D^ nsQKpiQSLa] om. D. 14. Z] 
corr. ex a D^. 15. mGxs] roctf v.ocl D. m] -a in ras. D. 

17. 8'] 8s D. at] ins. D^. 8vo] p BD. 18. nsQL- 

(p^QSLa] h« D, ^ del.jet renouat.Dl 22. ^] om. B. ES] 
coYi: ex i^ D^, mg. f^ D^ 



374 KAATAIOT nTOAEMAIOT 

av&sla T xccl iirjxo6tG)V dvo. TcdXiv^ iitel rj ^sv vjtb 
AEB yovCa xoiovtcov ^v qo^ v/3, otov aC dvo d^d^al 
r|, rj ds vjtb EBN tCbv avt&v 7cy fi/3, afrj av xal 
XoiTtr] [Eucl. I, 32] r] vTcb ENB yavCa tcbv avtav 
5 Qvd ~i. G)CtB ocal rj ^sv ijcl tf}g EtSj jt£Qi(psQEia toiov- 
tCQV i0tlv Qvd 7, O^iCOV 6 TtSQi t6 EN^ OQd-oycoviOv 
xvxXog tJ, avtrj ds rj ES svd^sta toiovtcov Qig vrj^ 
oicov i6tlv r} EN v7totsivov6a ^. xal oiov i^tlv 
ccQa rj nsv ElSl svd^sta 7 xal s^rjKO0tcbv /8, rj ds ^E 

10 iista^v tcbv xsvtQov 7 id"^ toiovtav xa\ rj EN s6tai 
T Trj. i6rjv ccQa syyi6ta tf] ^E trjv EN ccTtsCXrjipsv 
^ dia tov IILS60V TtsQiysCov tfjg BM svdsCag ijtl t6 N 
ysvo^svrj 7tQ66vsv6ig. 

haavtcog ds^ Iva xal ix tcbv avtixsi^svcov ^SQcbv 

15 tov ts ixxsvtQov xal tov iitixvxlov t6 avtb ^v^^atvov 
dsC^c^iisv^ Sikricpaiiisv Ttdliv ix tcbv vjtb tov ^IjtJtaQXOv 
tstrjQrj^svcjv, cjg scpa^sv^ iv ^Podc) diaatd^scov trjv 
dicoTttsv^svrjv ta avt<p q^j^' stsi ditb trjg ^Als^dvdQOV 
TsXsvtfjg xat ACyvjttCovg Uavvl i^' GiQag %' xal y\ 

1. E^riiiOGx&v] l^ B, I D, h,h, et flTjxoffrwv D^. 8vo] corr. 
ex § Dl 2. v^] corr. ex IHB D^. dio'] b B. 3. t|] r- 
corr. ex c in scrib. A. EBN] -N corr. ex H D^. 4. r\\ 
e corr. D^ 6. T] e corr. D^ nEqicpBQeia\ V" D, 9 supra 
scr. D^ 6. Qvd] -d corr. ex AjD^. 7. ^] q- e corr. D* 

9. ££/] corr. ex s^ D^, mg. fi D^ t^7]v.oaT<bv'\ f D, || 

_ /1/1 /1 
BD^; mg. 6cXXavov ovrcog k'xst, tg || |3 D^ per rC^ huc relatum. 

10. |Lifro:|v] ft D, ut saepius; corr. D^ v.ivxqoiv ovaa D. 
T id'] TT- e corr. D. 11. T Tif] TT- e corr. D^ f^v] corr. 

ex T?)t C^ 13. nQOGvsvats] -i- corr. ex o C. 16. xov] corr. 
exToD^. 17. Bv] ins. D^ 18. dLonxEvoiibvriv^QD^^ dtconxsvo- 
fiEvriv C, SLonxsviisvrjv D. Q^^'] -9- corr. ex i" D (cr). i'xsC] 
corr. ex b D^. 19. navvC] TLavvri {-7] e corr. in scrib.) post 
lac. 4 litt. D, deinde eras. wl. l^'] l- postea ins. D, Squ D. 
■nai] om. D. 



MA0HMATIKHS STNTASESiS E'. 375 

i; xaO"' 7]v^ (prj6i^ roi; yjXlov dLOTttsvo^svov xata KaQKivov 
(lOLQag Ta XsL7tov6ag dsTtdtco fiSQSi 7] 6sk7]V7] sfpaCvsto 
ijtsxov^a tov Asovtog %%' ^dXL^ta [^OLQag' ro^avrag 
ds Kal dxQLpag S7tsl%sv^ i7tSLd7]7tsQ sv ^P6d(p TtSQL td 
xslsvtala tov Asovtog ^istd ^Cav caQav syyL^ta tov 5 

1 fis07]^pQLVOv ocatd }i7]Kog ovdsv 7] 6sk7]V7] 7taQaXXd66sL. 
d7tSL%sv ccQa Tcatd tbv skksC^svov %q6vov y] dxQL^r^g 
6sX7]V7] tov dxQL^ovg r]XCov ^oCQag sCg td S7t6^sva 
JJL^ g. aAA' S7tSL ysyovsv 7] tr]Q7]6Lg ^std y Tcal y' 
&Qag xaLQLxdg tfjg iv tf] tj' tov Uavvl ^sOr^ii^QCag^ 10 
(xvtaL d' iTtoCovv iv ^P6da) t6ts L67]^SQLvdg &Qag d 
iyyLCta^ yCvstaL 6 dTth tf]g i^toxijg 7]^g)v ^s%ql tr]g 
xr]Qr]6s(x}g %Q6vog itCbv AlyvTttLaK&v TtdkLv %% xal 
i]^SQ&v 67t<S xal G)Qcbv L6r]^sQLVG)v d7tXcbg ^sv d, dxQL- 
P&g ds y r§* sig ov %q6vov cj^avtcog svqC^ko^sv tbv 15 
[isv b^aVov 7]Xlov i7ts%ovta KaQxCvov ^oCQag l^ i, tbv 
ds dKQLpfj ~L ^, tr]v 8s 6^ali]v 6slY]vr]v xatd ^rixog 

i fisv i7ts%ov6av Asovtog ^oCQag zj x, G)6ts xal t7]v tfjg 
b^aXrjg 6slr]vr]g dTtb tov dxQL^ovg r]XCov 8Ld6ta6LV 
6vvdys6d-aL ^olqcjv Ji^ /I, dvco^aXCag d' d7tb tov ^s6ov 20 
d^toysCov tov i^tLxvxXov ^oCQag tXy l^. 

tOVtCDV V7tOXSL^SVG)V S6tG) 7tdXLV 6 sxxsvtQog tfjg 

6sXr]vr]g xvxkog 6 ABF 7tSQl xsvtQOv tb z/ xal d^d- 



2. iiOLQag] y, CD. XsLTtovGav D. 4. inELTtEQ D. 5. 

TslsvtciLo] -a supra scr. C^. 6. TtccQuXdaasL CD. 10. t^] 

ttJ AC, corr, A*. zov] bis A extr. et init. lin. TlavvT] D. 

11. d' STtoLovv'] in ras. D^, deinde del. ovv D^ 14. d] corr. 

ex l D*. 15. rS] io ABC, mut. in Fg A, l? D, Sl^ D^, mg. 
ScUaxov ayiQLp&g ds r To D*. tov] corr. ex to C^ 20. d'] 
om. D, 7 supra scr. D*. 21. STtLyiv-KXov] STtL- in ras. D. 

^OLQag] A, ft BCD. 



376 



KAATAIOT nTOAEMAIOT 



liEtQov trjv A^r^ B(p' ijg s6t(o tb %ivtQov tov dto: 
^edcjv t&v ^cadicjv xvxXov tb E^ xal ysyQdq^d^a) tceqI 

t6 B 6Yl^BtOV 

6 ZH& i%i- ~ 

5 oivxXog trlg 6s- 

Xrjvrjg^ xal i%s- 

%svyp(o6av r\ 

ts AB Tcal rj 

E&BZ. 
10 STtsl toCvvv 

ri iis0rj ditoxri 

tov riliov xal 

trjg 6slrivrig di- 

7cXa6LaQ^si6a 
15 7tSQLS%SL iLoiQag 

9 X, stri dv 

dia td TtQotsd^scoQrj^sva rj VTtb AEB yovCa^ oCcov \jisv 

SL6LV aC d OQd^al t|, toiovtcjv 9 A, olcjv d' aC dvo 

oQd^al r|, tOLOvtcov Qjta. sdv sx^aXovtsg aQa tr^v BE 
20 xd^stov S7t avf^v dycj^sv ditb tov z/ triv ^K^ 

yCvstaL xal rj vjtb zJEK ycovCa tatv loLTtmv slg tdg 

dvo hQd^dg Qod" CD6ts xal r] ^sv snl trjg ^K TtSQLCps- 

QSLa tOLOVtCaV S6tLV QOd', OLCDV 6 TtSQl tb ZlEK OQ^-O- 

ycovLOv xvxXog t|, 'j^ d' stlI tfjg EK trjg AoLTtijg 




1. rov'] corr. ex ro D*. 7. 7] xe JB y.al 7] EOBZ] cct 

z/B E0 BZ D (f^ corr. ex s^ D^). 16. 9 1] corr. ex rd< T)\ 

17. rd itQOTsd-scoQrj^Evci] mut. in zb TtQorsdscoQriiiBv' D^ 18. 
1] e corr. D. 8vo] b B. 19. hpdXXovrsg D, corr. D^ 

BE] corr. ex B D^ 20. aycoiiev] ABC, ayc^yco^sv A^C^D, 
bene, sed cfr. p. 381, 2. z/A] corr. ex AK D^. 21. z]EK] 

z/- e corr. in scrib. C. 22. dvo] b B. TtsQKp^QSia] 9 D, 

9 in ras. D^ 23. 6] ras. 1 litt. B. 24. 17] corr. ex sC D^ 



MA0HMATIKHS STNTAlEjESiS E'. 377 

[Eucl. in, 31] £ig t6 Yi^LXvxhov ^OLgag a. xal Tcbv 
'bn avtag aqa Evd^sL&v rj ^lv ^K s^xai rocovvcov 
Qtd" vd"^ oXav i6rlv 7] ^E {}7tor6Lvov6a qk^ rj ds EK 
rav avrCbv a y. G)6r£ TcaC^ olcjv i^rlv rj ^sv ^E 
lierai^v rcov TiivrQcov T Ld-^ ri 61 B^ i% rov icivrQOv 5 
rov iTcxivrQov iid' Jia^ xal rj ^isv ^ K evd^sta i^rac 7 Ld' 
syyLdra^ rj ds EK o^OLCjg o i. jcal iitsl rb ditb rfjg 
B^ XsLipav [Eucl. I, 47] ro d%b rr^g 'ZlK TtOLst rb 
aTtb rijg BK^ s^ofisv xal oXrjv ^sv rrjv BK sv&stav 
]irj Ag, XoLTtriv ds rrjv EB rcbv avr&v ^JLrj la. TtcclLVj 10 
iitsl ri iLsv rrig o^aXrjg esXiqvrjg dnb rov dycQL^ovg 
r]2,Lov dLd6ra6Lg ^olqgjv rjv Ji^ ]jl^ rj ds rfjg dxQL^ovg 
^OLQCJV iiri s^, G}6rs TtQo^rLd^ivaL rb TtaQcc rr^v dvcj^aXLav 
dLd(poQOv fiOLQav d ^, v7toxsL6d^cj rj 6sX7]vr}^ insLdii 
TtSQl rb djtoysLOV fjv roi) ijtLXVKlov^ %ard rb H 6rj- 15 
^SLOV^ xal iTtL^svxd^SL^&v rrjg rs EH xal rrjg BH 
xddsrog djtb rov B 7]%^^ ^^^ '^V'^ ^^ r] BA. 

iTtsl ovv rj vTtb BEA ycovLa^ oXcov fiiv sl6lv ai 
6 OQd-al T^, roLOvrcov i6rlv a jcg, olcov d' aC dvo 6q- 
d-al t|, roLOvrcov (i v/3, sl'rj dv xal rj nsv i%l rfjg BA 20 
TtSQLcpiQSLa roLOvrcov /3 v/3, oXcov i6rlv 6 TtSQl rb BEA 
OQd-oymvLOV Tcvxlog t|, avrfi ds fj BA svd^sta roLOv- 



1. Tjfiiyiv-iiXLOv^ Q D. rcov] corr. ex tc5 D^ 2. avrccg] 

corr. ex avtfjg C^ 3. i"9'] in ras. D. z/E] in ras. D. Post 

EK del. fx D2. 4. a y] D^, Sy ABCD. ^ 5. (isra^v] | D, 
corr. mg. D^ BJ] JB B. 6. rov iK-nBvtQOv] corr. ex Jjt 
tov -nEvtQov C^ 7. o] corr. ex Q D. 8. ^fn/jav] corr. ex 

y 

alsLipav D^, supra add. tog. Supra pr. to add. v D^ 12. 

didctaGLg] -dataaLg in ras. D. 15. gthislov] c D, g7\ D*. 

16. inL^Ev%d-Ei6(bv] -(?- postea ins. A. 19. Svo] ^ BD. 21. 
•jtBQitpiqua] 3 D, ut saepe. 



378 KAATAIOT nTOAEMAIOT 

r(ov p vO", OLOV i6rlv ri EB v7Cor£Lvov6a ^. xal 
OLcov i6rlv aga 7] ilbv EB evdsta ]I7J Aa, '^ ds BH 
iz rov xsvrgov rov iitLxvxXov s Ts^ roLOvrcov s0raL 
Tcal ri BA svd^sta a t/3. adrs xat, oHov i6tlv ii BH 
6 v7torsLVOv6a qx^ roLOvrcjv ocal rj ^sv BA s6raL x^ Ad, 
ri d' ijc avrfjg 7CSQLq)SQSLa roLOvrcav zg Ad, olcjv iarlv 
6 tcsqI t6 BHA oQ%^oyG3VLOv xvxkog r|. Tcal '^ ^lv 
vTcb BHA ccQa ycovLa roLOvrcjv i6rlv xg Ad, olcov 
sialv aC dvo oQd^al t|, rj d' vtco ZBHUrj [Eucl. I, 32] 

10 rav ^sv avTwv xd' jc^, olcjv d' at d dQd^al tJ, Totot5- 
rcov cd ]iy. ro6ovrcov ccQa iarlv ^olq&v rj HZ rov 
iTCLKVTtlov 7CSQL(psQSLa rijv ccTcb rfjg GsXtjvrjg iicl t6 
axQLptsg ccTCoysLov 7CSQLSx,ov6a dLocara^LV. 

alk' i7csl rov ^s6ov ccTCoysiov aTCSL%s xaroc rbv %q6vov 

15 Tijg rr}Q7]0SG)g ^OLQag rky i/3, iav v^co&dy^sd^a t6 ^s6ov 
a7c6ysiov xara t6 M zal i^CL^sv^avrsg rr^v MBN xdd'- 
srov iTC avrf\v dyccycD^sv ccTcb rov E rijv ElSl^ sdrac 
ri fisv HZM oXrj TCSQLCpSQSia rcbv Iol7cS)v sig rbv 

TCVXXOV ^OLQ&V %^ ]l7Jy kOLTCfl Ss fj ZM ^OLQCOV ifi £, 

20 K)0rs xal f] [isv V7cb MB Z ycovia^ rovrs6rLV [Eucl. I^ 15] 
fl 'bTcb EB^^ oLcov ^sv si6LV ai 6 OQd^al tJ, roiovtcjv 
i6rlv iP £, OLCDv d' aC dvo OQd-al t|, roLOvrcov %d 7, 
aal rj ^sv iTcl rfjg E^ 7CSQL(psQSLa roLOvrov i6rlv xd 7, 
OLCov 6 7CSQL t6 BEIEJ oQd-oyaviov xvxXog t|, avrfj ds 



4. cc] postea ins. D. 5. ^otai] aqu D. 6. hazL D. 7. 
BHA] -A in ras. D. 8. I^] -^in ras. D. _9. 8vo\ tp D. 

ZBH] corr. ex ZB Dl 10. d] A, corr. ex Td D, dvo BC. 

11. fly] corr. ex fxS D. iazlv] comp. B, -v del. D^. 14. 
anBLxtv D, corr. Dl 19>. HZM] H- corr. ex E in scrib. C. 

21. EBS] EBZBC, corr. C^ 22. iatCv] comp. B, -v 

del. D\ T] ins. D^. 23. ElEl] ES &qa D. UzC D, 

comp. B. 



MA0HMATIKHS STNTAHESil! E'. 379 

'fj ES svd-sta roLOvtcov tcs J, oicov i6rlv y} BE vjto- 
rsLVOvaa qx. xal oiGiv e6rlv aga rj ^sv BE svdsta 
jirj Aa, rj ds ZfE fisra^v rcov %ivrQ(ov T iO", roiovrcov 
^al rj E^ E^raL 1 xal i^rjKoarav rj. TtdXLV^ BTtel i^ 
^LBv VTtb AEB ycovLa vTtoxBLrat roLovrav QTta^ oXcov 5 
sl6\v at dvo OQ^^al rl, r] 8b VTtb EBN BdBL%d-rj xd T, 
a6rs Tcal XoLTtijv [Eucl. I, 32] ri^v V7tb ENB xaraXsC- 
Tts^d^aL rcov avtcbv Qvg v, yCvsraL Tcal rj ^sv sjtl rrjg 
ElEl 7tSQLq)SQSLa roLOvrcov ^vg v, oXcov icrlv 6 TtSQl rb 
EN^ OQd-oyavLOv xvxkog t|, avri) ds rj ES roLovrcov 10 
Qit, Xy^ OLCov s6rlv rj EN vTtorsCvovaa ^. xal oXcov 
i0rlv ccQa rj ^sv El^ Bvd^Bta ~l xal s^r}K06rcbv ^, 17 ds 
^E ^sra^v rcbv xsvrQcov l t-O", roLovrcov xal r] EN 
sGtaL 1 X. xal ix rovrcov aQa l'6rjv syyL^ra rfj ^E 
lisra^v rav xsvrQcov rrjv EN TtdkLv aTtsClri^psv rj dLa 15 
rov M 11S60V djtoysCov rfjg MB svd^sCag iitl rb N 

7tQ66VEV6Lg. 

xal i^ dXXcov ds jtXsLovcov rrjQij^scov rovg avrovg 
Xoyovg syyL6ra 6vvayo^svovg bvqC6xo^sv^ cog ix ro-u- 
rcov ^B^aL0v6d-aL rb itSQl rr^v VTtod^s^LV rrjg 6sX7]vrjg 20 
xard rr]v rov iitLXvxXov %q66vbv6lv 1'dLOv rf]g ^sv rov 
xsvtQov rov iitLXvxlov 7tSQLaycoyf]g TtSQl rb E xsvrQOv 
rov dLa ^s6cov rcbv t,(p8Ccov djtorsXov^svrjg^ rfjg ds rb 
avrb xal rb xard rb ^b6ov djtoysLov rov iitLXvxkov 6r]- 

1. E£7] in ras. D. 2. 97 fih] infra add. D. 3. i#] -& 
e corr. D^. 4. ES] corr. ex £/ D. T — ?)] i^ tj D, rff^D^ 

6. d^] 8' D, idsix^r]] -%- corr. ex -a in scrib. C. 8. yC- 
vix(xi\ mg. D^, T D, Tx D^ 12. hi,r\%oGtoiv\ comp. BD. i\\ 
renouat. D^. 13. ziav\ corr. ex tco A*. 14. t'ffr]f| A\ t6ri\v L. 

21, TiqoGVivGiv — 22. iTii%vyCkov\ bis A, corr. A^. 23. |u,£- 
6Giv\ -6(o- e corr. D^ 24. x6 (pr.)] om. D; mg. aXXccxov ovxco 
xf]g ds v,axa xb (liaov ccnoysLov xov iiiL® 67^1. acpOQL^ova' avxca 
<r-o D^. 



380 KAATAIOT nTOAEMAIOT 

HStov d(poQc^ov6Y]g avtov dia^stQOV ^rjxetc TtQog tb E 
xsvtQOv tTJg d^aXfjg TtSQtaycoyrjg trjv 7tQ60vsv6iv GHjjtBQ 
iitl tOiv akkcov TtoLov^svrjg^ aXXa Ttdvtots TtQog tb N 
xatd trjv l'6riv sitl td stsQa dtd6ta0LV trjg ^E ^sta^v 
5 tG)v xsvtQ(ov sxj^stag. 

g\ Ilcog di,d tcjv yQa^^&v ditb tav TtSQtodtx&v 

XLVTJ^scjv ri dxQtp^^g trjg 6sk7]vrjg itdQodog Xa^- 

pdvstaL. 

Tovtcov ds ovtcog djtodsdsLy^svcjv dxoXovd^ov ts 

10 '6vtog 6vvdil)aL^ tCva dv tQ^itov ^al sjtl tcjv xatd 

^SQog trjg 6sXrjvr]g jtaQ6dcov tdg tcbv ^s^cov 7CLvrJ6scov 

S7io%dg Xa^pdvovtsg svql6xol^sv d7t6 ts tov trjg dito- 

ifig dQLd^^ov xal ditb tov zatd tbv sitLTivKlov trjg 

6sXrjvrjg tr^v yLVO^svrjv TtQb^d^s^LV rj dcpaLQs6LV tfj xatd 

15 iifiKog ^s6rj 7taQ6d<p tov JtaQd f^v dvo^aXLav dLacp6QOV^ 

dLd ^sv t&v YQa^iicbv rj tOLavtrj TcataXa^pdvstaL dLa- 

ZQL6Lg ditb t&v b^OLCjv tolg sntsd^si^svoLg d-scoQrj^dtcov. 

sdv yaQ VTtodsCypiatog svsxsv sitl tf^g v6tSQag tcbv 

jtQOXSL^svcov xatayQacpcbv tdg avtdg VTtod^cb^sd-a TtSQLO- 

20 dLxdg 7CLV7J0SLg aTtoxfjg xal dvco^aXCag^ tovts6tLv dito- 

Xfig iisv tdg sx tov dL7t2,a6La6[iov Gvvrjy^svag pioCQag 

9 A, dvco^iaXCag d' «jro tov ^s6ov dTtoysCov tox> S7tL- 



1. dtafiSTQOv] -ETQov in ras. D. 2. TtQoavsvGLvl -i- corr. 

ex 7] A. 4. [lExalv'] corr. ex ^ Dl 6. ?'] om. C, mg. D^ 
jrcos — 7. Xcni^a.vsxcci\ mg. superiore D^ fol. 109^^, eadem mg. 
sup. fol. 109^^ (17 axpt^ryg] diayiQL^eC^ naQodoi Xa^§a.vovxai) D, 
del. D^ 9. ds] Si] D. 10. dvrog] e corr. D^ 12. svqCgv.o- 
fisv B. 13. Supra xov add. ccQi^fxov D^. y.axcc] v.- corr. 

ex y in scrib. D. xov] corr. ex xo D. 14. yLvo^svriv] corr. 
ex l'' D^ 16. (isv] del. D^ 21. iisv xag sv, xov] in ras. 

post ras. 1 lifct. D. 22. X] e corr. A^ mg. 9X' A*. d'] di D. 



MAOHMATIKHS 2TNTASE^S E' 



381 



xvxXov ^OLQag rky tft Tcal dvtl ^lv rfig EH^ nad-erov 
tijv NS aycoybSVj dvrl de rfjg BA rrjv HA^ dud ^sv 
rCbv avrcbv TtdXiv i% rov dedo^d^at rdg JtQog ra E 

KBvrQCp yovCag 
xal rdg /t E 5 
}ial EN vTto- 
rBLvov6ag l'6ag 
ov6ag ixar£Qa 
^€v rCbv ^K 
xal NlSl £v- 10 
d^sccbv rOLOV- 
tcov dSLXd^TJ- 

6sraL T L^ 
syyLGra^ olcov 
i6rlv 7] ^sv 15 
^B iz rov 
xsvrQov rov 
ixTcsvrQov /LtO- fm, rj ds BH ix rov ksvtqov rov 
ijCLXvxlov s LS^ sxarsQa ds rcbv EK xal ElSl rcjv 
avr cbv o £, xal d^d rovro r] ^sv BK oXrj s0raL^ 20 
xad^ditSQ idsL^a^sv s^TtQoGd^sv^ rav avrcbv JTrj Ag, 
r} ds BE Oftotcog ]irj Xa^ r] ds B^ rCbv XoLTtcbv 
Jirj xg. G)ar iitsl xal rd dith B^ xa\ ^N 6vvrs- 
^svra TCOLst rb dTtb rfjg BN [Eucl. I, 47], xal ravrrjv 
s^o^sv iifjxsL roLOvrcjv ^d" Xa^ oXcav rjv fj iV^ svd^sta 25 
T Ld-. %al olcov i^rlv ccQa fj BN v7torsLvov6a ^, 

2. NS] N- obscumm, v^ supra scr. D. aydycoiisv D. 3. 
avtcbv'] supra scr. D*. 8. ovoag'] i'aag B. 18. 'h^vzqov] v.- 

corr. ex a in scrib. C. 20. o ?] s8 D. 21. tdBL^aiiiv'] post 
a ras. 1 litt. A. 22. Post ftr] del. xs D. 23. aiio] anb 

t&v D. v.aC (alt.)] supra scr. D. 25. olcov] olco C. ^v] 
supra scr. D^. 26. T lQ''] TT- corr. ex JV" D. 




382 KAATAIOT nTOAEMAIOT 

roiovtcov £6taL xccl 7] ii\v N^Sl svd^sta xs syyi6ta^ 7] 
6' m avtrjg TtSQifpsQeLa tocovtcov 7cd y^ oXav s6tlv 
6 TCSQi tb BNlSl dQd^oycovLOV tcvxXos t^. &0ts Tcal rj 
V7C0 NB^El ycovCa^ tovtsativ [Eucl. I, 15] i] vito ZBM^ 
5 otcov ^sv SL6LV at dvo OQd^al t|, tOLovtcjv s6xaL xd y, 
0LC3V d' at d oQd^al t|, tOLOvtcov t/3 a syyL6ta. to6ov- 

tCOV i6tLV CCQa 7] ZM tOV ijtLXVXXoV ItSQLCpSQSLa. 

«AA' ijtSL t6 H 6rj^SL0v trjg 6sX7]vrjg aitsiSL tov M 
[IS60V aTtoysLov tag loLitag stg tbv sva xvxlov ^OLQag 
10 xg ft^, xal XoLTtrjv s%o^sv tijv HZ TtSQLcpSQSLav holqcov 
id |Ltg' cj6ts xal rj vitb HBZ ycovLa^ oXcov ^isv sl6lv 
aC d OQ^^al t^, tOLOvtcjv i6tlv id ^^, oXg)v d' at dvo 
bQd^al t|, tOLOvtcov xd^ Ad, xal r] ^sv iitl tr]g HA TtSQL- 

(pSQSLa tOLOVtCOV i6tlv Xd" Ad, 0LC3V 6 TtSQl TO HBA 

15 6Qd-oy(bvLOv xvxXog t|, -j^ <^' ^^^ '^^S ^^ '^ojv XoLTtcbv 
[Eucl. III^ 31] slg t6 rj^Lxvxhov Iqv xg. xal tcbv V7t* 
aiJtag ccQa svdsLcbv r] ^sv HA s6taL tOLOvtav X AJ, 
oZcov i6tlv r] BH V7totSLvov6a qx^ r] ds AB t&v avtcbv 
^L^ j5. cD6ts xaC, oXcov i6tlv r] nsv B H ix tov xsvtQOv 

20 tov iTtLXvxXov s LS^ r] ds BE idsC%%^r] ]JLrj Xa^ totovtcjv 
xal i] ^sv HA s6taL a x^ r] ds AB o^oCcog s s. xal 



vr 



4. TovvEGTivl corr. ex t-,, D^. 5. sGtaL] bgtlv seq. ras. 1 
litt. D. 6. fy^icra D. 7. 17] yial 17 D. 8. ar}fieiov'] (Th D, 

og D*. anix^i'] corr. ex cctcslxs D^ 11. Hat] bis 'C extr. 

et initio pag. HBZ] HZB C, HBZ supra scr. C^, corr. ex 

BZ D^ 12. TOLOVTCOV 13. TOLOVTCOV] mg. D^ 12. i6TLv] 

comp. BD. d'] di comp. D. 13. rf] BD, supra add. 

A*, om. AC. toiovTcov] etiam in textu D. HA] HA 

aga D. 7tEQLq}8gsLa tolovtojv] mg. A^. 14. HBA] BH J), 

BHA Dl 15. d'] ds C. 18. Post BH del. H Dl ino- 
tSLvovGa] -V- corr. ex o in scrib. C. 19. Mg. toLovtcov ietlv 
ia fi^ oTcov ds at 8vo ogd-al t^ D. 20, Jirj] corr. ex ^ D^ 
21. a x] ax AC, ut saepe. AB] -B e corr. Bl 



MA0HMATIKHS 2TNTASE5iI! E'. 383 

oXrj ccQa 7] EBA roiovrcov i6rlv vy A^, otov Tcal i^ 
JIH ijv a %. xal STtsl Tidliv ra dn avvav avvrsd-evra 
TtoiEi rb dTCo rrjg EH rsrQaycjvov [Eucl. I, 47], s^o^sv 
xal rrjv EH ^TJxst rcbv avrcov vy A^ syyiGra. w6rs 
xai^ OLCov s6rlv rj EH vnorsCvovCa 'qXy roiovrcov xal 5 
ij ^sv HA s6rat p vd'^ rj d' sjt avrf}g nsQKpSQSia 
roiovrGiv p vfi^ oicov serlv 6 TtSQl ro EHA OQd^oyG)- 
VLOv TcvxXog t|. Tcal rj vjtb HEA ccQa ycjvta rov 
Ttagd rrjv dvco^aXiav diacpoQov^ oZg)v iisv Si0iv at dvo 
OQ^^al t|, roiovrciv s6tIv /3 v/S, otcov d' aC d oQd^al tJ, lO 

TOtOVTCOV d K^' OTtSQ TtQOSXSirO dsi^ai, 

l\ Kavovog jtQay^arsia rrjg Tcad-olov 6sXrj- 
vtaxfig dvGy^aXCag. 
"Iva 8s TtdXiv xal did rfjg aavovixfjg ixd^s^sog 
lisd-odsvcj^sv rr^v s^ sroC^ov didxQiOiv rQv xard ^SQog 15 
jtQ06d^aq)aiQS6SG)Vj 7tQ06avs7tXr}QG}6a^sv rb Tcard rr^v 
d:tXfjv VTtod-s^iv TtQOSxrsd^Si^svov rj^tv xavoviov rotg 
^fttt rr^v diTtlfjv dvcj^aXCav 7tQ0%sCQG)g diOQ&ov6d-ai 
dvva^svoig 6slidCoig did rcbv avrcbv yQa^^cjv %dkiv 
XQrjad^svoi ratg scpodoig. ^isrd ^sv ydQ rd TtQ&ra 20 
dvo 6sXCdia rd TtsQiiiovra rovg dQid^^ovg ivsd^TJxa^sv 
rQCrov 6sXCdiov 7tSQii%ov rdg yivo^ivag 7tQo0&a(paiQi6sig 



1. EBA] corr. ex EBJ D^ iazLv'] comp. B, -v del. D^ 

As] corr. ex v^ C^, corr. ex Jg D. 3. EH] corr. ex 

EiV D. 4. EH] corr. ex EN D. fiTjxtt — ^yy icta] in 

ras. D. 6. HA] EA JJ. 9. dvo] b B. 10. rl^pr.)] corr.^x 

T^ in scrib. D. iaxiv'] hatai B, om. D, comp. ins. D^ p v^] 

§N D. 12. ^'] om. A, mg. D. 'nccvovog — 13. avcoficcXia?] mg. 

superiore D. 15. ^t^odtvoj^nr] -co- corr. ex o in scrib. C. 

16. TtQoad-acpaLQFatcog D, corr. D^ 17. TtQOF-atsd-ti^^va^v C. 

21. Supra tovg add. -holvovs D^. aQi&\fiovg A, &QL\^iJLOvg A^. 



384 KAATAIOT nTOAEMAJOT 

t(p rrjg dvo^cclLag aQid^^a TCQog t6 rbv ccTth tov ^86ov 
ccjioyeCov^ rovre6ri, rov M^ Gvvayo^evov sk r&v ^e^cov 
TtccQodcov ^Erccq^eQsad-aL TCQog rb ccKQtpsg ccTCoysLOv^ 
rovrs6riv rb Z. ovtcsq yccQ rQoicov sjcl rijg sxKSL^svrjg 
5 dTCoxfjg r&v 9 X ^olq&v sdsL^a^sv rrjv ZMTCSQLcpsQSLav 
^OLQCjv otxJav i/3 d^ Lva, sicsLdyJTCSQ rov M ybsaov dico- 
ysLOv d%SL%sv 7] 6sX7]vrj ^oLQag rXy i/3, rijv dnb tov 
Z dKQL^ovg dnoysLOv dLd6ra6Lv avrrjg svqcj^sv 6vva- 
yo^svrjv ^olqg)v drjXovorL r^ Ty^ TCQog dg r] dLa rbv 

10 stclkvkXov TCQO^d-aq^aLQS^Lg tfjg ocard fifJKog ^s6r]g klvtj- 
6scog bipsLksL Xa^^dvs^d^aL^ ovrag Kal stcl rcbv dllcDv 
rrig d7Co%f]g dQLd^^cbv^ Sl^ o6cov 6v^iisrQ0v ^v r^rj^dtcov^ 
tdg yLvo^svag rfjg jCQOKSLfisvrjg TCQO^d^ag^aLQS^scjg tci^- 
^Korrjrag dLa rcbv avr cbv ka^pdvovtsg^ Xva ^fj Kad'^ 

15 SKa6rov ^aKQoXoya^sv^ jcaQsd^TJKa^sv OLKSLCjg SKd6t(p 
t&v dQLd^^&v sv r» tQLtc) 6sXLdLG). tcbv 8' scps^fjg 
6sIl8lc3v t6 ^sv tstaQtov tcsqls^sl tdg jCQOSKtsd^SL^svag 
S7CL tov a KavovLov dLacpoQag tfjg TcaQa tbv stclkvkIov 
dvcoiialCag cag tfjg ^syC^rrjg jCQo^d^acpaLQS^scog ^s%ql 

20 r&v s d ^OLQcbv syyL6ra g)d-avov6r]g xard rbv rav | 
jCQbg rd s Ts Xoyov^ rb ds s' rdg v7CSQ0%dg r&v yLVO- 
^svcov 8La(pOQcbv sk rfig 8svrsQag dvo^aXCag TCaQa tfjv 



1. aQLd-iiibv D, sed corr. 2. tov] corr. ex to C^ ovv- 

ayoiisvov] corr. ex 6vvayco[i^v(ov D. 4. tovTecTL D, comp. B. 

5. 9 1] 9a A, cfr. p. 380, 22. 6. fioLQav C. 7. "rXy] -y 

corr. ex f C. 8. awayo^^vriv] corr. ex 6vvayo[iivcov D^ 11, 

6cpdXBi] corr. ex otp^Clri D^ ovrcas] -xcog supra scr. D*. 

13. nQ0v.Si^BV7]g] corr. ex iyyisi^svrjg D^. TtQOod^acpaiQiescog] 
-&- ins. D^, -scog in ras. D^, deinde eras. cog. 14. la^ovtsg D, 
-s- supra ras. D^. 15. fxadraj] mut. in s-ncc^tov D^, co supra 
add. D^ 16. dQid-fimv] ^q D, renouat. D^. tQLta}] f BD. 

17. 7tQ06sv.ts&7]^svag D, sed corr. 20. a] om. D. xara] 
-td supra scr. D^ 22. Si-czcpoQov B. 



MA0HMATIKH2 l^TNTASESii: E'. 385 

TtQCJtrjv Gjg xal ivravd^a tfjg ^syi^trjg jtQO^d-cccpttiQE^scjg 
iSvvayo^ivrig [iolq&v J ri ocata tbv tcjv | TtQog ta rj 
Xoyov^ Lva tb ^sv d' deXcdiov fj tijg Tcata tb aTtoysiov 
tov ixxivtQOv TtSQt tag ^vt^vyCag ytvo^ivTjg d-i^scjg 
rov ijtLXvxXov, tb ds s' tav evvayo^ivcjv vTtsQox&v ix 5 
rij? xata tb TtsQiysiov tov ixzivtQov TtsQi tag dixo- 
to^ovg ccTtotsXov^ivrjg avcj^altag. 

svsKSV ds tov xal xata tag ^sta^v tcov dvo TOt;- 
Tcov ^i^sov jtaQodovg tov iTtizvxlov ta iiti^dllovta 
^iQrj tav JtaQaxsi^ivcov V7tSQ0%cbv dvakoycog Xa^ipdvs- 10 
^d^ai 7taQS%"ri%a^sv <s' ^skCdiOv %SQiiyov td s^rjxo^td^ 
d6a dst Tcad'^ sxa6tov trjg djtoxrjg aQi^^bv tov jtaQa- 
xsi^iivov diacpoQOv Xa^^avo^sya TtQo^tCd^s^d^ai tfi jtaQa 
rrjv TtQcotrjv dvcD^aXCav ixxsi^ivj] xatd tb d' 6skCdiov 
jtQoad-acpaiQi^si. xal tavta ds rj^tv 6vvtitaxtai tbv 15 
tQOTtOV tovtov. 

s6tco yaQ Ttdliv 6 sxxsvtQog trig 6slr^vrjg xvxXog 6 
ABF TtSQi xivtQOv t6 z/ xal did^stQOv trjv ^z/F, 
iq)' rjg VTtoxsCcd^ca tb xivtQOV tov did (li^cov tcbv 
^adCcjv t6 E^ xal dTtoXrjtpd^sC^rjg trjg AB 7tSQi(psQsCag 20 
yQacpivtog ts jtSQl t6 B tov ZH@K iTttxvxlov dirii^a 
rj EBZ. dsdo^d^co^av ds loyov svsxsv dTtoxrjg ^otQai 
^, G)6ts did td avtd totg jtQoaTtodsdsiy^ivoig slvat 
TtdXiV trjv VTtb AEB ycovCav tav di7tXa6i6vcov trjg 



2. r^] To BC et in ras. A, l§ D, Fb D^ ^ 3. Gaidiov y] 

corr. ex GhXCdiov D^, -ov in ras. A. 4. yLvo^isvrig] -V~ eras. A. 

5. f'] Ttsiiittov B. 8. fVfxoc D. >tai'] om. CD. 10. ccvcc- 

Xoyov D, V supra scr. D^. 11. l|7j%o(>ra] ^^ ^- l^- Supra 

-■nei^ivov add. ^ tw f' CEXLdio} D^ Xccfi^dvofiev C, corr. C*. 

14. TtQmtr^v] om. D. 15. nQOGcccpaLQSGtL D, corr. D^ 20. 

aTtoXrjip&eLGrjg] D, ccTtoXELtpd^EiGr^g ABC. 21. Tf] supra scr. D. 

23. tcc avtd] corr. ex tavtd D^. 

Ptolemaeua, ed. Heiberg. 25 



386 



KAATAIOT nTOAEMAIOT 




'hTCOKSt^svrjg aitoyriq ^oiQcov qtc^ xal rjxd^co ^ev xdd^srog ijtl 
XYiv BE iK^Xri^6i0av aTth xov A r\ /i A^ dcrjxd-co ds xal r^ 
HBKzf^TcalvTto- 
KSted^G) rj dito tov 
5 ExsvtQOvijtltriv 
6s^7]vrjv iTi^aXlo- 
lisvri svd^sta i(p- 
ajtto^svrj tov ijtt- 
xvkIov^ Xva ro 

10 %kst6tov dtd(po- 
Qov ysvritat tijg 
dvco^aktag^ (hg rj 
EMN^ ijts^svxd-co 
ts rj BM. 

15 inst totvvv ri vito AEB yovta^ otcov ^sv si6tv 
«i d oQd-al t|, totovtcov vTtoxsttat ^, oHcjv ds «r 
dvo OQd^al T^, totovtcov ^, stri dv xal r] vjtb AEA 
tcbv XotTt&v stg tdg dvo OQd-dg q%. &6ts xat rj ^sv 
i%l tfig jA A sv^siag 7tSQtq)SQSta totovtcov i6t\v QXy 

20 oicov 6 ^sqI tb ^EA oQd^oycovtov oivxXog t|, rj ds 
inl trig EA tcbv XoiTtav [Eucl. Ill^ 31] sig tb rj^txv- 
TcXtov ^. xal tcbv V7t avtdg ccQa svd^stav rj ^sv EA 
totovtcov s6tat J, otcov i] AE v7totsivov6a ^, r] da 
AA tav avt&v 'qy vs. jcal oXcov aQa i^tlv r] ^sv 

1. fioLQ&v] D, (i AC, ft B. 2. iyi^lr^Q-SLaoi B. JA] e 
corr. D^ 6 ^A B. dLrJx^co ds yiccl 7] HBKJ] om. BC. 3. 
HB^zi] corr. ex HBKA Dl 4. ^J om. BC. 7.sv&SLa 

icpuTitofisvr]'] om. A, -cpccnt- in ras. maiore D^ 16. ds] 8' D. 
17. dvo] B B. Ante oyi del. 7] D^. 18. 8vo] ^ BD. 19. 
JA] corr. ex AA D^ sgtlv] comp. BC. 20. JEA] corr. 
ex ^E^ Dl i]] corr. ex sC D. di] S' D. 23. sataL] 

satLv D. z/El seq. ras. 1 litt. D. 24. dA] A- corr. ex 

A D^ 



MA0HMATIKHS STNTAgEiiS E'. 387 

ZlE evd^sta ~i cd', rj ds ^ B o^oicog fid" Jicc^ tolovtov 
actai xal rj ^sv EA svd^sta s T syyi^ta^ 7] 8\ /1 A 
o^OLCjg rj vg. xal iits] tb ccTtb trjg B^d ksTi^av tb 
aTcb trig AA itoisl tb ccTcb tfjg BA [Eucl. I, 47]^ ^tJKSi 
aga s6tai xal oXrj }isv ij BEA svdsia Jirj vy^ Xoiicri 5 
ds rj EB toiovtcov ]iy Jiy^ oicjv s6tlv rj MB ix tov 

KSVtQOV tOV STCiKVKloV S iS. Xttl OiG)V CCQa S0tlv 7] 

EB v7CotSivov6a ^, toio-dtcjv satai Tcal rj ^sv BM 
svdsla id xs^ rj 6' sic avtrjg %SQiq)SQSia toiovtcov Ty 
^, oicjv s6t\v 6 tcsqI tb BEM dQd^oyaviov TcvxXog 10 
t|* Tcal r] vTcb BEM ocQa ycovia^ iqtig 7CSQis%Si triv 
%lsi6triv diacpoQccv tr]g dvcj^aliag^ oicov ^sv Si6iv aC 
P OQd^al tJ, toiovtov satlv Ty Jirj^ oicjv d' aC d dQ^al 
t|, toiovtcjv g vd. dit^vsyxsv ccQa xata tavtrjv f^v 
tfjg dicoxfig d7c66ta6iv tb TCaQcc tr^v dvco^akcav did- 15 
(poQov tG)v Katd t6 aTCoysiov yivo^svov ^oiQ&v s d 
^icc ^oiQoc Tcal s^rjxo6toig vy. s6tiv ds tb okov tb 

llS%Qi tOV TCSQiySiOV didcpOQOV liOiQGiV P kd" JCal OiCOV 

ccQa s6tlv tb ^syi6tov didcpOQOV |, toiovtcov s6tai tb 
tfjg ^iccg fioiQag xal tcbv vy s^riK06tcbv ^p Xrj^ d Tcal 20 



1. z/E] corr, ex AE D^, AE A. T 1-9-] T T- corr. ex H A, 
e corr. D, /^B] corr. ex ylE D^. 2. Hat] x- in ras. A. 

r] seq. ras. 1 litt. D, Te C, 3. BA] corr, ex BA Cl XsL^av] 
X- in ras. 2 litt. D^, supra -ft- ras. 6. fly (alt.)] infra add. D, 
supra scr. Dl MB] "BM' B. 9. 8''] 8s D. fV] corr. 
ex V7t' D^ a-yTT/c?] corr. ex uvtijv D^ 11. Tjri-g'] corr, ex 
d' tig D*. 13, pt] dvo C. iotLv] comp. B, -v del. D^. d] 
dvo C. 14. dn^vsyY.Bv] mut. in dL^^vsyns d' D^ yiatcc] corr. 
ex xar' D^. ttjv] supra scr. D^. 15. ccTtoxiig] cc- et -^g e 
corr, D, avo^aXCav A. 17, iil&l ^oCquL ABD, fttat iioiQu C. 

sh,7]v.oatOLg vy] -tj- e corr. in scrib, C, ^vy D, ^^ vy D^ 
i6tLv] comp, B, -V eras, D, to (pr,)] om. D. to (alt.)] 
corr. ex to5 D^. 19. satCv] comp. B, -v del. D^. tOLOvtcovJ 
corr. ex tmovtov C^. 20. e^rjyioGt&v] comp, D, ut saepe. 

25* 



388 KAATAIOT nXOAEMAIOT 

%aQa%"ri6o^Bv r<p xcbv qtc ccQL^jUicj trjg a7to%rjg iv rm g' 

G)0avt(og ds xal ijtl t&v XocTtcjv t^rj^dtcjv eTtiXo- 
yi6d^EV0i Ttdhv dia tCbv avtG)V td ovt cog Xa^^avo- 
6 ^sva ^eQTj trjg tcjv dvo dvco^aXt&v v7t£Q0%r]g JtaQsd^r]- 
xa^sv totg oiKsCoig dQid-^otg td STti^dXXovta S7id6t(p 
tfig TtaQaxsi^svrjg v7tSQ0%r]g s^rjxo0td tcjv oXcov ^ drj- 
Xovoti TtaQatid^sasvcov t<p di7tla(5iovi t&v 7, ^oiQ&v 
tfjg dTtoxrjg apt-O-^co, og s6tiv xatd tdg qti tov TtSQi- 

10 ySiOV tOV SKKSVtQOV. 

%al J' 8s TtQO^sd^rjxa^sv <5sXi8iov 7tSQiS%ov tdg 
ocatd TtXdtog yivo^svag TtaQodovg tfjg 6sXr]vr]g scp' 
sxdtSQa td ^SQr] tov did ^s6cov t&v ^codicjv cog STtl 
tov did tcbv 7t6Xcjv avtov tcvtcXov^ tovts6tiv tdg dito- 

15 Xayb^avo^svag tovtov tov kvxXov 7tSQicpSQSiag ^sta^v 
tov ts did as6(ov tcbv ^mdicov nal tou 7tSQl to avto 
TiSvtQOv Xo^ov tf]g (jsXrjvrjg xvtcXov xad-' sxd6trjv t&v 
Tcatd iiSQog S7tl tov Xo^ov ^taQodcov. TcsxQrj^sd-a ds 
%al 7tQog tovto dsi%si t^ avtfj^ di f]g xal tdg ^sta^v 

20 tov ta L6r]^SQivov Tcal tov did ^s6g3v tcbv ^Gsdicjv 
TtsQicpsQSiag tov did t&v 7t6Xcov tov i6r]^sQivov S7tsXo- 
yi^d^sd-a^ svd^dds ^svxol cjg tfjg ^sta^v tov did ^s6cov 
tcbv ^aydicjv xal tov ^oqsCov rj i^OTtov itSQatog tov 
Xo^ov xvxXov 7tSQi(pSQSiag tov di d^KpotSQCov tSrv 

25 7t6Xcov avtcbv yQacpo^svov ^syi6tov xvkXov Ttsvts ^oi- 
QG)V V7taQ%ov6r]g^ S7tSid7]7tSQ xal r]^tv^ xad^d^tSQ Tcal t(p 
^l7t7tdQ%cp^ did tG}V 7tSQl tdg PoQSiOtdtag %al voticotdtag 
7taQ6dovg (paivo^svcov S7tiXoyi^o^svoig tr^Xixavtr] sy- 

1. ro5 (pr.)] corr. ex ro C^ ccQtd-^oi] corr. ex agLd^^oiv D. 

5. ocvopLccXL&v C. 6. fxaffrco] -oj e corr. D. 8. ^] ins. D'. 

9. ccQid'(im'] corr. ex ccQL&fi&v D. og] corr. ex o D^, 8GtLv] 
comp. B, -V eras. D. 11, ^'] £§dofiov B. 12. yLvoatvag'] corr. 
ex yLvofiivovg D. 13. tcc] om. D. 14. v.vyiXov] om. C. roi;r- 
sGTLv] comp. B, -v eras. D. 16. nfQL to] tcsql post ras. 2 — 3 
litt. C. 18. ;io|ov] Xo^ov yiV)iXov D. ds] om. B. 23. ?)! 
votCov A*, r\ v\ot'LOv A. 24. loh,ov] inc. fol. 106^ B. 25. tto- 
Xa>v] corr. ex nolXcov D. 27. ^OQiLotdtccg] -d- in ras. D. 

rortorarag C. 



MA0HMATIKHS STNTASEiiS E'. 389 

YL6xa eg)' txdxsQa xov ^coSiaxov yj 7cX£l6x7j nccQodog 
X7}g ^skrivYig xaxaXa^pccvsxat^ zal Ttdvxa ^iedov xd 
tisqX xdg xr}Q7]66Lg avxrjg xdg xa TtQog xovg d^xeQag 
xal xdg dcd x&v OQydvcov d^scjQov^svag 6v^(pd)VG}g 
IfpaQiiLolexai xatg xrjXLxavxaLg xaxd TtXdxog ^eyC^xaig 
TtaQodoLg^ G}g xal dLcc xcbv ecpe^rig dTtodeLx^ri^o^evcov 
o^oloyrjd^tj^exaL. xaC edXLV xo xr\g xa%6Xov 6eXrivLaxr\g 
dvcj^aXCag xavovLov xolovxov 

1. fg?'] 7] iq)' D. 17] om. D. nccQoSog^ corr. ex nag- 
odo) D^. 2. 'KcctaXccfi^dvEtaL] mut. in 'natsXa^pdvsto D^. 7. 
tati, D, comp. B. to] in ras. D. 8. toiovtov^ des. fol. 136^^ A, 
fol. 136^ uacat. Post toiovtov add. fol. IQ&^ B: 

t6 tfiq %a^6Xov osXrjVLayiTig &vco^aXLag v,av6vL0V nsQL^x^L iv 
iilv toig ■jiQmtOLg dvo asXLdCoLg tovg yiOLVOvg ccQL&^ovg trig ts tov 
inLY,vv.Xov ccTtb tov anoyslov tov iwivtQOv 'HiVT^ascog Tial a^vtfig 
tfig GsXrivrig ccnb tov caiQL^ovg 6cnoysLOv tov inLyivyiXov xat stL 
tfig inl tov Xo^ov a^vtfig n^bg tbv dLCC (liacov tav t^codCoiv :<~ 

iv ds To5 y asXLdCco tccg dLacpOQCcg tov fisaov ccnoysCov tov 
iniyivyiXov nQog tb av.Qi^sg anoysLOV : — iv Ss to5 d tdg SLacpoQag 
tfig naQcc tbv iniv,vv.Xov avcofiaXCag tov inLvvvXov vata tb ccno- 
ysL^tatov tov ivvivtQOv tvyxdvovtog., tfig 8s asXrivrig inl tov 
inivvvXov slg to: nQorjyovfisva cpsQO^iviqg : — 

iv ds t(x> J vnsQOxdg (comp.) tcbv yLVO(iivcov avcoiiaXlag 
SLacp^QCov iv tfig vatk t6 nsQLysLOv tov iwsvtQOv d^iascog n^bg 
tbv vatd t6 ccnoysLov avtov d-iaLv tov inLvvvXov tf^g asX^^vr^g 
tccg avtdg iv sv.atSQcc ^sasL ccnb tov ccvQL^ovg ccnoysCov inL- 

vvvXov /x dcpLata^i^ : — iv ds ta '^ tdg vnsQOxdg t&v vatd tdg 
fista^v tov dnoysLov val nsQLysCov tov ivvivtQOv naQ^dovg tov 
inLvvvXov yLVOiiivcov (isyCatcov naQa tr]v inl tov inLVvvXov 
(liarjv tfig asX-rjvrig ^iaLV dLacpoQCOv n^bg tr}v ini tov dnoysiov 
tov ivyisvtQOv ^saLV tov inLVvvXov yLVO^isvrjv (isyCatr,v dvco^ia- 
XCav wg tfig iisyCatr^g vnsQOxf]g tf]g na^d tfjv B dvconaXiav n^bg 
trjv d i]tOL tfig naQa tfjv ini tov nsQiysCov tov iwsvtQOv ^iascog 

tov inLvvvXov vnSQO tf]g yLvoiiivT]g [isyCatr]g dvcoy^aXCag n^bg tf]V 
inl tov dnoysCov tov ivvsvtQov d^iaLV tov inLv,vvXov (isyCatr^v 

dvco[iaXCav tcov B X@ jx iistaXr^cpQ-sCar^g slg | s^r]voatd. 

iv ds To5 ^ tdg dnoXa(i§avo(iivag nsQLcpSQsiag icp' svdtSQa 
tov i^adLavov iista^v tov Slu [liccov t&v ^cpdicov vvvXov val tov 
Xo^ov tf^g asXr]vr]g vvvXov vaQ'' SY.datr]v t&v vatd (liQog inl tov 
Xo^ov KvvXov tf]S asXi]vrjg nuQ^dcov tov dLU t&v n6Xcov tov dta 
(liacov tcbv ^cpdCcov vvvXov : — 



390 



KAATAIOT nTOAEMAIOT 



7^'. Kttvoviov rfjg Tcad^okov 66lrjVLaxr}s 
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1. 7]'] mg. B, om. ACD. 
fol. 113^ D, totam tabulam fol. 106^ B, coll. 8—^ om. C. 



coll. a — 8 fol. 113'", reliquas 
4. 
i-nKSVTQOv'] corr. ex anoysLov D^ nXdtovg -Aal (iriv.ov£\ corr. ex 
S7tLv.vv.Xov D'^. 5. TtQoaO^aq^aLQsasLsi^Y.)] TtQoad^aq^aLQsascog BC, 
7tQoad'a(paiQ^a'' D, -d-acp- in ras.; TtQoad-acpuLQsa^^ D^. nQoa&- 
ucpuLQsasLg (alt.)] nQoad-acpaLQsascog B, nQoaQ-acpaLQsa^ D. 6. 
%olvol] add. D^ anoysCov'] om. D. snLvvvlov] om. D. 8. ^o- 
QSLov nsQag] A, om. BCD. 9. v8] vr] B. 10. t?]] tTjt D. x] 
i-S A. 11. vs] v D. 12. %d] Y.a D. 13. a] corr. ex J in 
scrib. D. y] et reliqua pars columnae ad lin. 43 in ras. D. 18. 
<j9^] rf)8 D, et similiter deinceps in hac col. (« = a). 20. /li'9'] 
(jis D. 31. Zg] ^5 D. 32. l^ (pr.)] ;ia D. 33. v.s'] v.8 D. 34. 
Qv.i\ QL? D. 35. Qvd-] QL& D. ^] y D. 36. l? (pr.)] g D. 

43. Xrj] corr. ex Xg in scrib. C. >i^ (alt.)] l^ D. 44. fe-] ls B. 

45. V5] corr. ex (ig in scrib. C. ls] l? D. 48. ^ (sec.)] l8 D. 

50. X^] X seq. ras. 1 litt. D. 51. (i&] in ras. D. 52. o (sept.)] 
in ras. D. voxlov nsQug] A, om. BCD. Infra add. A: 

rcc asXC^La tf]g vad^oXov asXr]VLavfig dvoofiaXCag slalv ovtcog 

7 « >f. /1/1/1/1/1 

sv t^ avvtat,SL r J s <; ^ 

> « / /1 /1 /1 /1 , , 

sv Tw nQOXSLQcp r s <5 j nXatovg 

v.av6vL asXT]vr,g 



392 KAATAIOT nXOAEMAIOT 

d"'. UsqI tfjg xad^oXov ^slrjVLaxTJg iprjcpocpoQLag^ 

'06dictg ohv ecLV TtQoatQa^ed^a trjv dia tfjg ixd^soecog^ 
tov xavovCov ^ri^pocpoQLav tfig CsXrjVLaxfig dvG)yi>akCag 
7COLi^6a0d'aL^ Xa^ovteg td xatd tbv vtcoxsC^svov iv 
5 'AXe^avdQeCa %q6vov ^e6a XLVfj^ata rijg 6e2,7Jvrjg ^yj- 
xovg te xal d7to%f]g xal dvcD^aXCag xal jcXdtovg xata 
tbv vjtodedeLy^evov tQOJtov tbv 6vva%%^evta TtQ&tov 
tfig d7to%rjg dQLd^^bv dL7tXa6Ld6avteg jtdvtote xal d(pe- 
kovteg^ edv e%(o^ev^ xvxXov el^eveyxovteg te eig tb trjg 

10 dvay^aXCag xavoviov tdg JtaQaxeL^evag avt(p ^oC^ag ev 
tm y' aeXLdCG) tov ^ev dQLd-^ov tov 8L7tXa6La6^evtog 
ecog QTt ^OLQG)v bvtog 7tQo6%^y']6o^ev tatg trjg dvco^aXCag 
lieGaLg ^oC^aLg^ v7teQ7tC7ttovtog de tdg QTt dcpekov^ev 
dTt avtav^ xal tbv yevo^evov dxQL^fj tfjg dvco^aXCag 

15 dQL&fibv eL6oC6o^ev eCg tb avtb xavovLOv xal triv 
TtaQaxeLiievriv avt(p TtQoOd^acpaCQeCLV ev ta tetaQtco 6e- 
Xl8C(p xal etL tb 7taQaxeC^evov ev tc5 7te^7ttG) 6eXLdCG> 
dLacpOQOv d^toyQail^o^ed^a %G)QCg. ^etd de tavxa xal 
tbv dedL7tXa6La6^evov tfjg iie6r]g d7to%fig dQLd^^bv ei6- 

20 eveyxovteg elg td avtd 6eXCdLa^ o6a dv 7taQaxerjtaL 
avta e^rjxo6td ev t(jj extco ^eXLdCcj^ td to6avta e^rj- 
xo6td Xa^ovteg^ ov dTteyQaxfjd^ed^a dLacpoQov^ 7tQ06d^7J- 



1. -&•' — ip7](po(poQLag~\ om. D. 2. sdv'] i- in ras. D^ ttjv] 
om. C. 3. asXrjViaKfjs] -i- in ras. 2 litt. D. 4. xa] om. D. 

8. Supra acphXovTBg acld. avixo[i D^ 9. v.vy.Xov iav s'xo)- 

^tv D. Tf] supra scr. D^ 10. (xoLQag ivj corr. ex fiiv D^. 

11. aQL&^ov] -&- in ras. D^ 14, yLvo^tvov D. 16. xt- 

TdQta)] j BC. 17. JTffiTrrw] f BCD. 18. ccTtoyQailxa^sd^a D^ 
sed corr. 20. av] idv D. naQdyitLvrai D. 21. t%za}] s 
BD. ra] corr. ex t6 C^, om. D. 22. dittyQaipd^ed^a] d- 

mut. in i- B^ nQoad-rjao^tvl A*, 7tQoad^r]aofit\v A. 



MA0HMATIKHS STNTASESiS E'. 393 

0o^£v aisl tfi SKtsd^si^evr] tov d' ^sXidCov TtQo^d-acp- 
aiQS^Ei Kal tag ^vvaxd-sc^ag ^ocQag^ iccv ^ev 6 trig 
avo^aXCag axQL^rig aQL&^bg kag QTt [LOiQcbv ijj dq)£- 
Xov^sv dito tG)v tov ^7]xovg xal tcbv tov nXdtovg 
^sGcov ^OLQCJV, idv (f V7i£Q tdg QTC^ 7tQo6d'7J0o^£V av- 5 
tatg. xal tCbv yEvo^ivcov dQtd-^cov tbv ^lv tov ^t]- 
xovg ixPaX6vt£g ditb trjg xatd triv i7to%riv ^OLQod^E^Cag^ 
ojtov dv TiataXri^ri^ iK£t tr^v 6£l7]vrjv (p7]6o^£v £ivaL 
dxQiPcbg, tbv d£ rov jtXdtovg tbv ditb tov ^oqeCov 
jtEQatog £L6oC6ofi£v £lg tb avtb xavovLOv^ xaC^ o6aL lo 
idv (h6LV aC 7taQax£C^£vaL avta ^otQaL iv t<p J' a£- 
XlSCco tov Ttkdtovg^ todavtag d(p£^£L tov dLd iii^cjv 
t&tv ^ipdCcjv t6 xivtQOV tf^g 6£X7]vr]g i^tl tov dtd tcbv 
7t6Xc3v avtov yQacpo^ivov ^EyC^tov ktjxXov^ xal idv 
^£v 6 ^C^EVT^vEy^ivog dQLd-^bg iv totg ^tQCJtOLg f If 15 
0tC%OLg^ cog 7tQbg tdg aQXtovg^ idv d' iv totg V7t 
avtOTjg^ cjg 7tQbg ^Earj^^QCav^ tov ^lv 7tQ(btov t&tv 
dQLd^^&v 0£hdCov 7t£QLi%ovtog tr]v dit ccQXtcjv 7tQbg 
^£6rjiiPQCav avtfig 7tdQodov^ tov dl dEvtiQov tr]v dTtb 
li£6r]ii^QCag 7tQbg tdg ccQxtovg. 20 



1. cciL D. ^'] TtraQTOv C. 2. 6] ^v 6 D. 3. (loi- 

Qdv QTt (corr. exQvJ)^)J). ^] om. D. 6. Q7i~\ -n e corr. D^ 

TCQQGd^riocoiitv BC. 7, iv.§dXXovT£g D, corr. D^ Post ccTto 
del. ToD^ 11. ^'] corr. ex | D^ 14. %at] comp. ins. D^ 

15. ?}] rj AC, om. B. ti] in ras, D. 16. Post 6TCxoig 

add. OTi firidiv d^LoXoyov F iv Tccig Gv^vyia ig rbv «W T7)g 6b- 
Xrivr\g v^ D, del. D*. 17. uvTovg'] corr. ex avrotg D^ 19. 
Triv] om. D. 



394 KAATAIOT nXOAEMAIOT 

l\ "Oti ^rjdhv ic^LoXoyov yivexai dLKCpOQOv iv 

ralg Gvt^vyCaig %aqdc rbv exxsvrQOV rfjg ^eXrjvrjg 

zijxlov, 

'ETtal S* axoXovd^ov i^riv 8i6rd6ai nvdg^ ^7]Jtors 
6 ocal TtSQl rag 6vv6dovg xal rag TtavGslrivovg Tcal rag 
iv ravxaig ioclsLxl^SLg d^LdXoyog rLg dLaipoQa TtaQaxo- 
Xovd'7]0'rj Tcal dLa rbv sxxsvrQOv rrjg 0sX7JvYig xvxXov 
ra ^Yj Ttdvrors xal Ttdvrcog iv avratg i% avrov rov 
ditoysLordrov rb tcsvxqov rov iTtLXvxXov rvy%dvsLv^ 

10 dkka Tcal d(ps(5rdvaL avrov TtSQLcpsQSLav LKavrjv dvva- 
^&aL dLcc rb rdg ^sv xc(:t' avrb rb ditoysLov d-i^SLg iv 
ratg ^s^og d^scoQOv^ivaLg 6vt,vyLaLg djtorsXstad-aL, rdg 
d' dxQL^stg ewodovg xal 7tav6sk7Jvovg ^srd rijg sxars- 
Qov rcDV (p(Drc3v dvco^aXiag Xa^§dvs0d-aL^ TtSLQado^sd^a 

15 7taQa6rfj6aL rr^v roLavrrjv dLacpoQav ^rjSs^Lav d^LoXoyov 
duaQrLav itSQL rd cpaLvo^sva nard rdg Ov^vyCag dvva- 
^svrjv dnsQyd^aOd^aL^ xdv ^rj ^vvsTtLXoyL^rjraL rb TtaQa 
rrjv ixxsvrQorrjra rov xvxXov dLdcpoQOv. 

s6rc3 yaQ 6 sxxsvxQog rfjg 6sX7]vr]g xvxXog b ABF 

20 TtSQL xivrQOV rb A xal dLd^sxQOv xijv AAF^ icp ^g 
SiXTJcpd^co rb ^sv toi) dtd ^i^cjv r&v ^(pdLCOv xivrQov 



1. (,'] BC, mg. A*, 7) mg. D. ori — 3. v.vv.lov] mg. 

superiore et mg. exteriore D^. 4. bnsC^ corr. ex iiil C*. 

EGxiv] comp. B, -V del, D^ 5. xdq (sec.)] om. CD. nav- 

GiXrivovg] 7tav([ ' D, ut saepius. 6. alioXoyog] corr. ex a:|to- 

Xoymq C^ naQwaoXovQ^riGei C. 7. Supra did scr. n'^ D^ 

8. ^v\ A\ s\v A. 9. dnoy£iovxdxov D, sed corr. 10. 

dvvaG^ai] 8C8oG%-aL C, " add. D^ et mg. ^ dCSoG&ai. 16. ^v- 

B 

yCaq D. 20. v.ivxQcov D, corr. Dl didiLtxQov] dia D, '^^ 

add. D*. AJF] mut. in JET D^. 21. sllijacp^co D, 

corr. D*. 



MA0HMATIKHS STNTAHE^S E' 



395 




Tcaxa xh E 6rj^stov^ t6 d' dvrixsi^evov tc5 z/ Tijg 
7tQ0&vsv6S(Dg 6r]^SL0v xara t6 Z, ^cat a7ColYi(p%'si0rig 

ano %ov A aTtoysiov rfjg 
AB TCSQLCpSQsCag ysyQacpd-co 
^sv tcsqI rb B 6 H@KA 5 
STtiKvxXog , S7ts^svx^(o6av 
ds rj rs BA xal ij HBKE 
ocal srv rj BAZ. 

STtsl roCvvv ^cojTa dvo 
rQOJtovg dvi/c^Tttt dcacpsQSLv 10 
t6 TtaQa rrjv dvco^aXtav 
ILsysd-og rr]g Tiard t6 A 
ditoysLOv ^s6s(x)g rov STtLxvxXov did rs rb nsQiysLorsQov 
avrbv yLVO^svov ^sC^ova JCQbg r(p E ycovCav djtola^- 
^dvsLv xal did t6 rr^v 7tQ66vsv6LV rrig Kard rb ^s6ov 15 
d:t6ysLOV xal TtSQLysLOV dia^srQOv ^rjxsrL JtQbg t6 E 
TcsvrQOv., dXXk itQbg t6 Z arj^stov yCvs^d^aL^ TtXstdrov 
ds 6vvC0raraL t6 ^\v TtaQa rrjv TtQ^hrrjv alrCav dLd- 
(pOQov^ orav Tcal t6 TtaQa rr^v dv(o^aXCav rfjg 6sXr]vr]g 
7tXst6rov ^, t6 df xard rrjv dsvrsQav^ otccv tcsql t6 20 
d7t6ysLOv t) t6 7tsQCysL0v rj 6sXr]vrj f] toi) STtLXVxXov^ 
dr]Xov^ OTfc, orav ^sv t6 7taQd rf]v TCQCjrrjv alrCav dLa- 
(poQov 7tXst6rov 6v^PaCvr]^ r6rs t6 ^sv Tta^d rr]v 
dsvrsQav dvs7CaC6d-r]rov s6raL TCavrsX&g dLa t6 rrjv 
6sXr]vr]v stcI rcbv S(pa7cro^svcov sv&SLcbv ov6av rov 25 

1. 6r]fii:tov'] G D, ut saepius. tc5 A] tcav ij D. 2. ano- 
Xr](icpd-£L6r}g, -ti- e corr., D; ft del. D^. 3. A] supra scr. D^ 

5. H@KA] H&KA D, ut uidetur. 6. snC%v7ilog] om. C. 

8. hi] -L postea ins. A, corr. ex iGxtv D, 14. to5] t6 D. 

16. TtSQiysiov] -V e corr. D. E] corr. ex Ix D. ^ 20. rf] 
corr. ex r^v Dl 21. xo] om. D. i]] t]v i] J) , ji i] D^. 

tJ] om. D. 22. Supra utticcv add. avcoftaXtai' D^.' 23. 

cva^ccCvsi D, corr. D*. 25. ovaav] corr. ex ovgcc C^. 



396 KAATAIOT nXOAEMAIOT 

iTCLXVKXov ijtl nokv tijv %Qo6^aq)aLQe6iv adidfpoQov 
TtoLstv^ dvvatbv d' £6raL xriv axQL^ri ev^vyLav tflg 
liierjg dLSvsyxsLV avva^cpotsQOLg totg itaQa tijv dvcs- 
^alCav dLacpoQOLg ixateQov t&v (pcDtov tov ^lv scatcc 
5 TtQoad^sOLv ovtog^ tov ds xat dcpaCQEGLVy otav dh tb 
;carft: tijv dsvtiQav tb tfjg 7tQ06vsv66(Dg dLacpoQOV 
7tk£t6tov 6v^PaCvrjy t6t£ tb ^sv TtaQa tijv TtQCJtrjv 
TtdlLV dvETtaC^d^rjtov ictLV dLcc tb xal oAov tb TtaQcc 
tr^v dvcj^aXCav rj iirjdhv i^ ^Qaxv jtavtd7ta0L yCv^ad-aL 
10 trjg delilvrjg TtsQl tb dnoy^LOv r) tb 7t£QCy£L0v tov iitL- 
xvkXov tvyiav ov6rig^ dLoC6£L d' rj dxQL^rig 6vt,vyCa 
tfig ^i^og d^EcoQOv^ivrjg ^ovo) rc5 TtaQa t^v rjXLaxriv 
dvoiiakCav dLacpOQCo. 

V7tOX£C6d-G) 8rj 6 ^£V ijXLOg Ti)i/ TtX^C^trjV 7tQ66d'£6LV 

15 7toLov^£vog tcbv p xy ^olq&v^ rj ds 6£X7]vrj TtQ&tov 
xal avtri trjv TtX^C^trjv d(paCQ£6LV ^toiov^ivrj tav £ d 
^OLQCJV^ Xva xal rj V7tb AEB ycovCa tdg ^vva^cpotiQCJv 
tcbv ^ xd liOLQcbv 6L7tla6Covag 7t£QLixr] lS ft^, xal d^- 
d^^C^rjg d7tb tov E icpaTtto^iivrjg tov i^tLXvxXov rij? 

20 E0 fWgfv^t-d-cj ri B& xdd-£tog [Eucl. III, 18], xal itL 
djtb tov /i i7tl trjv BE xdd^Etog rjx^(0 rj ^M. 

i7t£l ovv r] V7tb AEB ycovCa^ olcjv ^iv £l6lv at 
d OQd^al tJ, tOLOvtcov ictlv lS Jirj^ oXcov d' ai /3 
OQ&al T^, TOtovrcov xd" Ag, £l'rj dv xal rj ^lv iTtl tfjg 

1. adLacpoQov'] siipra scr. D, corr. ex didcpoQov C^. 5. ticct'] 
mut. in zccTd D^. 6. to] om. D. 7. gv^^uCvei D, corr. D^ 
xo] supra scr. D^ 8. iidUv'] -iv in ras. D. laxLv] comp. B, 
ictcci D, r^ supra scr. D^ 9. navtdnaGiv BC. 10. anoyuov] -s- 
e corr. in scrib. A. nsQlysLov] -i- postea ins. A. 11. d'] 
di D. 12. Tw] rd C. 18. nhQLExn C. 21. JM] post z/ 
ras^l litt. D. 23. tGtCv] comp. B, -v del. Dl_ id] D*, 

l\ 8 D. 8'] 8 D, ds Dl §] dvo C, corr. ex Zp' D. 24. 
il'7] — p. 397, 1. iotLv] supra scr. D^ 24. tfjg] ^ supra scr. D. 



MAGHMATIKHS STNTASESiS E'. 397 

/JM 7tSQig)8Q6ia roiovx(ov %%• Ag, oXc3v i^tlv 6 tcsqI 
t6 ^EM oQd-oycjvLOv xvxkog r|, i^ d' stiI rrjg EM 
rcov XoL7CG)v [Eucl. in, 31] slg ro rjnLxvxXLOv ^ xd' 
y.ccl r&v V7t avrag aQa svd^sicov rj ^sv z/M roLovrcov 
£6raL X Ad", oXov s6rlv r] AE v7CorsLvov6a qtc^ r} ds 5 
EMr&v avrCbv Qig a. &6rs TcaC^ otW s6rlv rj ^sv /lE 
Hsra^v rCbv xsvrQCov l 1%-, r] 8s B^ sk rov xsvrQov 
xov SKXsvrQov ^d- Jia, roLOvrcjv %al rj ^sv z/M s6rai 
^ At^, r] ds EM o^OLCog %• vd'. xal stcsI t6 aito rrig 
jBz/ Isl^av t6 aTto rrjg ^M TtOLst rb ccjto rrjg BM 10 
[Eucl. I, 47], yCvsraL Tcal rj ^sv BM svd^sia fiO" Af, rj 
6 6 BME oXrj roLOvrov vd' Ag, otcai/ sarlv xal rj B@ 
SK rov Tcsvrgov rov STtLXvxlov s Is. ocal oicov s6rlv 
ccQa rj EB v%orsCvov6a qtc^ roLOvrcov xal rj ^sv B@ 
svd^sta s6raL T kd^ rj d' cV avrrjg jtSQLCpsQSLa xolov- 15 
tGiv T Kal s^r}xo6r&v g, oicov s6r\v 6 TtSQi rb BE& 
ogd^oycovLOv xvxXog t|. xal r} VTtb BES ccQa ycovCa 
rov 7tlsC6rov dLacpoQov rfjg dvco^aXCag^ oXcov ^sv sl6lv 
ai dt5o oQxl^al rj, roLOvrcov s6rai T xal £^rjxo6rmv g, 
otcov d' aC d OQd-al t|, rotovrov s y dvrl 1 d rcov 20 



1. 6 — 2. t|] supra scr. in ras. D*. 2. JEM] JM D. 

17] otcov Igxlv ccQa otibq (corr. in 6 nEQi D^) tb JEM ogd^o- 

ymvLOV v.vv.Xog t| tOLOvtcov ictlv 17 E7tl tfyg /J M v.d' X? 7] D. 

3. XoLTtcbv'] ccvtav B. fjfnnv-nXLovl 17- corr. ex N in scrib. A. 

qT']1i Qv J). 5. 1] e corr. D^ 6. EM] ME B. 7. iyi\ 
A\ ijx A. 8. h-nivtQOv] s- in ras. 2 litt. D. z/M] e 

corr. D^. 9. insl to] supra scr. D^ 11. (isv BM Evd-eLo,] 
in ras. D. 12. BME] -M- corr. ex E in scrib. D. iatCv] 
comp. B. xat] om. D, 14. B&] corr. ex K@ A\ 16. 

tlccl] comp. supra scr. in ras. D^. s^-q-noatcbv] comp. e corr, D. 

g] corr. ex xat D^. 19. dvo] ^ BD. l] Siyia corr. ex 

-xat D^, r supra scr. ■nocl s^rivoatcbv] e corr. D*. ?] corr. 
€x %at D^ 



398 



KAATAIOT nXOAEMAIOT 



yivo^evcDV xara ro A aTCoystov 'ovrog rov btilxvkXov. 

dirjvsyxEV aga icaQa ravrrjv rrjv atrCav t6 TtaQa rrjv 

dvto^aUav dtdcpoQOv i^r}xo6rotg dv^lv ^iag ^oigag^ 

ccTtSQ ovds 1(5' dvvarai ^Ldg S^ag diaipsv^aGd-aL. 
5 Ttd^LV vTtoxsL^d^co Tcard rb A ^s6ov TtSQLysLOV rj 

6sX7]vr]^ Xva drjXovorL rj vjtb AEB ycovLa rdg dtTtka- 

Otovag syyL0ra%SQLS%ri 

^idvrjg rf]g rjXLaTcfjg dvco- 

^akCag ^OLQag d jiZg, 
10 xal STtL^svx^sCdrjg STtl 

rrjg byboCag xarayQa- 

g)rlg rfjg EA svd^sCag 

Ttdd^sroL rii^GiCav inl 

rfjv BE dnb iisv rov A 
15 rj ANc, dnb ds rofj z/ 

rj ziM, dTtb ds rov Z 

iitl rfjv BE ix^Xrj^st- 

0av rj ZlSl. xard ravrd 

d^ rotg s^TtQoed-sv^ iTtSLdrjTtSQ rj TtQog rc5 E yavCa^ 
20 oCcDV [isv sl6lv aC d OQd^al ir|, roLOvrov idrlv d fZg, 

oXg)V d' at dvo oQ^^al t|, roLOvroiv 0" A/3, sisv dv 

xal ai lisv icp' sxarsQag [Eucl. I, 15] r&v ^ M xal 

ZS TtSQLCpSQSLaL rOLOVrCJV d' Aj3, olcOV SL61v oC TtSQU 

rd E^M xal EZ^ dQd^oyavLa xvxXol tJ, «i d' icp 




1. A^ supra scr. D'. 3.. Svci B, ^ D. 4. tg'] T' g' 

ABC. 5. yf] supra scr. D^. 7. TtEQitx^'- ^- H- >tar(v- 
yQCicpfig'^ seq. ras. C, -t- corr. ex l D^ 13. tTtl rrjv BE 

TJx^meav D. 14. BE] B0 BC, corr. Cl 15. ccTib ds tov A 
17 z/M] A, om. BCD. 17. hnX tT]v BE] A, om. BCD. ix- 
^XrjdsLGa B. 18. tu avra D, 20. ictiv'] comp. B, om. D. 

22. ettatutsQug C. xat (alt.)] om. D. 24. xai] om. D. 

yiMoCj yy D. ^] ^ AIA TO ICHN eiNAI THN AG TH eZ D, 
corr. D^. 



MA0HMATIKHS STNTASEiiS E'. 399 

ixareQas rcbv EM xal ElSl rcbv koLTt&v [^ucl. IIT, 31] 
sig ra rj^LXVKlta qo tctj. xal r&v vtc avrag aQa 
svd^sL&v ixatSQa ^lv tSiv ^M xal ZS roLOvrcov e6raL 
-9" vrj^ OLCov iarlv ixareQa rcov zJE xal EZ v^oret- 
vovCcbv QKy ixareQa de rav ME xal ES evd-eLcov r&v 5 
avrcbv Qid" Xe' &6re Tcat^ olov i6tlv ixateQa fiev t&v 
/lE xal EZ evd^eLcbv T Ld', r} de ^B ex roi) xevrQOv 
rov exxevrQov ^d' Jia^ e6raL xal ixareQa ^ev rcbv z/M 
xal ZS evd^eLcbv o va^ ixareQa de rcbv ME xal El^ 
r&v «vr^v T l^. xal eTtel tb ano tr^g Bzl ^etil^av tb lO 
ccTtb tfjg z/M TtOLet ro aTtb trjg BM [Eucl. I, 47], e6raL 
xal rj BM ^TJxeL tcbv avtcbv eyyL^ra ^d' ^a. &0re 
xal r] fiev BE evd^eta e6raL vd' vrj^ rj de BlSl oXrj 
roLOvrcov b ti, oicov xal rj ZS ijv o va. dLcc ra avrcc 
de xal rj BZ vnoreCvoviSa r&v l6cov eyyLOra e6raL b 15 
Te. xaC edrLv^ cog ri BZ TtQbg ixareQav rcbv ZS xal 
BlSl^ ovrog r] BA TtQog ixareQav tcbv AN xal BN 
[Eucl. VI, 4]* Sate xaC, oCcov iatlv r} fiev BA ix rov 
xevtQOv tov ijtLXvxXov e Te^ rj de BE ideCid^ri v-O* -i^, 
rotovrov xal r} ^sv AN e6raL o d^ rj de BN t&v 20 
avrrav eyyL^ta e ti, XoLTCr} de rj NE tOLOvrcov vd ]iy, 

1. v.aC'] om. D. 3. %ul Z£/] corr. ex v.cil <^Z C, corr. 
ex Z Dl 4. z/E xat] Ez/ D. 5. ^] seq. ras. 1 litt. D. 

ME v.ai'] EM D. E,^] -57 e corr. A. tv^siibv — 7. bv- 
Q^Eicbv] mg. D^, in textu xoiovrcov ql& ?.e v.al otcov aqa SGzlv 
EvatsQa x&v z/E, EZ EvQ-Eicbv D. 7. T i^'] in ras. D, i lQ" C. 

z/B] corr. exJA D. 8. Eaxai] seq. ras. 1 litt. D. 9. Ttat (pr.)] 

comp. supra scr. D^ o] o D, o D^ 13. EvQ-ELaa C, coit. C^. 

14. o] AC. ZS^ SZD, S- renouat. D^. ^v'] corr. 

ex 71 D. 15. o] A, 6 C. 16. x&v — 17. BN'] mg. D-, 
in textu x&v AM, BN D. 17. BlSl] -S in ras. A^ ovxco 
CD. AN] post ras. 2 litt. D. 18. BA] corr. ex BJ Dl 

20. Tj (alt.)] in ras. D. hyiaxa xa>v avxav D. 21. NE] 
EN B. 



400 KAATAIOT nTOAEMAIOT 

oXg)V rj AN i]V o d. ijtsl de dicc ra TtQoxsi^sva xccl 
rj EA VTCOtSivovCa ddiacpOQSt xCbv avtcov vd ^y^ 
6vvdystat^ ott xai^ otcjv s6t\v rj EA vjtotsivovefa qx^ 
toiovtcov %al 1] ^sv AN sv^sla satat o rj syyi^ta^ rj 
5 ^' S7t' avtfjg 7tSQi(pSQSia toiovtcjv o tj jtdXiv^ oicov 
s6tlv 6 JtSQl tb EAN OQd^oyaviov xvxXog r|. xal rj 
vjtb BEA ccQa yavCa^ r^v dnqvsyasv rj 6sX7]vrj TtaQa 
trjv STCi tb Z 7tQ66vsv6iv^ oXov fisv slcnv at dvo 
OQd^al r|, toiovtcov o rj^ oHcov d' at d oQd^al t|, toiov- 

10 tCDv o d. G)6ts Tcal svd-dds tb TtaQa tijv dvcj^aXtav 
trjg 6sXrivrjg ditjvsyxsv s^rjxo6tOig d, djtSQ ovd' cfvra 
TtoiSi tiva d^ioloyov d^aQtCav TtSQi td xatd tdg 6v- 
^vyCag cpaivo^sva ^rjd^ oydoov syyi6ta dvvd^sva iiidg 
KtQag^ o6ov %al TtaQ* dvtdg tdg tr]Q7]6sig ov jtaQado^ov 

15 s6tac TtXsovdxig dia7ts6siv. 

tavta [isvtoi jtaQsd^s^sd^a ov^ ag iii] ovtog dvva- 
tov xal TtQbg tdg t&v 6v^vyiav S7ti6KSifjsig 6vvs7tiXo- 
yC^s^d^ai xal avtdg tavtag tdg dia^pOQdg^ xdv PQa%v- 
tatai tvy%dvc36iv^ dX^ hg ^r]dsvbg r]^tv at^d-r^tov 

20 8iriiiaQtr]iisvov xatd tdg did tav SKtsd^Si^svcjv 6slr]- 
Viaxcov sxXsCtl^scov d^todsC^sig 7taQd tb ^i] ^vyxs^Qr^^xtai 
tf] did tr]g SKXSvtQotr^tog dvaTtSTtXrjQco^svr] did t&v 
s^rlg v7tod-s6si. 



1. AN] corr. ex AN D^. xat'] comp. supra scr. D-. 2. 
vTtoTSLvovaa] -a supra scr. D^, adLcccpiQeL D, corr. D^ 3. ^ 
— 4. ^yyLGxa] mg. D^, in textu dLa^psQSL x&v avx&v seq. spatio 
14 litt. (del. D^) et deinde svd^sta ^oxaL o r] syyLGxa D. 5. 
TCBQLcpSQELa] comp. ius. D^. ndXLv'] om. D. 9. o] IgxIv o D. 
d'] de D. 6] dvo C. tolovxcov] -v ins. Dl 10. o ^J 

o^ A; o ^ D, ut saepe. H. ^] corr. ex A D^ 14. ogov] 
OTCSQ D, 060V mg. D^ 22. ava7isnlT]Qcoiisv7]q D, corr. D*. 



MA0HMATIKH2 STNTASESiS E'. 401 

La'. UsqI t&v rfis 6slijvr}g TtaQaXld^ecctv. 

Ta ^£v ovv TCQog tccg xataXijil^sig t&v aKQi^Cbv tfjg 
6£lrjvr}g TCaqodfov TCaQaXa^^avo^eva 6%sdov tavta av 
slrj. 6v^^aCvovtog d' ijtl tfjg ^eXr^vrjg xal tov [iridh 
jCQog alad^rj^LV tr^v avtrjv yivs^d^ai, tijv q^aLVO^svrjv 5 
avxfjg TCccQodov tfj axQL^si dLu to ^rj 6rj^8L0v Xoyov 
s%£LV^ cog scpafiEv^ tijv yfiv TCQog tb a7c66trj^a trlg 
6(paLQag avtfjg avayxatov ctv str] Tcal axoXovd^ov tcbv 
te alXcov cpaLVO^svcov evsxev xal ^dXL6ta t&v iceQL 
tdg tov rjXLOv exXeLiljeLg d^ecoQOv^evcov tbv jceQL t&v 10 
^aQaXXd^ecov avtfjg 7C0Lri6a6^aL Xoyov^ ^l Giv dvvatbv 
e6taL dLa tcov TCQbg tb ocevtQov tfjg yfjg xal tov dcd 
lie6cov tcav t^cpdCov xvxXov voov^evcov dxQLpmv TcaQo- 
dcov xal tdg dicb tfjg oil^ecjg tcbv hQCDVXcov^ tovte6tLV 
dTCo tivog eiCLCpaveCag tfjg yfjg^ d^ecoQOv^evag dLazQCveLV 15 
xal TcdXLV ro evavtCov dicb tcbv (pacvo^evcov tdg dxQL- 
^elg. TCaQaKoXovd-ovvtog de tfi tOLavtrj eTCL^xe^eL tov 
firjte tdg aatd ^eQog TCrjXLxdtrjtag tcov TCaQaXXd^ecov 
dvev tov dod^fjvaL tbv tov d7Co6tr]^atog Xoyov dvva- 
6^aL TCQay^atevd^fjvaL ^r^te avtbv tbv rov djco^tf}- 20 
fiatog Xoyov dvev rot) dod-fjvaC tLva TCaQdXXa^LV eTcl 
^ev tcbv ^r]dev aL^^r^tbv 7CaQaXXa6 6 ovt cov ^ tovte6tLV 



1. m'] C, m B, om. AD, -O" mg. D-. tcsqC — nuQaXXd- 

y 

^ecov] mg. superiore D^, in textu (j^ a^ supra scr. D^. 4. Btri\ 
supra scr. D^. sTtLGvfi^aivovtog D. 6. t^] corr. ex r?Jv D. 

Xoyov] X- corr. ex z/ A. 10. tov] corr. ex r&v D^. 16. 
ccnQi^Sig'] &yiQL§SLg TtccQodovg D. 18. Tra^aHalfioc^] -a|f- in 

ras. C. 20. Ante ju-tjts add. xag xmv TCccQccXXd^sGiv diSoad^ccL 

avsv xov d-fivciL xbv xov cc7to6xi^}ic(xog Xoyov D, del. D*. ccvxov'] 
supra scr. D^. 21. xlvo] xriv D. 22. naQaXccaaovxcov C. 

xovxiatLv] comp. B, -v del. D^. 

Ptolemaeus, ed. Heiberg. 26 



402 KAATAIOT nTOAEMAIOT 

TCQOS cc 'fj yfj 6riiiEi0v Xoyov i%u^ ovds rbv tov a7to6t7J- 
^atog Xoyov drjXovott dvvatbv av yivoito Xafieiv^ STtl 
dl t&v TtaQakXae 6 ovt G)V ^ co6jc£q ml ti]g ^slT^vr^g^ 
ccQ^o^OL av ^ovcjg tb dtd ttvog TtQ&tov do^si^rjg 
5 7taQaXld^£G}g tbv tov djto6tif]^atog Xoyov £VQ£iv did 
tb toiavtrjv ^£v tiva TtaQaXXaKtiKiiv t7]Qrj0iv Tcal xad'^ 
iavtrjv dvva6d-ai xataXrjipd^rivai^ tijv de tov «tto^tij- 
liatog TtrjhxotTjta ^rjda^cbg. 6 [lev ovv "IjtTtaQxog 
ditb Tov rjkiov ^dXi6ta trjv toiavtrjv £^£ta6iv Ttejtoi- 

10 r]tai' £7t£idr] yaQ d%6 tivcov dlXcjv 7t£Qi tbv r]li0v 
xal tr]v 6£Xr]vr]v ^v^p^prjKotayv^ V7t£Q av iv tolg £^r]g 
7toir]66^£%^a tbv Xbyov^ dxoXovd^^t t6 tov xatd t6 
£t£QOv t&v cpcatcDV d7to6tr]^atog do^dvrog xal t6 xatd 
t6 £t£QOv 8ido6^ai^ 7t£ioatai t6 tov r]Xiov xata6toxa- 

15 ^6iL£vog ovt(o xal t6 tfjg 6£lr]vr]g d7tod£iO{vv£iv t6 ^lv 
TtQcbtov v7toti^£^£vog tbv r]XiOv t6 £kd%i6tov ai^d^rjtbv 
li6vov 7taQakkd66£iv^ iva xal t6 d7t66tr]^a avtov Xd^r]^ 
^£td 81 tavta xal 6id trjg V7t' avtov 7taQatid-£^£vr]g 
r]lia%f\g ixXei^^cjg, Ttots ^hv cjg ^rjdhv ai6d-r]t6v, 7tot£ 

20 dl xal cog ixavbv tov r]liov 7taQaXkd66ovtog ^ ^vd^^v 
dvtfp Kal ot kbyoi tov tfjg 6£Xr]vr]g d7io6tr]^atog did- 

(pOQOi Xad-' £xd6tr]V tCOV £7Ct£^£i^£VCJV V7tO^£6£G)V Kat£- 

(paivovto di6ta^o^£vov 7tavtd7ta6iv tov xdtd tbv rjXiov 
ov ^6vov iv tm 7t66ov^ dlkd xal £i oXcog ti 7taQaXld66£i. 



1. a\ a.v 0, a av C^. 2. Post Xoyov del. a D^ SrjXov- 

otl] -7]- e corr. D. 3. TcagaXaGOovrcov A et -ga- supra scr. D. 

7. yiataXr} ^cp&fivai D, corr. D^. 10. Tiv(ov] -i- corr. ex si D^ 

xbv TjXiov] xr]v asXtjvT^v D. 11. xiiv asXTjvrjv] xbv rjXiov D. 

15. ovx(£)c D. 16. xo] supra scr. C. 17. naqaX^asiv A, 

naQaXdaatn> D. avxov] corr. ex avxrj D. 18. TtaQaxEd^a- 

\iivrig D. 20. xat'] om. D. naQaXdaaovxog D. 22. iv.a- 

axdaxrjv C. 23. TtavxditaaLv] -v del. D^, comp. B. 24. oXcog] 

oX- ins. in lac. 3 litt. D^. xc] supra scr. D. icaQaXdaau D. 



MA0HMATIKH2 STNTASESiS E'. 403 

i^\ IIsqI xatadxsvrjg oQydvov TtaQallaKXLTiov. 

'H^stg df, tV(X fii^dhv rcbv ddriXcDV elg tiiv roLavtrjv 
87Ci6y,sjl)iv TtaQaXa^pdvco^ev^ 7cats6K£vd6afisv OQyavov^ 
di ov dvvrjd^scrj^sv av (bg svi ^dli6ta dxQiP&g trjQfi- 
6aL^ 7t66ov %a\ aTio 7tri2.ixrjg tov xatd xoQviprjv dito- 5 
6td6£(og rj 6£Xr]vr] 7taQaXld66£i G)g £7tl tov did t&v 
TtoXmv tov oQi^ovtog xal avtfjg yQacpo^ivov a^yC^tov 
xvxXov. 

£7tOL7]6a^£v ydg xavovag dvo t£tQa7tX£VQ0vg tb ^lv 
fifjocog ovx £Xd66ovag t£66dQ(ov 7tr]X£(ov TtQog tb tdg lo 
diaiQ£6£ig £ig 7tX£iOva ^£Qr} dvva6^ai y^vd^d-ai, trjv ds 
7t£QiOiriv 6v^^£tQ0vg C36t£ ^ij 6ia6tQa(pfjvai did tb 
^fixog^ dXXd d7tot£td6^ai 6cp6dQa dxQi^&g xal £7t 
£v^£iag xad'' ixd^trjv t&v 7tX£VQ&v^ £7t£ita TtaQayQd- 
7jjavt£g ^vd^^iag yQa^^dg £cp ixat £qov xatd ^£6rjg tfjg 15 
7tXatvt£Qag 7tX£VQdg 7CQo6£d^rjxa^£v ta £t£QC3 tmv xa- 

v6v(OV £7ti t&V dxQCJV d^(pOt£QC3V OQxtd 7tQi6(ldtia 

t£tQdyc3va 7t£Qi ^e6r]v tfjv yQa^^fjv i'6a t£ xal TtaQdX- 
XrjXa oTtfjv £%ov £xdt£QOv xatd tb ^£6ov rjXQiPcj^£vr]v 
tb ^£v 7tQbg tfi 6il)£i £66(i£vov X£7ttfjv, t6 ds 7tQbg tfj 20 
6£Xr]vrj ^£i^ova^ ovtcjg a6t£ ^taQatid^E^^vov tov ivbg 
tCbv ocpd^aX^av ta tfjv iXdttova OTtfjv £iovti 7tQi6^a- 
xCco did tfjg tov it£Q0v xal fjr' ^vd^^Cag o^trjg tfjv 6e- 

1. t|5'] mg. AC, m B, om. D, i mg. D^ naQttXccv.xLv.ov D. 

4. ccY,qi^&g'] -«? euan. C. 5. roi)] corr. ex ttJ? D^ 6. 

■jiuQaXdG6EL D. 7. 7t6X(ov\ corr. ex noXXfov D, 'caoXoiv C. 

10. nfixoiv D. 11. ftg] ins. D^ yiv£6^uv D, corr. D^ 

13. ccXX' D. ayLQL^&sl supra scr. D^ Bn fu-d-ftag] sv 

Bvd^sia D, mg. yial in' svQ^sCag D^ 14. tnBiTa'] -8- corr. ex t 

in scrib. A. 15. ixsGr^s] corr. ex fisaov D'. 17. xcbv ayiQcov] 

corr. ex t6 ayiQov C. 18. naQccXXrjXa] supra scr. D^. 19. 

7)KQi§(o^8Vov D, corr. D^ 22. iXdoGova D. 

26* 



404 KAATAIOT nTOAEMAIOT 

kTJvrjv oXrjv dvvcc^d-aL y.ccxa(paCv£6%-aL. dLatQ7]0avrsg 
ovv «l l'6ov BKdrsQOV rcbv xavovcov Tiara fisamv r&v 
yQa^^cbv STtl rov SreQov rmv TtsQarcov JtQog r(p rijv 
^SL^ova OTtrjv s^ovrL 7tQL6^arLG) xal svaQnoOavrsg Sl 

5 d^cporsQcov d^ovLOv^ &6rs ^vvdsd-rjvaL ^sv vjr' avrov 
rdg nQog ratg yQa^^atg r&v xavovcav TtksvQag &67tSQ 
'bjtb xsvrQov^ itSQLaysad^aL ds 8vva6^aL rov rd 7tQL0^drLa 
s%ovra Ttavraxfi zal ddLadtQocpcog^ dLa6(pr]VG)(3avt£g rs 
pd6SL rbv srsQOV rcbv xavovcjv rbv ^m) s%ovra rd 

10 7tQL6^drLa iXd^o^sv sjtl rfjg ixarsQOv ^s6rjg yQa^iifig 
6r}^std rLva TtQog rotg jtaQa rfi ^d6sL 7tSQa6Lv rb l'6ov 
xal orL 7tkst6rov d7tb rov xard rb d^ovLov KsvrQov 
dq)s6rrjx6ra Tial SLSLXofisv tfjv dq)C0QL6^svrjv yQa^^ijv 
rov rrjv pd6Lv s%ovtog xavovog slg ^SQrj | ocal rovrcav 

15 stc s7ca6tov^ slg o6a idvvd^sd^a t^Tj^ata^ ^taQsd^TJxa^sv 
ds xal o^tL^d^sv tov avtov xavovog 7tQbg totg 7tSQa6L 
7tQL6^dtLa tdg i^tl td avtd ^SQrj 7tXsvQdg 7tQbg tfj 
avtfj yQa^^fi i7t svd^SLag dlXfikaLg s%ovta xal tb t6ov 
d(ps6tr]7c6ta ^tavta^bd-sv tfjg avtfjg aal ^s6rjg yQa^^fjg 

20 TtQbg ro dt avtcbv ocad-stLOv TCQL^vafisvov dvva^d^at 
tbv xavova dQd^bv xal d^taQsyxkLtov 7tQbg tb tov 6ql- 
tfivtog i7tL7tsdov L6ta6d^aL. s^ovtsg ds xal ^s6r]^PQLvriv 
yQa^^rjv 7tQodLa^s^Xri^svriv iv i7tL7ts8ca ^taQaXkfjXG) 



2. syi.atiQcov D, corr. D^. 3. itQov C. 4. 67tt]v] corr. 
ex olnfiv A*. ^t'] ins. D^, 5. &ii,(potsQG)v~\ -^ in ras. D. 

6. tdg] td B. rarg] corr. ex tas D^ Y.avovCtov D. coaTrfp] 
corr. ex cbff D^. 7. ^^] om. C. 9. ra] om. D. 10. snC\ 
corr. ex tc^sqC) D^ 11. tcsqocglv] -v del. D^. 12. xara] hoj D. 

13. disClofisv'] -X- in ras. D^. d(poQi,a(iivr}v C. 14. ii4q7}] 
ft£- in ras. A. 15. ogcc idvvdfis&cc] -cc s- e corr. D. 17. 

TCQLGfidtia] ante -a ras. D. 18. to] tov C. 19. iiavtaxo^^sv] 
corr. ex navtaxots D*. 23. TtQoSia^s^XrjfifJLSvqv C. tckq- 

aXXfjXo)] ^ in ras. D, J^ D^, corr. mg. Dl 



MAeHMATIKH2 STNTASESiS E'. 405 

ta XOV OQL^OVtOg fW tLVog dv67tL6xotYitov %g3qCov 
L6tafisv t6 oQyavov OQd-dv^ co6t£ tag TcXevQag tmv 
xavovcov^ Tcad'' ag ijvcovtaL aXkriloLg vtco tov d^ovLOv^ 
TtQog ^£6r]^PQLav t^tQacpd^aL TCaQaXXrjXovg yLvo^svag 
tf] 7taQax£L^£vrj ^£6r}^PQLvfj yQa^fifj xal tbv fi£v tr}v 5 
pd6Lv £xovta xavova oQd^bv dxXLvcbg xal ddLa^tQocpcog 
£tv t£ d^fpaXcbg £6tdvaL^ tbv 81 £t£QOv jt^QLdy^ad^ac 

6Vli^£tQG)g tfl 6(pLy^£L %£qI t6 d^dvLOV £V tfp tov 
^£0r}^PQLVOV £7tL7t£dG). 7tQO0£d-7]Xa^£V dh Xal £t£QOV 
XaVOVLOV X£7ttbv Xal £Vd"V 7tQ06r}Q^06^£V0V ^£V £V£X£V 10 

tov xal aiftb ^t^QLdy^^d^aL 7t£Q0VL<p ^Qa%£L xatd Toi) 
7tQbg tfi pd6£L 7t£Qatog trjg dLjjQrj^svi^g yQa^iirjg^ 
(pd^dvov d£ liL£%QL tr]g 7tX£L6trjg 7taQa(pOQag tov t6 
l6ov d(p£6tcbtog 7t£Qatog tfig tov £t£Qov xavovog 
yQa^fLrjg^ &6t£ dvva^d^aL 6v^7t£QLay6^£vov avtip t6 15 
^sta^i) tmv dvo 7t£Qdtcov yLv6^£vov £7t ^vd^^Lag dta- 
6trjfia d£LXvv£LV. 

£7toLov^£%^a dr] tovtov tbv tQ67tov tdg tfig 6£lr]vrjg 
tr]Qr]6£Lg xatd tdg m avtox) tov ^£6r]^pQLVov xal 

7t£Ql td tQ07tLXd 6r]^£La tOV dLa ^£6C3V t&V ^(pdLCOV 20 

xvxXov yLVO^svag 7taQ6dovg^ S7tSL8r] xatd tdg tOLavtag 
6%s6SLg oX ts dLcc t&v 7t6Xcov tov bQL^ovtog xal tov 
xsvtQov tfjg 6sXr]vr]g yQa(p6^svoL ^syL6tOL xvxXol oC 
avtol syyL6ta yCvovtaL totg dLa tcbv 7t6Xcov tov dLa 



1. To5] in ras. D^ 3. cc^ovlov^ pr, o corr. ex i in scrib. C. 
4, t8tQdq)9-ca^ corr. ex tetdx^ca D^. 5. ^EGr]^§Qivy] -v^ e 
corr. D. 6. &v,Xiv&g\ corr. ex axpt(3o6s D^ 7. hi\ mut. in 
^nC D^, InC C. ta] mut. in to D^. 8. ovfi^hgoog tjj^ -g t- 
e corr. D^ 13. TtXeLGtrjg'] corr. ex nlsvQag tfjg D. tov tb 
i'6ov\ corr. ex tovtoig/ov D^. 15. GvvTCEQiayoyiEvov AC. 18. 
8ri] di D. 20. iiscov D. ^cpdtov D, sed corr. 22. tibv] 
corr. ex tov D. 24. yCvovtccC] corr. ex t' D^. 



406 KAATAIOT nTOAEMAIOT 

fi86(DV t&v t,(pdCcov yQacpo^EvoLg^ TtQog ovg aC Kata 
TtXdtog TcdcQodoc trlg 66l7]vrjg d^ecjQovvtat^ %al ri dxQv- 
pi^g d7C0%ri tov xatd xoQvtprjv 6r]^6L0v dtd tovtov av- 
tod^ev xal 7CQOX6LQ(og dvvataL Xa^pdvedd^aL. jtaQa^pe- 
5 Q0vt6g ovv tbv td 7tQL0^dtLa 6%ovta xavova JtQog tijv 
66X7}vriv ;car' avtdg tdg 67tl rov ^e^rj^^QLvov TtaQO- 
dovg^ 6(og dv dt' diKpoteQcov tcov dTt&v xatd tb ^66ov 
tfjg ^eL^ovog OTtfig tb %6vtQ0v avtfjg dtOTCrfv-O-iJ, %a\ 

6ri^6L0Vll6V0L 67tl tOV l67ttOV %aVOVLOV tijv [leta^v 

10 t&v d%Qcov tcav 6v tolg %av66LV ei^d^eLGiv dLd6ta6LV 
7tQo6^dlXovt6g te avtrjv tfj dLr]Qrj^6vr] eig td | r^itTJ- 
^ata yQa^^fi tov oq^ov %av6vog 6VQi6%o^6v^ 7t66c3V 
66tlv t^r](idtcjv r] tfjg 7tQ06LQr]^6vrjg dLa6td66cog ev- 
d^eta^ OLcov 66tlv rj 6% tov %6vtQ0v tov 'bTtb tfjg ^tSQta- 

15 ycDyfjg yQatpo^ivov iv rc5 roi> ^66riii^QLVov 67tL7t6d(p 
%v%Xov drjXov6tL |, %aL la^6vt6g tfjv vTtb tfjg trjh- 
%avtr]g ev^-eCag {}7tot6LV0^6vr]v 7t6QLcp6Q6Lav tavtrjv 
6L%oiL6v^ r]v d7t6l%6v t6t6 tov %atd %OQV(pr]v 6r]^6Cov 
ro (paLv6^6vov %6vtQov tf]g 66kf]vr]g 67tl tov d^d tcov 

20 7t6XG)v to\) oQC^ovtog %al avtov yQacpo^evov ^6yC6tov 
%v%lov^ og b avtbg iyCveto t6t6 %al ta did tcov 7t6X(ov 
tov te C6rj^6QLVov %al tov d^d ^i6c3v tcbv t,cp8Ccov 
yQa(po^iv(p ^66r]^pQLva. 

6V6%6v ^6V ovv tov tf]v yLvofiivTjv %atd Ttkdtog 

25 7tksC6tr]v 7tdQodov tfjg 6r]X7]vr]g d%QL^cbg i7tLyLyvco6%6LV 



1. fiiacov] seq. ras. C, corr. ex fi^aov D^ yQacpofiel D, 
corr. D*. 3. tovtov] corr. ex tovto D^ 6. TCUQoSovg] e 

corr. D. 7. onaiv] -tc- e corr. D*. 10. rmv (alt.)] -m- corr. 
ex ot in scrib. C. 11. di£iQr\{iivr} CD, corr. D^ 13. saTi D, 
comp. B. 18. ansLxsv] -v del'. D*. 21. og] corr. ex ag 

C^D^ noXXcov D, -XX- eras., mg. X J)\ 22. ts] om. D. 

(isaov D, corr. D^. 25. STtiyivmayisLv D. 



MA0HMATIKHS STNTAgESiS E'. 407 

6vv£XQ(0{ied-a xi] 8L07tt£v6ei JtSQi rs t6 d-eQcvbv tQO- 
TCLxbv 6rj^£tov ^dkiOta avxriq v7taQiov6rjg xal £tL 7C£Qi 
avtb tb tov Xo^ov avtfig xvxlov ^OQ£i6tatov TtSQag 
dtd t£ t6 7t£Ql ravra ta erj^sta icp^ ixavbv dLaatrj^a 
tYjv avtrjv TtQbg afGd^rjaLv xata TtXdtog TtdQodov d(poQt- 5 
^£6%"^^ xal did tb 7tQbg avrco tc3 xatd xoQvcprjV 6rj^8LC) 
t6t£ trjv G^Xrjvrjv yLVo^evrjv iv t^ dL ^Al£^avdQ£Lag 
7taQaXXril(p ^ zad-' ov i^tOLOv^^d-a tdg trjQr]0£Lg^ tr]V 
ccvtrjv iyyL^ta 7tOL£tv trjv (paLVo^dvrjV d^idLV tfj dxQL- 
^£t. 7cat£Xa^pdv£to d£ 7t£Ql tdg tOLavtag 7taQ6dovg 10 
a%£%ov d£L t6 7C£vtQ0v trjg 6£k7]vr]g tov xatd aoQvcprjv 
0r]^£LOv /3 Tcal r]' £yyL6ta ^oiQag^ cjg xal ix tf]g tOLav- 
rr]g i^£td0£(og £ ^olq&v d7tod£iKvv0^ai tr]V 7tk£i6tr]v 
€cvtr]g xatd 7tXdtog i(p £xdt£Qa tov did pi£6(av tav 
^c)8lcov TtdQodov^ o6aLg 6%£dbv v7t£Q£%ov6Lv aC d^tb tov 15 
xatd xoQV(pr]v 0r]^£iov i^tl tbv i0r]^£QLvbv iv ^Ak£^av- 
dQ£L(z d£d£Ly^£vaL ybotQaL k vrj X£L7tov6ai tdg trjg (paL- 
vo^£vr]g d7to6td6£(og ^OLQag /3 xal r]' tcbv d^tb tov 
i6r]^£Qivov i7tl t6 &£Qivbv tQ07tixbv 6r]^£tov d£d£iy- 
liivcov noiQ&v xy vd. ' 20 

£V£K£V d£ tov xal tr]v TtQbg tdg 7taQakXd^£ig i7tC- 
6K£^iv ^toi^t^d^ai 7taQ£tr]Q0v^£v 7tdliv xatd tbv avxbv 
tQ67tOV tr]V 6£kr]Vr]V 7t£Qi ^ilv t6 x£L^£QLvbv tQOTtixbv 



2. hi TCSQi] -tv 7CBQL iD. ras. A. 3. avTfjg] om. B, supra 
scr. D^ 4. rd] ins. D*. 6. rc5] tots tm D. 7. t6tB\ 

om. D. 10. 'AatsXccii^avo^sQ^a D. 11. atsC D. 12. <>rj- 



yiiov A. v.aC (alt.)] comp. mg. D-. r?y? toiavtrig] corr. ex 
rijs avtiis avtfi^ D. 14. (liGov D, corr. D*. 15 ogul D, 

corr. D^ 17. dsdiyfisvaL A, sed corr, 20. fioLQ&v] (i seq. 

ras. 1 litt. D, ft D^. 21. tov] supra scr. C^. ■aal triv] supra 
scr. D*, corr. ex v.al tov C. 



408 KAATAIOT nTOAEMAIOX 

6rj^£tov TvyxdvovGav did ts ra TtQOSLQrjiisva xal dioi 
t6 7cXei6xov xoxE avrriv a(p£6t€b6av cog iTtl trjg b^otag 
Ttata tbv ^£0rj^PQLvbv TCaQodov tov xata xoQv^prjV 
6ri^£Cov jcal trjv TtaQdlka^iv ^£L^ova xal £v6rj^avtot£- 
5 Qav 7CaQ£X£LV. dnb itX^iovcov drj tcov xatd tdg toi- 
avtag TtaQodovg t£trjQrj^£V(ov rj^tv 7taQakkd^£(ov ^Cav 
TtdXvv £x&rj66^£d'a^ dC rjg tov t£ tov ijtLXoyt&^ov 
tQOTtov d^a 7taQa6trJ6o^£v xal tijv t&v kotTtcov d7t6- 
d£t^tv xatd tr^v £(p£^fjg dxoKov^Cav Ttotrj^^^^d^a. 



i 



10 ty\ 'A7t6d£titg tcov trjg 6£Xrjvrjg dTto^trj^dtcov. 

'Etr^Qrj6aii£v yaQ ta x' fVft ^AdQtavov xat AiyvTC- 
tCovg Ad-VQ ty' ^£td £ C y' &Qag C6rj^£Qtvdg tfjg 
li£6ri^^QCag ^eXXovtog tov rjUov xatadvv£tv trjv 6£- 
Xt^vrjv iTtl tov ii£6riii^Qtvov y£y£vr}^£vr}v^ xal icpaCv£to 

15 rj^tv dtd tov OQydvov tb xivtQov avrijg aTti^ov tov 
xatd xoQV(priv 6r]^£Cov ^ioCQag v /.' y' t/3'* r] ydQ ijtl 
tov X£7ttov xavovCov dtd6ta6tg totovtcjv r]v vd /.' i/3', 
£tg ola dirjQrjto r] ix tov xivtQOv tov trjg 7t£Qtaycoyr]g 
xvxkov I, r] de trjXtKavzr] ^vd^^ta V7tot£Cv£i 7t£Qi(piQ£iav 

20 toiovtov V C y' cp\ oicov i6tlv 6 xvxkog t|. dkkd 6 
d7tb tcbv iv ta a' £t£i NaPova66dQOv i^toyJSiv XQOvog 
li^XQt' tov xatd ti]v ixx£t^ivr]v tr]Qr]6iv itcov i6tiv 
Aiyv7ttiaxS)V cj7tp xal r]^£Qcov o/3 xal coqcov i6r]^£Qi- 

5. ■naxd'] xa corr, in y.cc A. 10. ty'] yi B, om, ACD, 

mg. A*, L mg. D*. 11. ydg'] ds B. x'] x« D, -s in ras.; 

79. rw H supra scr. D*. sTft] e corr. D^ 13. fxElovtog C. 
14. Post inL del. to D^. YsysysvrjfiEvriv D. 18. 17] ins. D^ 
20. ToiovToov] om. D. ccix' D. 6] corr. ex ot D^ 21. 

Tw a'] Tco ict A. hsi] e corr. D^. Ncc^ovaceov C, Na^o- 

vaaaQov D. XQOvog] corr. ex xQOvol D^ 22, s-n^si^svrjv A. 
sGxiv] corr. ex steiv mg, D^, 



MA0HMATIKHS STNTASESiS E'. 409 

vcjv ccjtXcjg fisv £ /.' y\ ccKQL^&g ds € y'' sig bv 
XQOvov tbv ^av t^Xlov £VQt6K0^6v ^£0(og fi£v iTtiyipvxa 
tcbv Xrjl&v fiOLQag ^ Aa, axQL^cag d£ £ tcyj^ rriv d£ 6£- 
Xrjvrjv ^£6cDg £7t£xov6av To^otov ^OLQag 7C£ fid^ xal 
trjv ^£v aTCoxrjv ^olq&v otj ly^ tag d* ccTto tov fiE6ov 5 
aTtoyELOv tov ijtixvxXov ^OLQag 6^^ z, tag d' ccjtb tov 
^OQ£Lov 7t£Qatog tov TtXdtovg ^OLQag tvd ji. 7tQ06£- 
tLd^EL dh dLa tavta xal tb TtaQcc trjv dvco^aXLav did- 
q)OQOV Jtavtaxod-Ev ix, tov oi%£Lov xavovog dLaxQL%^£v 
^OLQag 5 %g, cjg xal tr^v dxQL^fi trjg 6£Xr]vrjg d^i^LV lO 
xat ixELvrjv tijv aQav iitixsLV xatd (ilv tb ^rjxog 
AiyoxEQco ^OLQag y T, xatd d£ tb itXdtog iitl ^£v tov 
Xoiov xvxXov ditb tov ^oqelov itiQatog ^OLQag ^ g, 
ijtl d£ tov did tG)v TtoXcov tov dtd fii^ayv tcbv ^ojSlcov^ 
og 6 avtbg £yyL6ta rjv t6t£ tm ^£6rj^PQLV^^ ditb tov 15 
dtd ^i6G)v tcbv tjcpdCaiv TtQbg tdg ccQXtovg ^OLQag d vd". 
d7tixov6LV d£ xal at fihv tov Aiy6x£QG} ^otQaL y T tov 
i6rj^£QLV0v JtQbg ^£6r}^PQLav ijtl tov avtov xvxXov 
liOLQag xy 11%-^ 6 dl i6ri^£QLvbg roi) iv 'AX£^avdQ£La 
xatd X0QV(piiv 6rj^£L0v JtQbg ^£6r]^PQLav o^OLog ^OLQag 20 
X vrj' tb ccQa xivtQOV tr]g 6£Xr]vr]g djt£LX£v dxQL^&g 
djtb tov xatd xoQvcprjv 6r]^£Lov ^OLQag ^d" Jir]. icpai- 
v£to dh djtixov {lOLQag v v£' jtaQr]XXa^£v ccQa rj 6£- 



1. [_'] corr. ex ^ D^, ut saepe. 3. XsiX&v D. Xa] e 
corr. D*. e] ft « D, ft £ D^ 4. Post ^sGcog ins. ^iv D^ 

fid] renouat, D*. 5. d'] Si D. 6. tov (pr.)] renouat. C. 

STtLTivv.Xov] STCi- B COTT. D*. 7. Tvd] -V- 6 corr. D^. 8. 

dia zavxcc] mg. D^ 9. TtuvtaxoQ^Ev] supra scr. D^, ^ add. A. 

£x] Slo. tavta sy, D. 11. a:7r«;ufti; D. 13. y.vtiXov Scnb rov] 
mg, A^. 15. 6] om. C, 17. cctisxovglv] -v del. D^ 20. 
biLoia^g] bis D extr. et init. pag. 21. -KsvtQov] x- corr. ex a 
in scrib. D. 



410 



KAATAIOT nTOAEMAIOT 



Xt^vrj xccra t6 TtSQi rijv eKXSL^svrjv TtaQodov aTcd^rri^a 
fLOLQav d xal i^rjKoOra ^ stcl rov dC avrrjg %al r&v 
:t6?yG}v rov dgL^ovrog yQa(po^svov nsyC^rov kvkXov 
a7Ct%ov6a dxQLpcbg rov xara xoQvq)rjv 6rj^SL0v ^iOLQag 

5 U'9' JLt^. 

rovrov drjXcod-svrog ysyQcctpd^cj^av sv ra STCLTtsdci} 

rov dLU r&v noXcov rov oQL^ovrog zal rrjg 6sX7]vrjg 

^sytaroL xvxXol tcsqI 

ro avrb xsvrQov 6 
10 fiev rrjg yrjg ^syL6rog 

xvockog 6 AB^ 6 ds 

dLcc rov xara rrjv 

riJQrj6LV xsvrQov rrjg 

6skrjvrjg 6 JTz/, JCQog I 
16 bv ds 7} yfi 6rj^SL0v \ 

Xoyov sxsL 6 EZH@^ 

xal xsvrQov ^sv s6rci) 

xoLvbv Ttdvrcov rb K^ 

rj ds dLcc r&v xard 
20 xoQvtpriv 6rj^SLCov 

svd^sta r] KAFE^ V7toxsL6d'cj ds rj ^sXrjvrj xard rb A 

6r]^SL0v d7ts%ov6a dxQL^cog rov xard xoQViprjv 6rj^SL0v 

rov r rdg TtQoxsL^svag ^OLQag ^ ^rj^ xal S7tst,sv%- 




1. xara] corr. ex naqd D*. neQC] corr. ex xara D*. 2. 
_ a 

i^TjyiOGra ^] |^ D, H ^ Dl tov noXov D, corr, I>\ 6. drjXco- 

d-ivrog} mut. in di} doQ^ivrog D^, sed rursus corr., iccpccl supra 
scr. D^ 7. ticcl rfjg OEli^viqg] supra scr. D^. 8. fiiyLGroi] 

yQacpofiivov fisyiGrov D, sed (isyiarov corr. in (liyiaroL. y.vKXoi] 
corr. ex ■kvtiXov D. Deinde rep. anixovoa lin. 4 — tivkXol D (ut 
in textu, 5 /Z^ eras., 6 rovrov, add. D*, 7 noXXcov, corr. D^). 
16. EZHG] -Z- e corr. D. 21. i] (pr.)] corr. ex N in 

scrib. A. di] om. C. //] corr. ex A A*. 



MA0HMATIKHI: STNTASESiS E'. 411 

S^(X)6av 7] xe KzlH xal t} AJ&^ xal hc aTtb tot) A^ 
o yCvaxaL bif/Lg xCbv 6q(ovxg)v^ Tcdd^axog fiav rjx^^ ^'^^ 
ri)v KB ri AA^ TtaQaXkTjXog ds xfi KH r\ AZ. 

bxc ^£v ovv XYjv H& 7t£QL(p8QSiav xotg aTto xov A 
^scoQOvai TtaQTJXXa^sv r] 6£?,7Jvri^ cpav£Q6v' &6x£ £l'rj av 5 
^iag ^oiQag xal £^7]xo6zcbv f xg)v ix xrjg xr]Q7]6£(og 
xax£LXrj^^£V(ov. iit^l dl dSia^pOQCo ^£l^(ov i6xlv 7] Z@ 
%£QL(p£Q£La xfjg H® 8Ld xb xrjv yrjv bkrjv 6r]^£Lov X6- 
yov £%£LV TtQbg xbv EZH0 xvxXov^ £l'r] dv xal ij 
ZH0 7t£QL(p£Q£La XG)v avxcjv £yyL6xa a f. cj6x£ xal 10 
ri VTtb ZA& ycovia Sid xb TtdXLv ddLa(poQ£LV xb A 
6rj^£Lov xov xivxQov JtQbg xbv Z® xvxXov^ olcjv fiiv 
€i6LV ai d OQd^al rj, xolovxcdv i6xlv a J, olcjv d^ ai 
/3 OQ&al r|, rotovTfiji; /3 lS. xcbv d* avxav i6XLv xal 
ri i'6r} [Eucl. I, 29] avxfj ycovia rj vnb AA A p lS' xal 15 
rj ^£v iitl xfjg AA ccQa ^vd^^iag 7t£QL(piQ£La xocovxcov 
i6xLv ^ td, OLCJV 6 7t£QL xb AAA oQd-oy^ovLov xvxlog 
r|, avxri &£ rj AA ^vd^^ta xolovxcov /3 xd^ oicov i6xlv 
ri AA v7toT£ivov6a [Eucl. III, 31] qx. xavxrjg dh ddta- 
(p^QO) ikd66G)v i6xLv 7] AA' xal oicov aQa i6xlv rj 20 
AA ^vd^^ta /3 xd^ xolovxcov i6xlv rj AA £v%^£ta qx 

TtaUtj Q^ 

3. naQccXXrjXog] — oc D, iflfi D^. 6. /Liot^ag] ft supra 

scr. D, ^ D^ sh,ri%oataiv f] U D, f | ^ D^. 7. icdiacpoqco] 
a- e corr. D°. jift^coi'] mg. D^, m D. 8. rijg] corr. ex t<, D^ 

10. Zif©] Z@ D. syyiGta'] -a postea ins. A. a] /t a D. 

11. ZA@'\ corr. ex ^Z0 D^ 12. Z0] mut. in ZR@ Dl 
13. toiovtoiv — 14. rf] supra scr. D^ 13. ^'] 8i D. 14. 

§ (pr.)] 8vo C. ^'] 8b D. fffttv] comp. B, -v del. D^ 

15. 71 (pr.)] ins. C-. AziA p] corr. ex ^ I^ D^. 16. 

dqa'] comp. supra scr. D. 17. sotCv'] comp. B, -v del. D^. 

19. Jz/] corr. ex ^A D^ 20. iatlv BXdoocov D, deinde 

gupra add. -p D^ A/i'\ AA D. xat — 21. AA] supra scr. D^ 
21. AA\ AA D. Ad\ JA D. 



412 KAATAIOT nTOAEMAIOT 

syyieta. TtdXiv^ STtsl ri Jz/ 7ieQiq)SQ£ia vitoKEixai ^oiQ&v 
fid' Jltj^ stri av ocal rj vjtb FKzl ycjvia JtQog tco xevtQa) 
ov0a tov Kvxlov^ oZcov iiev Ei6iv ai d OQd^al t|, toiov- 
t(DV fid" Jirj^ oXov d' aC dvo OQd-al ir|, toiovtcov c,d' Ag» 
5 cj6ts Kol rj ^sv STtl trig AA svd-sCag jtSQicpsQSia toiov- 
tcjv £6tlv 9-^ Asr, oicov 6 TtsQl to AAK OQ^oydiViov xvx- 
Xog t|, ri d* STtl tfjg AK t&v Xoiit&v [Eucl. III, 31] slg 
tb rj^ixvTcXiov Tt xd. xal t&v v7totSivov6&v ccQa avtag 
svd-siQV ri ^sv AA s6tai toiovtcov 9« AO*, oicov s6tlv 

10 rj AK v7totSivov6a qx^ r] ds AK tcbv avtcov ot, xt,' a6ts 
xaiy oiov svog s6tiv rj AK ix tov xevxqov tf^g yfjg^ toi- 
ovtcov xal rj ^sv AA ^6tac o JLtg, rj ds KA Oftotcog o Xd'. 
aXkd^ Oicov r]V riAA svd^sta ^ jca, toiovtcjv r] AA sds- 
dsixto QX' xal oicov ccQa s6tlv rj AA svd^sta o ft^, toiov- 

15 tcov s6tai xal rj AA svd^sta A^ g. t&v d' avtcbv rjv xal 
rj ^sv KA sv&sta o A'9', rj ds KA ix Toi) xsvtQOv 
xrig yfig svog' xal oiov ccQa i6tlv rj KA ix tov xsv- 
tQOv t7]g yfjg svog^ toiovtov s6tai xal rj KAA oXrjy 
7tSQiS%ov6a ds t6 ^caTOJ tfjv t7]orj6iv tfjg 6£Xr]vrig djto- 

20 6tr]}ia^ Xd' JTs. 

tovtov dsdsiy^svov s6tco 6 tr]g 6skf]vr]g sxxsvtQog 
xvxXog 6 ABF jtSQl xsvxqov t6 z/ xal did^stQov tf]v 
AAF^ icp' % sikrjcpd^co t6 ^sv tov did ^s6cov tcbv 



4. dvo] § BD. 6. 6 nsQL^l corr. ex onsQ D. AAK] 

AAK D. 11. AK^ -K e corr. D. Snpra KsvtQov add. 

ovaa D*. 13. fiv] ins. D^ AA] corr. ex AJ Dl Ante 
7] (alt.) del. fiv D\ ididsLnzo] add. D^. 14. 0] o D, o D^. 
16. svd-sr D, svd-tl D*. 0] corr. ex o D*. KA] -A 

renouat. D^. 17. xat] corr. ex ?<xt Dl ccqo] comp. reno- 
uat. D*. BGxCv] d< D, 'l- D^, mg. iott D^. 18. ticcl] %g corr. 
ex ot D*. oXt]] corr, ex D^ 19. tfig] t- corr. ex ri in 

scrib. C. 21. lcc mg. D. SY.Y.svtQos] ^xxfi'- in ras. D. 



MA0HMATIKHS STNTAHEiiS E'. 



413 



^G)di(Dv TcvxXov xivtQov tb E^ tb dh trjg 7tQo6v€v0eG}g 
tov eTtixvxXov 6rjiistov tb Z, xal yQacpevtog tisqI tb 
B 0rjiistov tov H@KA STtcxvxkov S'jtst,sv%%'G)6av rj ts 



I 




HB@E xal ri B^ xal r} BKZ, vTtoxsL^d^cj d' stiI trjg 
TtQOXSL^svrjg trjQTJ^scog rj Gskrjvri xata tb A ^rj^stov^ 5 
xal S7tst,sv%%'G)6av ^sv aC AE xal AB^ xdd-stOL d' 7^%- 
^•Gy^av s%l tijv BE ditb ^sv tov A \sx^'kri%'SL6av^ ^ 
AM, ditb ds tov Z rj ZN. 

BTtsl toLvvv xatd tbv xqovov trjg trjQ7]6SG)g 6 tijg 
dTtoxrjg dQLd^^bg rjv orj Ty^ strj dv dLa td TtQOts^SG^Qrj- 10 
^sva rj ykv 'bitb AEB yG^vCay olg)v sldlv aC d oQ^al 

t|, tOLOVtG)V QV<5 Jjg, SXatSQa [Eucl. I, 15] 8s tG)V VTtb 

ZEN xal AEM tcov ^sv loLTtobv sig tdg 8vo OQ^dg xy 



3. STti-Avv.lov] b\^ D, ^ supra add. D*. 4. BJ] z/B B, 
-z/ corr. ex A D^. yiaC (alt.)] corr. ex h D*. 6. ^' rix^oi- 
6av\ di7]x^cooccv C, corr. ex d' ax^oieav D^. 7. hv.QlTiQ'EL6av'\ 
corr. ex i-A^XriQ^stGa C^, Bv.^X7]%'Etaa B, ante Scno coll. Halma; 
puto delendum esse. 8. ZiV] -N e corr. D*. 10. xa\ supra 
scr. Dl 13. 8vo\ mut. in J K\ § D. 



414 KAATAIOT nTOAEMAIOT 

Ad, 01C3V d' ei^lv aC dvo OQd-al t^, roiovtcjv /ij rj^ 
&6ts xal ^i ^BV i(p' ixatSQag tav z/M xal ZN itSQi- 
(pSQsia toiovtcov s6tai ^^ rj^ oXcov sloIv ol :tSQl ra 
ixxsL^sva oQd-oycovLa xvxXoi t|, dLcc tb L6rjv slvai rijv 
5 ^E tfj jBZ, rj d' icp' sTcatsQag tcbv EM xal EN tcbv 
avtcbv Qlp vp [Eucl. III, 31]. xal t&v vtc avtag ccQa 
svd^SLcbv sxatSQa ^sv t&v z/ikf xal ZN toLOvtov i6tlv 
li^ vd^y oLcov sxatSQa t&v ^ E xal EZ 'b7CotSLVov6cbv 
QX^ sxatSQa 8s tcbv EM xal EN t&v avtcbv ql o* 

10 C30ts xaC^ olcav i^tlv sxatSQa ^sv tcbv ^Exal EZ svd^SL&v 
r ^O", rj ds z/5 ix tov xsvtQOv tov ixxsvtQOv ^d' jita, 
tOLOvtcjv xal sxatSQa ^sv tcbv z/M xal ZN s6taL d rj^ 
sxatSQa ds t&v EM xal EN tcbv avtcbv d' x^. xal 
iTtsl tb ccTcb trjg B^ Isti^av tb ocTcb trjg z/ikf tcolsl 

15 tb aTcb trjg BM tstQccycovov [Eucl. I, 47], s%o^sv xal 
trjv ^sv BM oXrjv ^tjksl tav avt&v ^d' Aa, trjv ds 
BE b^OLCjg ft d, XoLTCrjv ds trjv BN tOLOvtcjv X AJ,, 
OLCov xal rj ZN r]v d rj. xal iicsl ta cctc^ avtcbv 6vv- 
tsd^svta 7C0LSL t6 ccTcb tr]g BZ [Eucl. I, 47], s%o^sv 

20 xal trjv BZ v7CotsCvov6av ^rjxsL t&v avtcbv X vd' 
G)6ts xaC^ oXcQv i0tlv rj BZ v7CotsCvov6a qx^ tOLovtcov 
xal rj ^sv ZN s6taL T^ ^^ rj d' i-x avtfjg TCSQccpSQSLa 
toLovtov Ts xa^ olcjv i6tlv 6 tcsql t6 BZN oQd^o- 
yavLov xvxXog t^. xal rj VTcb ZBN ccQa ycjvCa^ olcov 

1. dvo] § B. Ti] ins.Dl 3. ^atai] a D, ^ D^. 4. t|] 
corr. ex rov I)'\ 5. d'] di D. 7. sarCv] comp. B, -v del. D^. 
8. zJE] corr. ex AE D«. 9. o] 6 ABCD^, D, o mg. D^ 
11. r L&] corr, ex hQ- D^ 12. (i^v — 13. ayiarsQa] supra. 
scr. D. 12. xat (alt.)] ins. Dl hrai,] ^ D. 16. jid- Xcc] 
in ras. D. 17. li d] ^ AD, corr. D^, Jjid' A\ 18. ZN] 
NZ D. 22^ ^i D^ If D. 23. Te] corr. ex ? B^C^ -se 

corr. D^. xa] corr. ex xi Dl 24. ZBN] -B- e corr. D. 



MA0HMATIKHS STNTAgESiS E'. 415 

fiBv 8L0iV cci dvo dgd-al t|, toiovrcjv i6rlv le za, oiGiv 
d' at d OQd-al T^, t0L0VT(av ^ [1 syyLOta. to6ovx(ov 

aQa ^OLQCJV £6tLV Yj @K tOV mLXVXXoV 7t£QL(paQ£La. 

tcccXlv^ £7t£Ldrj Tcata tbv %q6vov trig trjQ7J6£(og a7C£i- 
%£v 7] 6£lrivri tov ^lv {idaov aTCoyaCov tov £7ClkvxXov 5 
^OLQag 6^p jc, tov dh K roi) ^idaov 7C£QLy£L0V tag 
XoLTCag drjXovotL ^£ta tb rj^LXvxhov fiocQag tc^ jc, 
£6taL xal rj ^£v KA 7C£QL(p£Q£La noLQ&v 7r/3 %, ri dl 
®KA olri iLOLQ&v 9 o- oQd^ri ccQa £6tlv rj vnb @BA 

yCJVia. &6t£ £7C£L^ OLCOV £6t\v rj ^£V Zl B £X rOl) X£V- 10 

tQov roi) £xx£vtQov /LtO' fta, r] d£ BA ix tov xivtQov 
tov £7CLXvxkov ~£ t£, tOLOvtov xal rj EB idid^LXto Ji 
xal £^rixo6tG)v d, ra d' a7C avtcbv 6vvt£^£vta 7Col£l t6 
arcb tfjg EA t£tQccycovov [Eucl. I^ 47], eio^sv xal tijv 
EA ^7]X£L tcbv avt&v ji x£. tb ccQa xata trjv tTjQrjOLV 15 
aTCoatrj^a tfjg a^Xyjvrjg tOLOvrcav iotlv ]i xf, olg}v xal 
rj ^£v BA ix tov xavtQOv tov i^CLXvxkov v7c6x£LtaL 
£ tf, r] de EA rj ccTcb tov xivtQov tfjg yrjg iTcl tb 
a7c6y£Lov tov ixxivtQov |^ ri de EF rj ccTtb tov xivtQOv 
tfjg yfjg i^cl tb 7t£QLy£L0V tox) ixxivtQov k^ x^. alXa 20 
i6£tx^rj tb xata trjv t7JQrj6LV tfjg a^krjvrjg d7c60tr]fia^ 
tovtidtLv r] EA £vd-£La^ tOLOvtcov ^.d- Ji£^ olov i6tlv 



1. dvo] B B. iaxLv] comp. B, -v del. D^. 4. insidij] 
corr. ex iTtsc D^. 5, Supra aTtoyELOv add. tag Xoiitdg D*, 

sed del. 6. <j^^] corr. ex sl^ D. tov (alt.)] om. D. 8. 
sarai] ^ D, ^ D^ ^'azca mg. D^ 9. ©BA] supra scr, C^, 
@AB C. 10. &at' D. 17] e corr. post ras. 2 litt^ D^. il. 
tov iv.yiivtQOv] mg. D^ 13. s^riyioat&v] ^^ BD^, 1/ D. 16. 
iatLv] comp. B, -v del. D^ 17. tov v.ivtgov] mg. D*. 18. EA 
7]] C^D, socri AC, EA seq. ras. 1 litt. B. 19. iy.v.ivtQov] 



iyiYrJ), iw.^J)^, mg. £xx^'D2. %ivtQOv] D^, comp. D. 20. 
iv-yiivtQov] i-^ D, f>trjt- D^ 



416 KAATAIOT nTOAEMAIOT 

ivbg rj sx rov kbvxqov r^g yfig' xal olcov ccqk idtlv 
Yj ^ev EA svd^eta xov xara trjv tt^Qrjaiv trjg ^skijvrjg 
a%o6tri^atog A-O" /*£, r] d' ix tov ocivtQov tfjg yrjg svog^ 
tOLOvtcov e&tau xal rj fisv EA svd^sla tov xata tag 
5 6vivyLag ^s6ov a7Co6tri^atog vd' o^ rj ds EF tov xat^ 
tag di%ot6iLOvg ^s6ov aito^tri^atog krj Jiy^ r] d' ix, 
tov xivtQov tov iitiKvxXov t&v avt&v s 1' ajtSQ 
TCQoixsito dst^ai. 

dsdsiy^ivcov d' ri^tv aata tbv ixtsd-si^ivov tQOTCOv 

10 tcav tfjg 6sl^vr]g d7to6tr}^dtcov dxoXovd^ov dv sl'rj xa\ 
t6 tov rjXiOv 6vva7todst^ai 7tQO%SiQov xal tov toiov- 
tov yivo^ivov did tcjv yQa^^&v^ sl jtQo6do&stsv totg 
xatd tdg 6vt;vyiag trjg ^sXrjvrjg d7to6tr]fia6iv at TtrjXi- 
xotrjtsg t&v iv ai)tatg 6vvi6ta^iva)v TtQbg tfj o^Si 

15 ycovicbv 'i}7c6 ts t&v dia^itQcov r]XiOv xal 6sX7]vrjg xal 
6xiag. 

id\ IIsQi tfjg 7tr]kix6trjtog t&v iv tatg 6v^vyiaig 
cpaivo^iivcav dta^itQCJV r]XiOV xal 6skf]vr]g xal 
6xiag. 
20 T&v di] 7tQbg tf]v toiavtrjv i^ti^xsifjiv icpbdcjv tdg 
^hv dlkag^ o6ai di vdQo^stQi&v rj tcbv xatd tdg i6r]- 
usQivdg dvatoXdg %q6vcov doxov6i tr]v tcbv cpcatcov 
Ttoist^d^ai xataiiitQr]6LV^ TtaQytrj^d^s&a did tb ^f] vyicjg 
dvva^d^ai did tcbv toiovtcov ro tcqoxsl^svov ka^i^dvs- 



2. Gihfi^GsXfjvris A. 3. xov Y.BvrQov\ corr. ex t6 h- D^. 4. 
%axa\ v.a\ C, xa C^, %a| D. 5. 6vv^vylas D, corr. D^. v-d-] 
corr. ex vo D*. o] o^ D, v supra scr. D^ 7. y.^vxQov xov] 
om. D. 11. rjXiov'] tjXlov kccl D, -aaL del. Dl 15. rf] om. D. 
17. Ld'] mg. AC, 'ji B, om. D. tvi-ql — 19. 6}iL&g] mg. 
superiore D. 21. Supra ij add. Hcct? D^. 



MA0HMATIKHS STNTA^ESiS E'. 417 

^^•avy xara6Kevcc0avt6g de xal avtol trjv vTtodsdsLy^Evrjv 
vjtb rov ^lTtTtccQxov ^i^cc tov tstQaTiYJxovg %av6vog diOTt- 
tgav Kal dca tavtrjg Ttoiov^evoL tag 7taQat7]QrJ6stg tijv 
(isv tov YjUov did^stQov vjtb trjg avtfjg syyi^ta ycavCag 
Ttavtayri %SQis%oyisvriv svql0xo^sv ^rjds^tag d^LoXoyov 5 
fLVO^svr^g dLacpoQag sx tcbv dito^tri^dtcov avtov^ tr^v 
ds rijg 6sXr]vrjg tots ^ovov xal avtrjv VTtb trjg a^dtijg 
tm r]lL(p ycovLag TtSQLSXo^svrjv ^ otav sv talg 7tav6sXr]- 
voLg t6 iisyL6tov dno^trnia tfjg yfjg d7ts%ri xatd ro 
dTtoysLOtatov ov6a tov STtLXvxXov^ xal ov% otav t6 10 
IIS60V dxoXovd^cog tatg t&v jtQotSQcov v7tod-s6s6LV. 
TtQbg ds tovtoLg xal tdg ycovCag avtdg d^Lokdyco tLvl 
iXdttovg aataXa^^avo^sd^a t&v TtaQadsdo^svcov^ ovxstL 
^svtoL dfcd tfig sv rra xav6vL xata^stQiqOscog S7tLkoyL- 
i6^svoL t6 to^ovtov, dXXd dLa tLvcov askr]VLaxav sx- 15 
ksCipscov. t6 ^sv yaQ 7t6ts l'6r]v v7totsCvsL ycovCav 
sxatSQa tcov dLa^stQcov 7tQ6%SLQov sx tfjg tov xav6vog 
xata6xsvfjg rjdvvato yCvs6%-aL dLa t6 ^irids^Cav S7taxo- 
kov^SLv STtl tov tOLOvtov xat a^stQrj6Lv^ t6 ds xal 
7trjkCxr]v Ttdvv rj^tv xatscpaCvsto dL0td^L^ov tfjg sv 20 
tatg S7tL^okatg tov S7tL7tQo6d-r]6avtog Ttkdtovg S7tl t6 
^fjxog Toi) xavbvog t6 d7tb tfjg oi^scog STtl t6 7tQL6^d- 
tLov 7tXsC0trig ov6r]g 7taQa^stQ7]6scog dLatl^sved^flvaL tfjg 
dxQLpsCag dvva^svr]g. i^tsl d' ajr«| i] 6sXr]vr] xatd t6 

2. zBzanrixovg C, q supra scr. C^. 5. Ttccvxaxfj'] -t- corr. 
ex 7t in scrib. C. fir]dsfiL&g] corr. ex iir]8£fiiav C^ 8. ratg] 
roLs C. TtavasX^qvoig] -ol- in ras. D. 10. tov] t- corr. ex 
g in scrib. C. 11. aTcoXovd-oig A, corr. A*. vTto&sasGi D. 
13. iXdz^ovg D. 14. iisvzol] corr, ex ^sv tl D^ seq. ras. 2 
litt. tfjg'] corr. ex t? in scrib, D. 15. Post iK?.sL^S(ov del. 
xa| D. 18. yLvsad-aL] corr. ex I^ D^. 20. tfjg] corr. ex 

taCg D. 22. ^fiv.og] (i- corr. ex x A*. to (pr.)] tov D. 23. 
nXsCataLg o^aaLg D, corr. D^ 24. d'] 8s D. 

Ptolemaeus, ed. Heiberg. 27 



418 KAATAIOT nTOAEMAIOT 

lieyiatov iavrilg a7t66trj^a triv Harjv rc3 -^Atco TtQog tfj 
otp£L ycDvtav icpaCveto 7totov6a^ dta tcbv TtSQl tovto tb 
aTto^trj^a tstrjQrj^evcov ^sXrjviaKcov aKlsttfjscov trjg vjto- 
tstvo^svrjg 4}% avtr]g ycovtag tb ^sysd^og S7ttXoytt,6^svoi 
5 xal trjv tov riUov dvvajtoSsdstyfisvrjv stxofisv avt^d^sv, 
tbv ds tQ^Ttov tfjg totavtrjg STtt^okrig dta dvo TtdXtv 
tmv vitotstay^svcov sxXsttlJscDV svxatavorjtov Ttottjeo^sv. 
t(p yccQ s' stst Na^07toXXa66dQov ^ o s(Sttv Qnt,' 
stog d7tb Na^ova06dQov ^ xat Aiyv7tttovg ^A^vq k^' 

10 sig trjv xr]' S^ag ta Xrjyov6rjg sv BafivX&vt r]Q^ato 
rj 6sXr]vrj sxXstTtstv^ xal s^sXstTtsv ro 7tXst6tov aTtb 
v6tov tb d' trjg dta^stQOv. S7ts\ ovv rj ^sv aQX'^ tfjg 
SKlst^scog ysyovsv ftstd s coQag toi) ^s6ovvxtiov xat- 
Qtxdg^ 6 ds ^s6og XQ^^^^S /"-£Ta g syyt6ta^ ai rj6av sv 

15 Ba^vXcbvt t6ts i6r]^SQtval 's i' y' dtd tb tbv r]Xtov 
dxQt^ag STtsxstv KQtov ^iotQag xt, xal s^r]xo6td y, dr]Xov, 
ort ysyovsv 6 ^s6og %^ovo? tfjg sxXsiipscjg^ ots tb 
7tXst6tov sig tr]v 6xtdv s^7tS7ttG)xst tfjg dta^stQov^ iv 
^sv BaptvXcbvt ^std s L' y' cjQag i6r]^SQtvdg rov 

20 iis6ovvxtiov^ iv ds 'AXs^avdQsia TtdXtv ^std i ^6vag, 
xal 6vvdyst 6 aTtb tfjg iTtoxfjg %^oVoff str] Aiyv7tttaxd 
Qx<s xal r]^SQag Ttg xal aQag i^rj^isQtvdg d^tXcbg ^sv 

1. avTfis D. 2. ymviav] corr. ex yoyvCa A^, yw D. rd] 

e corr. D^ 4. uvtfjg] -xfig e corr. D^ y(oviag] Yoj D, y D*. 
5. GvvanodBLKVvfi^vrjv D, dsdscy(iivr}v mg. D^. £l'xo(isv] s, 
supra scr. D^, sed del. 7. svv.axav6r]zov'] pr. t in ras. A. 

8. s'~\ BD et postea ins. C, is corr. ex v.s A. sxsi\ comp. D, 
corr. D^ Na^OTiaXXaoccQOv BC; alt. X add., alt. o del. D^ 

9. sxog] om, D. Na^ovaoaQov D. 'AQ^vqI 'A- ins. D^. 10. 
slg] corr. ex ss A. rrjV] supra scr. D^ Ba^vXcovr} C. 

11. i^sXsLTtsv] -V del. D^. 12. rd] om. A. 13. ysyovsv] 
-V del. D^ 16. &%Qi^(bg] -QL^&g in ras. minore A^. s^r}- 

%0Gxd'] ^ B, If D. 19. iisv] om. D. 22. Wg] renouat. Dl 



MA0HMATIKHS 2TNTASEiiS E'. 419 

tj, jCQog ds xa b^aka vv%^Yi^EQa Ig Ll ^' ^<^^^ ^«^ 
7] ilIv iis6r} xata ^ijycog TCaQodog rijg aeXrivrig iicslxa 
XrjX&v ^oiQag xs X^^ rj d' ccnQi^rig ^oiQag 7it,~s^ r] d' 
ajtb tov ajtoyeiov tov sTtLXvxXov iLOiQag t^ xal s^rjxo^ta 
f, 17 d' ccTtb roi) ^oqsCov itSQatog sitl tov Xoi^ov ocvkXov 5 
^OLQag % ft. xal g^avsQOV^ ort, orav 0- xal y' ^OLQag dg)- 
s6triKri t&v 0vvds6^cov ro xsvtQov trjg 6sXrivrjg s%l 
tov Xo^ov xvxlov TtSQL tb ^syL^tov ov6r}g aTto^trj^ay 
Tial y STtl rot) yQa(po^svov dt' avtov %Qbg oQd^ag tfp 
Ao|^ ^syCctov KvxXov ro xsvtQOv tf^g 6mag^ xad'' rjv 10 
d^s^LV aC ^syL6taL yCvovtat sjtL6K0t7]6SLg.^ ro tstaQtov 
avtfig sCg tfjv 6xLdv s^TtCTttSL tfjg dLa^stQOV. 

TtdlLv dfj rc5 ^ stSL Ka^fiv6ov^ s6tLv 67cs' stog 
dnb Na^ova66dQOv^ Tiat ACyvittCovg Qa^svhd' Lt,' sCg 
tf}v Lr]' TtQb iLLag wQag tov ^s6ovvKtCov sv Ba^vX&VL 15 
s^sXsLTtsv fj 6skf}vri d% ccQxtcov ro 7]^l6v tfjg dLa^stQov. 
ysyovsv ccQa xal avtrj fj sxlsLil^Lg sv 'AXs^avdQsCa itQb 
d C y' &Qag C6r]^SQLvfig syyL6ta tov ^s6ovvxtCov. 
Tcal 6vvdysL 6 ditb tfjg STto^f^g XQOvog str] ACyvTtttaxd 
67cd xal f]fisQag Qgg xal &Qag C^rj^iSQLvdg aTtXcog ^sv 1 20 
xal g', dxQL^cag ds d" /.' y', dLa tb tbv f]XL0v S7ts%SLV 

1. i' S'] U' ^D, U" ^" Dl 2. yiata] xai a D, xaor D^ 
3. XriX&v] corr. ex XsiX&v D^, 4. lnL%vv.Xov] corr. ex ocno- 

yivyiXov D*. s^rjyioGtd] ^^ B, |" D. 6. acpsat^tiSL D. 9. ^] 

corr. lex fiv seq. ras. D. dt,' avtov] mg. D^, dca tov supra 

scr. D. 11. yivovtai] corr. ex I^ Df tstagtov] j' B, d- D, 

d D^ 13. Toa] t&i C, t eras. ^'] corr. ex t,^' D*. hsC] 

JV 

corr. ex h D*. istiv] comp. B, -v del. D^ 14. Na§ova- 
accQOv D, -ZV del. D^. Atyvnt^ovg D. 16. s^iXsLTCsv] -sl- 

corr. ex i D. i](iiGv] U' D. 17. sv.XsLip^ D, ^x^len/)^ D^. 18. 
^(TTjju-f^tv^ff] corr, ex £67](iSQLv^fjg D^. ^yyKXra] pr. y e corr. A^ 
20. 67id] ffx- e corr. D*. 

27* 



420 KAATAIOT nTOAEMAIOT 

KaQTcCvov ^OLQag Trj t/3* &6t£ Tial rj 0sk7]vrj xata iiriKog 
^£6(og iiEV i7t8L%Ev AlyoTceQG) ^OLQag % x/3, axQi^&g de 
Trj t,d. aq)£i6t7]K£L de Tcal ccTtb ^lv tov ccjioyELOv tov 

£7tLXVZX0V ^OLQag KTj £, CCJtb d£ tOV P0Q£L0V 7t£Qatog 

5 tov Xo^ov xvxXov iioLQag 6^p t/3. Tcal ivt^vd^Ev aga 
dfjXov^ otij orai/ 5 ^OLQag xal d Tti^itta tcbv 6vvd£- 
6^C3v a7t£%ri "^o K£vtQOV trjg 6£kr]vr]g iitl tov Xo^ov 
tcvkXov 7t£Ql t6 avtb ^iyL^tov ov6r]g a7t66tr]^a tov 
xivtQOv tfjg 6xLag tr]v £iQr]^ivr]v £%ovtog 7tQbg avtb 

10 d^i^LV, t6 i]^L6v ^iQog £Lg tr]v ^xlccv i^7tL7tt£L tf]g 6£- 
Xr]VLaxrjg dLa^itQOV. 

akXd^ ictv ^£v d" y' ^OLQag a7ti%r] tS)v 6vvdi6^cov 
i7tl tov lo^ov xvxXov t6 xivtQov tf]g 6£kr]vr]g^ Jirj L! 
£^r]xo6ta inLctg ^OLQag a7tix£L tov dia ^i6c3v iTtl tov 

15 TtQbg oQd^ag tco Ao|« dL avtov yQa(po^ivov ^£yL6tov 
xvxkov^ OTai' de J ^OLQag xal ti66aQa 7ti^7tta d^tiyr] 
tcbv 6vvdi6^c3v iTtl tov lo^ov xvxXov^ ji xal rB i^r]- 
xo6td tov did ybi^cov d7ti%£L ^Lccg ^OLQag i^tl tov 7tQbg 
OQd^dg ta Ao|ffii Sl avtov yQacpo^ivov ^£yL6tov xvx- 

20 kov. i7t£l OVV r] ^£V tCbV dvO ixX£Li)£CJV V7t£Q0%r] t6 

8' 7t£QLi%£L tfjg 6£kr]VLaxf]g dLa^itQov^ rj d^ tGiV ixxst- 



2. inEL%£v^ -tv e corr. D^. 3. l3] corr. ex la D^. acp- 
fKyrrjHft] D^, acpiotijyieL ABCD. %at] comp. supra scr. D. 

7. dnsxrj] D, anixEi ABC. 8. iiiyLatov'] corr. ex m D^ 

9. y,ivzQOv\ ?^ D, >t-^ D^. 10. iqyi,L6v] [_' B. GsXTqvLayifjgl 

corr. ex GsXrivr]a%^ D*. 12. aW CD. y'] y A, %at y BCD. 
^oiQag] corr. ex Jid D^ 13. Xo^ov] X- corr. ex z/ A. 14. 

rov (alt.)] tbr A. 15. Sl' avtov] did tov CD, corr. D^. 

16. Ss] comp, ins. C^ tsacaQa Ttsiinta'] J s's' B^ d E D. 

17. r'?] Fo ABCD. s^Ti-noGtd] H B, |a D, H D^ 19. di' 
avtov] ^ta tov CD. 21. ^'1 supra est ras. A, j D, A' D^. 

csXriVLav.fjg] -Xt]- supra scr. D. 



MA0HMATIKHS STNTASEiiS E'. 421 

^svcov rov 7C£vtQ0v avtijg dvo di,a6tcc6s(ov ajtb tov dio: 
^edcov tcbv ^cydLcov^ tovt£6tiv d:tb xevtQOv tijg 6xLag^ 
£^7jxo6td iiLdg fiOLQag J L' y\ (pavegov, ort xal o2.rj ri 
di,d^6tQog tijg ^sXtjvrjg vTtotsCvEL ^syC^tov xvxXov 
TtSQLCpSQScav s^rjxo6tS)v ^Lag ^oCQag la y'. 5 

sx)xatav6rjtov d' avtodsv^ on xal ri sk tov xsvtQOv 
trjg 6XLag tfjg xatd ro avtb ^syL^tov dTto^trj^a trjg ^sXr]- 
vrjg vTtotsCvsL fisv ^Ldg ^oCQag s^rjxo^td Jl xal r^^ sjtSLd'^- 
TtSQ^ ots td to6avta s^rjxo6td tb xsvtQOv tfjg 6sXr]vrjg 
tov xsvtQov tijg 6xLdg aTtstxsv^ sq^rjjttsto tov xvxXov tijg 10 
6xLdg dLd tb tb r]iiL6v tijg 6slriVLaxi]g dLa^istQOv sxXsXol- 
TtsvaL^ ddLacpoQO) ds sXdttcav s6tlv tJ dLitXa^Ccov xal stv 
totg y Tts^TttOLg ^sC^cov tijg sx tov xsvtQov tijg 6slrjvrig 
s^r]xo6tG)v ov6r]g ls r§. xal d^d TtXsLovcov ds tOLOVtcov 
tr]QrJ6sc3V 6v^(pd)vovg syyL6ta tdg sxxsL^svag 7tr]XLx6- 15 
tY]tag xataXa^pav6^svoL 7tQ6g ts td dXXa td TtSQl tdg 
sxXsCipSLg d^scjQov^sva ^vyxsxQrj^sd^a avtatg xal vvv ys 
TtQbg tr]v dst^Lv tov r]lLaxov d7to6tr]^atog xatd td 
avtd s6o^svr]v^ f] xal 6 "l7t7taQ%og rjxoXovd^rj^sv, xal 
G)g tcbv TtSQLla^^avoiisvcDv VTtb tcov xmvcov xvxXcov 20 
r]XCov xal 6sXr]vr]g xal yijg ddLacp^QCo slatt6vcov bvtcov 



3. s^r}%06Tci] comp. BD, ut saepius. 17] e corr. A. 4. 
vnotEivsLl -SL corr. ex i in scrib. D, 5. Xa'] X- e corr. in 

scrib. D. 6. svv.axocvoritov] sv- corr. ex cc- D. ■ksv- 

tQov] comp. ins. D, corr. D^. 8. ftj corr. ex ft D^. r'*] 

lo ABC, rs D. 9. ots] supra scr. D^. 11. rd] om. CD. 

7]fiiav'] [_' B. GsXrivLcciiris] corr. ex gsXt^vtjs D^ i-nXsXoL- 
TtEvaL] -y,- dimid. eras. B. 13. 7] tQL6L in ras. minore D^. 

Tts^TttoLg] corr. ex s seq. lac. Dl 14. r'^] U ABC, 

i^ D, Fs D^ tOLOvtoav] -l- corr. ex v D^ 16. ■nataXccfi- 

§av6^svoL] -av- renouat. D*. ts] corr. ex to D^ td (alt.)] 
om. D. 17. ^XXsLipLg D, sed corr. GvvnsxQVt^^^^ ^^ corr. D^ 

19. ijyioXovd-Tqesv] -v eras. D. 21. y^g] corr. ex tfjg D. 

sXaGGovoav D. 



422 KAATAIOT nTOAEMAIOT 

t&v iv tatg 0(paiQatg avt&v yQacpo^svcjv ^Eyt0t(ov 
xvxXcov avtGiv te xal t&v dia^stQCJv. 

le'. IIsqI tov rjXcaxov ajto^tTJ^atog xal t&v 
6vva7tod6LXvv^ev(DV avr«. 
5 Tovtcov toCvvv dsdo^evcDv^ xal ot^ t6 xata tag 
^vt.vyCag ^ieyLatov aTto^trj^a trjg eEXTJvr^g tOLOvtcav 
£6tlv |d 7, OLOv iiStlv ivbg rj ix tov xivtQOv tfjg yfjg^ 
Slcc tb t6 ^£v iii6ov dedstxd-aL t&v avtcov vO", tfiv d' 
iyi Tot) xivtQOv tov iTtLxvxXov i T, fdco^sv^ TtrjXLXOv 

10 ^vvdyetaL xal t6 tov yiXlov ocTtoatrj^a. 

£6tco6av yaQ oi ^iyL^tOL xal iv ta avTco iTtLTtidco 
t&v 6(paLQ&v KvxXoL tfig fi£v fjlLaxfig 6 ABF 7t£QL 
xivtQov t6 z/, Ttjg d£ 0£krivLaxfig %ata t6 ^iyL6tov 
avtrjg dnoCtrj^a 6 EZH jt£Ql xivtQOv t6 @, tfjg ds 

15 xatd triv yrjv 6 KAM TtSQl xivtQov t6 iV, t&v dl dtd 
tcbv xivtQCOv iTtLTtidcav tb fihv tijv yfjv xal tbv rjXiov 
7t£QLXa^pdvov t6 AlSir^ t6 dh tbv tjXlov xal tfjv 6£- 
Xtjvrjv t6 ANF^ xal a^Giv ^hv xoLvbg 6 A@N^, aC 
ds d^d tcbv iTtacpcjv Evd^EtaL TtaQdXXrjXoL drjXovott 

20 yLyv6^£vaL xal tatg Sia^itQOLg l'6aL TtQbg atdd^rjeLv 
tov ii£v fjXLaxov xvxXov fj AAF, tov dl 0£XrjVLaxov 
fj E@Hy Tov d£ tfjg yfjg fj KNM, tov dh Tijg CxLdg^ 



1. GcpaCqaig] 6(p^ D, -^atg add. D^. 2. ts] om. BC. 3. 
tf'l mg. AC, ft B, om. D. 5. ro] ins. C^. v.axd'] corr. ex 
v,a\ A^ 6. 6v^vyCag\ gv- ins. D, supra -ag add. rd, sed del. 
8. xo ftsV] ins. C^ iiiv B. 9. ?] post ras. 1 litt. D. 11. 
H,EyiGToi\ corr. ex m D^; supra add. xQsig, sed del. , mg. ot 
(ifyiGTOi D^. inBLTtido) C, sed corr. 12. GcpaiQcbv y,v%Iol] 

corr. ex c^ «^ D^, mg. GtpcciQoiv. ABF] corr. ex ABV D^. 
19. ^7raqpc6v| A^, B7tciq)&\v A. 20. yLvofisvat D. diafis- 

tQote] corr. ex ^ D^, mg. OtO D^. 21. AdF] corr. ex 

AAr D^. 22. Toi) (alt.)] in ras. D. 



MA0HMATIKHS STNTABESiS E'. 



423 




sCg 7JV i^TCiTCtsi, xata tb iiiyi- 
0tov aTCo^trj^cc rj ^slnjvrj^ ri OTIP^ 
C30ts l'6rjv slvac triv ®N tfj NU 
xal ixatiQav toiovtcjv |d 7, 
Oiov i6tiv rj NA ix tov xiv- 5 
tQOv tfjg yfjg ivog. 

dst drj svQSLV^ bv s%sl koyov 
ri N^ svdsla tov rjXiaxov aico- 
6trjy,atog JCQog tr^v NA ix tov 
xivtQov tfjg yfig. 10 

ixPspX^^^&cj toCvvv r] EHS. 
xal iTCSid'^ id£L%a^sv^ ort rj tfjg 
6sXr]vr]g did^stQog xata tb ix- 
xsL^svov iv tatg 6vt,vyCaLg ^i- 
yL(5tov ccTCoatrj^a vicotsCvsL tcsql- 15 
(piQsiav rot) ^far' avtrjv yQa- 
fpo^ivov nsQl tb xivtQov tfjg 
yfjg xvxkov tOLovvcav o la %, 
oXcav i6tlv 6 xvxXog t^, stri av 
rj ^sv vjcb ENH yovCa toL- 20 

1. Ug\ e corr. D^, supra scr. C^. 

simLTCXBi] -InxBv renouat. D*. 2. 
7] OUP] 7) O- e corr. A\ O- reno- 
uat. D*. 3. wCTf] wGxs Y.ai C, xat 
supra add. D^. t^] xfii corr. ex 

ti) A}. 5. oiov\ -i- supra scr. C. 

NA] corr. ex iVz/ A. %s\xqov D, 
corr. D^. 8. N^] corr. ex NA Dl 

9. NA] corr. ex N^ Dl 13. 
dvdybEXQog] ^ D, OtO mg. D^ fx- 
v,£LlL£vov] -L- corr. ex V in scrib. A. 
r 

14. ^LiyLGxov] corr. ex m D^ 18. 

livyiXov] corr. ex x^ D^. x] corr. 
ex vrD^. 20. [liv] corr. ex jLtf| D^. 
ENH] -H e corr. Dl 



424 KAATAIOT nTOAEMAIOT 

ovtcjv o Xa 3c, OL(DV at d oQd^ccl r|, ri ds rj^L^SLcc avzrig 'ffl 
VTcb SNH roLOvtcjv icdlLV o ka z, oZc3v el^Xv aC p OQ^al 
t|' a0ts xal ri filv sjtl tijg 0H 7tSQL(psQSLa toLOvtcai 
S6tlv O Xa X^ OLCDV 6 TtSQL to NH@ dQd^oyihvLOv tcv- 
5 TcXog t|, rj d' stcI tfjg @N t&v XoLJtav [Eucl. III, 31 
sig tb rj^LTcvxXLOV Qod" zrj ji. xal tav vit^ avtccc 
ccQa svd^SLcbv rj ^jlsv H® s6taL toLovtcov o A/3 jirj, olcov\ 
s6tlv rj NH dLcc^stQog qx^ rj ds N® t&v avtcbv qxa 
syyL^ta' &6ts xaC^ oXav s6tlv r] N@ svd^sta ^d lA 

10 tOLOvtcov xal rj ®H s6taL o l^ ly. tov d' avtom 
s6tLv xal r] NM sk tov ocsvtQOv tfjg 'yrjg svog. akX*\ 
STtsl Xoyog s6vlv tfjg IIP TtQbg tfjv @ff, ov s%sl tdA 
P Ag syyL6ta TtQbg tb sv^ yCvstaL xal r] HP tG}v\ 
avtcov o JjLS krj. 6vva^q)6tSQaL ccQa i] ts ®H xal 

15 HP tOLOvtov SL6lv a y ta, olov s6tlv r] NM svogA 
aXlcc 6vva^(p6tSQaL r] ts HP xal r] &U oXr] tcbv\ 
avtcbv si6Lv /3 dLcc tb l'6ag avtag sivaL dv6l tatg NM' 
jtaQccXXr]XoC ts yccQ^ cjg scpa^sv^ si6lv 7ta6aL, xal i6r}\ 
r] NH tri N@' xal koLTtf] ccQa r] HU xataksCitstao 



1. at] eialv al D. tiiiCgelu] mg. D^, U' D. i] vno] ^ 
V- e corr. D^ 2. ^] dvo CD. 3. enC] -n- corr. ex c in 
scrib. A. 4. 6] hrLv 6 D. 6. iiiii-Av-AXiov'] ^^ D, Q D% 
mg. riiiLv,'^ D^. 1. H©] @HJy. Supra ol(ov add. -* 17 de 

6>JV Qi^ vQ- iif\ D^, -* supra syyiata lin. 9 adp. D^. 9. F] e 
corr. D^. 10. toLovrcov] x- e corr, C. @H] H@ corr. 63 

NSJy^. >Ly] corr. ex At D^. 11. iffTt-v] comp. B, -v del. D^ 

%at] om. C. NM'] -M e corr. Dl aXXd D. 12. htCv] 
comp. B, -v eras. D. oV] corr. ex o D^ 13. ^ ^g] |3ig AC, 

xo\ corr. ex tov C*. yCvstaC] y+ D, "^ supra add. D^, rx D*. 

15. bIgIv] ins. D*. 16. aXXa\ om. C. 17. eIglvI comp. B, 
-V del. D^. SvgCv D, corr. D^ rats] corr. ex toLg in 

scrib. C. 18. daCv'] comp. B, -v eras. D. 



MAeHMATIKHS LTNTASESiS E'. 425 

tOLOvrcov o vg ^d', olov e6r\v rj NM avd^sta ivog. 
xaL ianv^ cjg tj NM TtQog rriv HU^ ovrcog rj ^ev NF 
JtQog f^v HF^ Y} ds iVz/ TtQog ri^v 0z/* olov aQa idrlv 
il NA ivog^ rotovrcjv xal ri fiev z/0 66raL o vg fid^^ 
XoLJtrj ds r} @N rcbv avrcbv o y Ta. G)6rs KaC^ olcdv 5 
ierlv ri fisv N@ sv^sla |d 7, r] ds NM fVdg, roLOv- 
rcov s%o^sv Tcal rr^v Nzl rov rjhaxov djto6rr]iiarog 
^a6L syyLdra. 

G)6avrc3g d' ijtSL^ otov i6rlv rj NM svd^sta svdg^ 
roLovrcov r^ UP idsL%^ri o ~^s Xrj^ cog ds r] NM TtQog 10 
rrjv UP^ ovrcog rj iV^ TtQog rrjv ^U [Eucl. VI, 1], 
xal oZov ccQa rj N^ svd^sta ivog., roLOvrov r] ^sv iSln 
s6raL o Jis Irj^ XoLTtr] ds r] HN rcov avr cbv o td x/3. 
xal 0LC3V i6rlv ccQa r] ^sv HN svd^sta |d 7, r] ds NM 
ix rov xivrQOv rr]g yr^g ivog^ roLOvtcov xal r] fisv l^H 15 
s6raL &y v syyL6ra, r] ds ^N oXr] 6^r]. 

6vvY]KtaL r]^tv ccQa^ ori, olov i6rlv r] ix tov xsv- 
tQOv tr]g yfjg ivog^ toLovtcov i6tlv ro ^isv tr]g 6sX7]vr]g 
iv tatg ^v^vyLaig ^s6ov d7t66tr]^a v^, t6 ds roi) r^Uov 
^a6L^ tb d' djtb tov xsvtQOv trjg yrjg iisxql tr]g xoqv- 20 
(pY]g tov XG)VOV tr]g 6xLag 6^r]. 



1. o] D, ut saepe. iGxCv] comp. supra scr. D^ 2. 
7] (pr.)] supra scr. D^. JVM] renouat. D*. rrjV] supra scr. D^. 
H2] corr. ex HTjp^. 6. iV0] N- in ras. D. 7. N^'] 
JN, N e corr., D; Sv mg. Dl 8. aat] corr. ex fif D^. 9. 
OLOv] corr. ex ov C^. svog] post ras. 1 litt. A. 10. rj (alt.)] 
seq. ras. 1 litt. D. TtQog] f\ I). 11. Ttgog — 12. N!s^] supra 
scr. Dl 12. £/77] mg. D^ Hls; D. 13. ds] de /• D. 16. cy] 
6y D. 6^7]] -7} corr. ex w C^ 17. ccQa r]fiLv D. 18. iativ] 
om. D, comp. BD^ csX-^vrjg] 6i- add. D^ 20. aOL] diOL D, 
^iiGL D^, uOL mg. D^ 21. <>|rj] corr. ex ^rj D^ 



426 KAATAIOT nTOAEMAIOT 



I 



tg'. IIsqI fieysd^&v rjXLOv xal ^slTJvrjg xal y^g. 

EvKatavorjtog d' avtd^av yCvetaL xal 6 tav 6tSQEG}v 
^sysd-cjv Xoyog djtb tov tCbv dia^stQov rjliov ts xal 
^sXTJvrjg xal yr]g. 
5 STtsl yaQ dsdsLKtai ^sv^ ort, olov svog s6tLV r} NM 
sx tov xsvtQov trjg yrjg^ tOLOvtcov s6tlv rj ^sv @H 
sx tov xevtQOv trjg asXTJvrjg o ig Xy^ rj ds N@ svdsta 
^d 7, s0tLV ds xaC^ d)g ri N® TtQog ®H, ovtcog rj N/i 
itQog tiiv AT [Eucl. yi, 1], rrav avtcbv xal tfjg iVz/ 

10 dsdsLy^svrjg ^aol s^o^sv xal tr^v ZlF sx tov xsvtQov 
tov rjXCov tc3v avtcbv s /.' syyL6ta' xal tcbv dLafis-' 
tQcov ccQa OL avtol s6ovtaL koyoL. G)6ts xaC^ olov ictlv 
rj trig 6sl7Jvrjg dLa^stQog svog^ tOLOvtcov xal r} ^sv trjg 
yfig s6taL y xal dvo Tcs^jttcjv syyL6ta^ rj ds tov rjlCov 

15 Trj xal d Tts^Tttcjv. rj ^sv trjg yfjg ccQa dLcc^stQog tfjg 
GskrivLaxfig tQL7tXa6Ccjv s6tlv xal stL totg dv6L jts^jt- 
tOLg ^sC^cov^ rj ds roi) rilCov tfjg ^sv 6sXr]VLaxfjg oxrco- 
xaLdsxa7tXa6CG)v xal stl totg d jts^ntOLg /Ltftjcov, tfjg 



1. tg'] mg. AC, il B, om. D. nsQi — y?)?] add. D^ 2. 
6 Tcoi'] 6 t- absumpsit lac. pergam. D, v.al 6 r&v atSQS&v 
mg. D^. 4. %at] ins, D^. yi^g] e corr. D^. 5. ol'ov] corr. 
ex ov C\ ex oaov D. 7. Mg. o t^j^^y D^. 8. T] corr. ex 
r D, mg. ^di' D^. faziv] comp. B; s- e corr., -v del. D^. 
4«^^ 

TtQog] TtQog xriv D. 9. r»jV] supra scr. D^. 10. aai\ Jccci B, 
corr. ex o<aL D^. 12. otov] post -C- ras. 1 litt. A, -ov e 

corr. D. 13. >tat] om. B. 14. Svo] b B. TtefiTcroov] e e B, 
supra scr. D^. 15. ^] A D, corr. ex Cj ABC. TcifiTtzcov'] 
«'e' B, e D, s" D*. 16. zQLTtXocaLcov] corr. ex.tQLTtXdcLo] D^. 

satLv] comp, B, -v eras. D. ^zl] corr. ex STtt D^, ns^ntoLg] 
7t- e corr, D, s' s' B. 18. 8] mut. in tstQaL D^, TtsfiTttoLg] 

s s' B, s D, s D*. t^sL^cov] M D, m D^ 



MA0HMATIKHS STNTASE^S E'. 427 

dh yfjg TtsvtaitkaaCcov xal hu ta ri^Caei syycOta fisC^av. 
xata tavta d\ stcsI xal 6 ^sv aith tov svbg Kv^og tov 
wbtov s6tiv svog^ 6 d' aTtb tmv y xal ^ TtsiiTttcov 
tCbv avtcov syyt0ta Xd" d\ 6 d' aTtb t&v Irj xal d 
Tts^Tttcjv o^oCcog ^^Xiid C syyc6ta^ evvijxtat [Eucl. 5 
XII, 18] ri^tv^ otL xaC^ oIlov sv6g s6tiv t6 tY^g 6sX7]vrjg 
6tsQsbv ^sysd^og^ tocovtov s6tlv tb ^sv t7}g yTJg A-d* 
d\ t6 ds tov rjXCov ^^x^^ /-'• sxatovtaxatspdonrjxov- 
ta7tkd6L0v ccQa syyi6ta t6 tov r]XCov tr]g yr]g. 

i^\ UsqI tcbv xata ^SQog jtaQaXXd^scjv riXCov lo 
xal 6sXrivrig. 

Tovtcjv toCvvv ovtcog vnoxst^svcov dxoXovd^ov dv 
str\ TtQO^aTtodsl^aL Ttdltv dLa ^Qaxscov^ tCva dv tLg 
tQOTtov SK tr]g t&v djto6tr]^dtcov TtrjXLXotrjtog rjlCov 
ts xal 6sXrlvr]g xal tdg xatd ^iSQog avt cbv yLvoybsvag 15 
TtaQalXd^SLg smXoyC^OLto xal itQcbtov tdg sjtl tov dtd 
tov xatd xoQV(pr]v 6r]^sCov xa\ avtav yQag)o^svov 
lisyC6tov xvxXov d-scjQov^svag. 

s6tco6av dr] sv ta tov sCQr][isvov ^syC6tov xvxkov 



1. hC\ corr. ex snC D^ tc5] coit. ex rd C*. r]yiC6si] 

-s- e corr. in scrib, A, rjfiLGsi fisgsL D. (isC^cav'] m D, et 
similiter saepius. 2. xavtd] mut. in ta. ccvtd C^, ta avtd D. 

d'] 8s v.aL D, 8i Dl xat] om. D. , 3. d'] S s D, -s e 
corr. D*. niyiittcav] s s B, s" D, ut lin. 5. 5. j^xiid] ,5- 
e corr. D*. 6. ort xat] xai oti D. satLv] comp. B, -v 

del. D*. 7. satCv'] comp. B, -v eras. D. 8. <5xyid D, corr. D*. 

sv.atovtav.aLS^doyiriyLOvtanidaLov a^a] corr. ex SY.atovtav,aL- 
s^doiirivovtanldcLOL 6' Dl 10. t^'] mg. AC, ^t B, om. D. 

14. tav] corr. ex t D^. 15. avt&v] avt corr. ex avi D*. 

16. 8La tov] om. D. 18. fisyCatov yivyiXov] corr. ex (t x^ D, 
et similiter saepius. 



428 



KAATAIOT nTOAEMAIOT 



iTtLJCedo) 6 ^sv tfjg yfjg ndXtv ^eyL^Tog KVKkog b ABj 
6 ds xata tbv ^Xlov rj tijv 6EX7]vr}v b Pz/, TtQog bv 
df i^ yij ^rj^SLOV Xoyov exsL, b EZH®^ xal xsvtQov 
lisv Tcdvtcov tb K^ rj ds dta tav xata xoQvq^rjv 6rj- 
5 iLSLOv dLa^stQog riKArE. 
xal d7Cokr](p&sC6rig aTcb 
tov r zaro; xoQvtpriv ^rj- 
^SLOv trjg FzJ TCSQicps- 
QsCag toLovtav loyov 

10 svsxsv vTCoxsL^svrjg A, 
OLCov s6tlv b JTz/ Kvxkog 
r| s7Cst,sv%^G)6av ^isv jcd- 
Ilv 7] ts KzJH Tcal rj 
AJ®^ dnb ds tot) A 

15 TCaQdXXrjXog ^^v ^^-O-co 

f^ KH rj AZ^ Tcdd-stog d' stc avtrjv rj AA, 

S7CSL toCvvv ^rj ^svovtog dsl tov avtov djco^tt]- 
^atog 7CSQL sxdtSQOv t&v cpcbtcjv rj ^sv 7Csqi tbv tjXlov 
s^o^svrj dLa tovto tcov 7caQalXd^sc3v dLa(poQd ^Qaxsta 

20 7Cavtd7ca6L %al dvsTcaC^d^rjtog ^6taL Te5 xal trjv sxxsv- 
tQotrjta tov xvxXov avtov ^LXQav slvaL xal t6 dTCo- 
6trina iisycc^ r] ds 7CsqI tijv ^sX^^vrjv xal 7cdvv dv 
ysvoLto aC^d-rjtii xal trjg xatd tbv i^cCxvxXov XLV7]6scjg 
avtrjg svsxsv xal trjg avtov tov iTCLXvxXov xatd tbv 

25 sxxsvtQOv ov liLXQav 7C0L0v6rjg 7CSQL tdg d7C06td6sLg 
dLacpOQav sxatsQag^ tdg ^sv tov rjXCov TCaQaXXd^SLg 




4. K] renouat. Dl 5. KATE] A, corr. ex KFE D^, 
xa r 8 BC. 8. rj] corr. ex z/ D. 9, roiovttov] -i- corr. 
ex in scrib. C. 11. 6] add. A^. 17. ahC D. 19. tovto] 
corr. ex xov D. naqaXd^EGiv D. 25. iiiv.qdv] -t- corr. 

ex rj A. 



MA0HMATIKHS STNTASESiS E'. 429 

inl ^ovov tov ivbg loyov dsi^o^sv^ Xeyco de rov xcbv 
JU0L TtQog t6 £v, tag de tfjg 6£?.7]vrjg £7tl t£66dQov 
r&v ^dXi^ta £lg tdg i^rig itpodovg £vod(ot£Q(ov i^o^i- 
vcov. £iXYiq)a^£v de t&v t£66dQcov tovtcnv d7to6trj- 
lidtcov TtQ&ta fi£v dvo td yivo^^va tov iTtiXvxlov 5 
xatd t6 djtoy^iotatov tov ixKivtQOv tvy^dvovtog Tcal 
tovtcov jtQ6t£Qov ^£v To ^ixQ'' ''^ov aTtoy^iov tov iTti- 
tcvkXov^ o 6vvfiy,tai did t&v %Qoa7tod£d£iyybivcov [p.422,7] 
TOtovTcov |d 7, oXov i6tlv 7} ix tov xivtQov tfjg yfjg 
ivog^ d£vt£QOv dh t6 ^ixQi' f^ov 7t£Qiy£tov tov i%i- 10 
avTiXov 6vvay6^£vov xal tovto tcbv avt&v vy v 
[p. 416, 5], td dl loiTtd dvo yiv6^£va tov ijtiKvxXov 
Tcatd t6 %£Qiy£i6tatov tov ixxivtQov tvyxdvovtog^ 
xal tovtcov dh Ttdliv 7tQ6t£Qov ^£v t6 ^ixQi' t^ov dito- 
ysiov tov ijtiKvxXov 6vvay6^£vov did td jtQoaTtods- 15 
d£iy^iva [p. 416, 6] TotovTCDv ]iy vy^ oiov ietlv r^ 
ix tov xivtQov tijg yfjg iv6g^ 8£vt£Qov dl t6 fA£%()t 
Tov 7t£Qiy£iOv tov iTtiXvxXov 6vvay6^£V0v xal avtb 
tG)v avtcbv ly ly. 

iTtii toivvv r\ Fzf 7t£QicpiQ£ia i)7t6K£itai ^oiQ&v A, 20 
si:rj dv xal r} VTtb FKzf ycjvta^ oicov ^iv £i6iv at d 
OQ^al t|, toiovtcov A, Oicov d' aC dvo OQd-al t|, to^- 
ovtcov f. co6t£ Kal 7] ^£v i^tl tf]g AA 7t£Qi(piQ£ia 
toiovtcov i6tlv J, oX(ov 6 7t£Ql t6 AKA oQd-oycoviov 



1. d^] corr. ex Srj D^. 2. aci} ac t. A, S^at D, ^Kai D^ 
fV] BC^D, sv AC. 6. ytccTo] post ras. 1 litt. D, infra %- 

add. ^ A. 7. Mg. a BCD^ tcqoxeq(ov A. 10. Mg. u 

BCD^ rov (alt.) — 18. nsqiyEiov'] bis D. 12. dvo'] dvo td D 
utroque loco. 14. y mg. D^ rov] corr. ex ro C^. 15. 
TtQodsdsiyfiiva B. 16. oroi;] -t- in ras. C. 17. z/ mg. D*. 
d£v\d8vtsQov D priore loco. 22. toiovtcov — r^] supra 

scr. Dl d'] ds D\ dvo] § BDl 



430 KAATAIOT nTOAEMAIOT 

xvxXog t|, ri d' STtl trjg KA tav XoiTt&v [Eucl. III^ 31] 
sig t6 ij^LXVTcXtov ^. xal t&v v% avtccg aQa ev- 
^BLG)v 7] fisv AA toiovtcov E6tai J, olcDv eotlv ri AK 
dLa^etQog qoc^ ij ^^ ^^ "^^^ avTwi/ Qy va. xal ovov 
5 ccQa B6tlv ri AK ivogy toLovtcjv xal rj ^av AA £6taL 
o X^ ri ds KA Evd^Eia o v^. tcbv d' avt&v £0tLv xal 
rj KAA svd^sta Eitl ^sv tov rjXLaxov djcoatijiiatog 
^a6L^ ETtl dh tcbv 6EXrjvLaK&v xatd fisv tbv TtQcotov 
OQOV ^d ~L, xatd ds tbv dsvtEQOv vy v, xatd dh tbv 

10 T^tTov Jiy vy^ zatd ds tbv tdtaQtov ky ky xal XoLTtrj 
ccQa rj ^z/, tovt£6tLV rj ^z/, EJtEl ddLacpoQip £l61v 
dvL60L^ ETtl ^EV tov rjXLaxov d7to6triiiatog E6taL a^d' 
rj^ £7tl ds tcov 6EkrivLaxcbv xatd ^ev tbv TtQ&tov oqov 
^y Trj^ Ttatd ds tbv dEvtEQOv v^ vrj^ xatd ds tbv tQLtov 

15 JLty a, xatd ds tbv tstaQtov A/3 Jid. &6tE xaC^ oZcov 
£6tlv r] AA v7tot£Lvov6a qx^ toLOvtcov £6taL rj AA 
Evd^Eta VTtaxovo^Evrjg^ Xva ^rj tavtoXoya^Ev^ trjg avtrjg 
td^EC3g o p vd" xal o v^ vfi xal d l vr] xal d xy ]id 
xal d V %" xa\ r] ^ev iTt^ avtfjg aQa JtEQLCpEQELa tOL- 

20 ovtcov £6taL o p V xal o v6 T^ xal d d vd xal d x 
xal d ji£ £yyL6ta., oicav i6tlv 6 jtEQl t6 AAA oq^o- 
ycoviov xvxXog t|, 17 ^' ^^0 AAB ycDVLa^ tovt£6tLV 

2. rjiiLyiv-AXLov] comp. macula obscur. D, corr. D*, q" mg. D*. 

6. AA] corr. ex AJ D. 6. X] seq. ras. 1 litt. D. d'] 
supra scr. D. 8. 001] hoi D, 6i6i D^, ut saepius. STri] -t 
in ras. A. 9. ^f (pr.)] ins. D. Tor^pr.)] supra scr. D. vy] 
corr. ex ny D^, 10. xiTaQTov] j seq. 1 litt. deleta D. 

Xy (alt.)] e corr. D^ 11. sIglv} st- ins. D*. 12. aviaoL] 
-OL in ras. A. 13. oq(ov C. 17. xavtoXoy&yi^sv] -0- pr. in 

ras. C. 18. %at(pr.)] om. BC. (alt.)] o seq. ras; 2 litt. A. 

xy] mut. in xa D^, sed rursus corr,; xy mg. D*. 19. v %•] 
corr, ex v%^ A, ex vri^ D^, nBqKpiqiia] comp. postea ins. D. 

22, d'] di D, 



MA0HMATIKHS 2TNTASESiS E'. 431 

rj V7tb ZAS [Eucl. I, 29], otW /xsV u6iv ai dvo oq- 
^al Tr|, roiovxGiV o ^ v Tcal o vd Trj xal a d vd xal 
a % Tcal a ftf, otov d' aC d OQd^al t|, toLovtcov o a tcs 
xal o xf -9" xal o A/3 ^J xal o ^ o xal o i//3 L «^r' 
£;r£t ;cat ro ftfv ^ 6rj^8tov ddiacpOQSt tov K TcsvtQOv^ 5 
i^ ds ZH& 7tSQL(psQ6ta ddLacpoQco ^SL^cov s6tlv tfjg H@ 
dtd ro trjv yrjv olr^v 6rj^SL0v Xoyov s%slv TCQog tbv 
EZH® xvxXov^ Tcal r] H@ trjg jtaQaXXd^scog jcsQLCps- 
QSLa^ OLCov s6tLv 6 EZH® xvxXog r|, tOLOvtcov snl 
lisv tov rjXLaxov d7to6t7]^atog s6taL o d xs^ stcI ds la 
t&v 6sXrjVLaKC3V xatd ^lv tbv TtQ&tov oqov o x^ '9*, 
xatd ds tbv dsvtSQOv o A/3 x^^ xatd 8s tbv tQLtov o 
yb o, xatd 8s tbv tstaQtov o v^ l' ditSQ itQosxsLto 
dsL^aL. 

tbv avtbv ds tQOTtov xal S7tl tcbv koLTtcbv d7to6td- 15 
6SC0V tov xatd xoQvcpriv 6r]^SLov tdg yLVO^isvag xad"' 
sxa6tov OQOV TtaQaXXd^sLg STtLXoyL^d^svoL d^d ^olqcov 
^ ^iSXQL tcov tov tstaQtriiiOQLOv ^OLQ&v 9 dLsyQdt(ja^sv 
xavova 7tQbg tdg 8LaxQL6SLg tcov ^taQaXXd^scsv STtl 
6tL%ovg ^sv 7tdXLV Jis^ ^slCdLa ds '9, (bv sv ^sv tw 20 
7tQcota) TtaQs^^iqxaiiLSv tdg roi) tstaQtrj^oQLOV ^OLQag 9 



1. dvo] B B. 2, o vd LTi] corr. ex ov 81(1 in ras.) 7] D, 
et similiter saepe. 3. t|] supra scr. D. 4. o (sec.)] in 

ras. A. o (quart.)] eras. D. 5. ccdLCicpoQei:'] corr. ex dLa- 

cpoQBL D. 6. ccdLacpOQcp] corr. ex dLacpOQa) C^D^ s6xCv'\ 

comp. B, -V del. D^ 7. ai^^BCov] c^ D, c^ft D^, et similiter 
saepe. iiQoql f\ D, ut alibi. 8. H&] N& B. 10. IWat] 
1A B. 13. ccTisQ TtQOE-KELto diL^cct] D*, : r>o D , supra add. 

aTtSQ (uel onsQ) sdsL dsL^ccL D^ 17. TtccQccXd^sig D, corr. D^ 
18. Tcbv'] om. C. TSTaQxrjfioLQLOv D, corr. D^. SLsyQaif}SV C, 
corr. C^. 19. ^avovLa C. 20. ndXLv] om. D. 21. 9] corr. 
ex bd C^ 



432 KAATAIOT nTOAEMAIOT 

dca dvo drjXovotc rijv TcaQav^rjaLV avxcbv 7tOLrj6d^£voi,^ 
£v de tw dsvtSQip ta eTtipdlXovta 8xd6tc) t[i7]^atL 
£^r]%o6ta tcbv rjXLax&v 7taQaXXd^£C3v ^ iv dl ta tQLtG) 
tag xatd tbv TCQcotov oqov tfjg 6£^7]vrjg itaQaXld^^Lg^ 
6 £v de rco t£tdQt(p tdg v7t£Qoxdg tcbv tov d£vt£QOv 
OQOV 7taQalldi,£G)v TtaQa tdg tov TtQcotov^ iv &£ tm 
Tte^TttG) tdg }catd thv tQLtov oqov 7taQakXd^£Lg^ iv d£ 
t<p £xtG) tdg 'b7t£Q0%dg r&v tov t£tdQtov oqov TtaQaX- 
Xd^£G)v 7taQd tdg tov tQLtov^ oiov cjg i^tl tfjg tG)v k 
10 ^OLQcbv ^taQad^ia^cjg td o a %£ tov r]XLOv^ £7t£Lta £|ijg 
td o Tit ^ T^ov 7tQG)tov OQOV tfjg 6£Xr]vrig xal i^rlg td 

O £ Lrj, Olg 'b7t£Qi%£L 6 d£Vt£QOg OQOg tbv ^tQCOtOV^s 

elta 7tdkLV td o Jl tov tQLtov oqov xal i^fjg td o t/3 A, 

olg V7t£Q£%£L Xal 6 titaQtOg OQOg tbv tQLtOV. £V£X£V 

16 d£ ro-D xal tdg iv totg ^£ta^v tav d^toy^LCov xal tcbv 
7C£QLy£LG)v d^to^tij^aGL 7taQalXd^£Lg dvakoycog tolg xatd 
^iQog r^7]^a<3Lv d.7tb t&v xatd tovg ixx£L^ivovg ti0- 
6aQag OQOvg 7tQ0X£LQG)g ^£^o8£v£lv dLd tf]g tcbv i^r]- 
7co6tG)v 7taQa%^i6£G)g td loL7td 7]^lv tQLa 6£UdLa 6vv- 

20 f]7ttaL 7tQbg ti]v 7taQd%£6LV tcbv tOLOvtcov dLacpoQcbv^ 

2. IxaffTo)] 1« (||« D^) tv.d6xa} D. Tftrjfiart] ty,ri(idTa)v D, 
THi^fiaTL T(bv D^. 3. ^h,r]%oGTa tcov] om. D. tw t^itq)] tcoiI 
ly D, t- eras. 9. tqCtov] r' B, y D. OLtov CD, corr. D*. 

T7)g] om. B. Tcbr 1] corr. ex ^ D*. 10. xd'] supra scr. D. 

Post ETtsLTa del. Tci'? D*. B^fig] mut. in s^^ ? D^. 11. Td (pr.)] 
del. D^ Mg. Ta o d xs D^. GsX^^vrjg] corr. ex csXr]v Lav.fi? D^. 

12. dsvTEQoq] corr. ex ^ D^. oqos tov tcq&tov] corr. ex 

6QQ-bg tbv d Dl l;^. Ji] corr. ex ]id D. tov] corr. ex t6 Dl 

a 

TQkov] y D, ut saepe. s^fjg Td] || B, s^rjvooTd C. 14. 
tov] corr. ex tov D^. 15. fista^v] comp. D, corr. D^, ut 

saepius. 16. d7to6t7]fia6iv D, -v eras. Supra avaXoyag scr^ 

ov D^ 17. t&v] tJ D, ^ add. D^ ixsL^svovg C, syKSLfii- 
vovg D. 18. s^iqyioGtav] ^^ BD^, ^ D, ut saepius. 



MAeHMATIKHS STNTASE^iS E'. 433 

G}v xal avx&v xov STtt- 
loyi6^hv TCSTtof^^sd^a xov 
XQOItOV xovxov. 

B6XC0 yccQ 6 ^lv xrji; 6e- 
kTJvrjg STCLKvxXog 6 ABF^ 5 
tcbqI K8VXQ0V xo E^ xo ds 
xov dia ^80(DV xcbv ^cjdLOV 
Tcal xfjg yfjg xsvxqov xb 
Z, xal i7CL^6vx^£i0rjg XTjg 
AEAZ ^iYii^Gi 7} ZTB, 10 
%al E7CBt,ev%%'G)6av ihbv ij 
XB BE xal 1] FE^ xdd^BXoc 
ds YJx^co6av Bjcl xriv AA 
ccTCo luv xov B ri BH^ ajco 
ds xov r r] r@^ xal vtco- 15 
XBL^d-co TCQ&xov r] aBXijvr} 
xijv AB TiBQLcpBQBLav dcp- 
B6xcb6a xov xaxd xb A 
dxQLpovg xal TCQbg xb Z 

XEVXQOV d-BCOQOV^BVOV aTtO- 20 

yBLOv ^oiQ&v Xoyov bvbxbv 
ov6av J, G)6XB xal xrjv VTcb 
BEH ycjVLav^ olcdv ^bv 
bl6lv at d OQd-al r^, xol- 
0VXG3V BLvac ^, otcjv 6' at 25 
/3 oQxi^al r|, xolovxg}v qk^ 
xal dLa xovxo xrjv ^bv 

BTCl Xrjg BH TCBQLCpSQBLaV XOLOVXCOV yLVB^d^aL QZ^ OLCJV 




1. ojv'] supra scr, D. 12. v.d&BTOL ds 7]x^o)6ocv'\ v.cd %d%'Bxoi 
dLTJxd-coGav D. 25. flvat] in ras. B. 28. yLvsod-aL] corr. ex 



D«. 



Ptolemaeus, ed. Heiberg. 



28 



434 KAATAIOT nTOAEMAIOT 

s6tlv 6 Tts^l ro BEH OQd-oycbvLOv xvxXog t|, triv d' inl 
tfjg EH t&v XoLTCcjv [Eucl. III, 31] sig tb rj^Lxvxhov J. 
Kal tcbv vjtot£Lvov6G)v ccQa avtag evd^SL&v ri ^sv BH 
s6taL toLOvtcov Qy v£, 0LC3V s6tlv rj EB dLcc^stQog ^y 
6 rj ds EH tcov avtcov |. «AA' otav tb E xsvtQov rov 
sitLKvxXov STtl tov ccTtoysLOv fj tov sxxsvtQOVy Xoyog s6tlv 
trlg ZE TtQog trjv EB b tcbv g itQbg ta 's Ts' xal olcjv 
ccQa s0tlv rj EB svd^sta s ls^ toLovtcov xal r] ^sv BH 
sataL ~d Xy, ri ds EH svd^sta p J^, rj ds HEZ oXrj 
10 1/3 Xrj. xal sjtsl tb ccTtb trjg ZH ^sta tov aitb tf^g 
HB TtOLsl tb ccTtb tfig ZB [Eucl. I, 47], s6taL xal avtrj 

tOLOVtCOV 5/3 Jl^iy 0LC3V S6tlv TO ^SV ZA tOV :tQG)tOV 

OQOv a7t66tr}^a |£ Vs^ tb ds Zz/ rov dsvtsQov oqov 
vd ju^, t6 ds AA dLd(poQOv trjg tcbv dvo tovtcov oqcov 

15 v7tSQ0xf}g L X. Tcal tb xata tb B ccQa dLcccpOQOv TtQbg 
tbv 7CQG)tov OQOv toLovtcjv s0tlv /3 ^ij, OLCov oXov tb 
dLcccpoQOV 1 X' w6ts xaC^ oicov i6t\v tb oXov dLcccpOQOv 
I, tOLOVtcov s6taL xal tb tots dLcccpoQov l8 o. tavta 
ccQa 7taQa%"iq6oiisv sv ta t,' 6sXl8lco t<p 6tL%(p ta TtSQLS- 

20 %ovtL t6 i]^L6v tov tcbv I aQLxf^iiov^ tOVtS6tLV 7tQbg 
tolg Xy dLcc t6 xal oXag tccg sxxsL^svag sv tco 7tQcotc> 



1. S'] ds B. 4. dLccfistQog] comp. in ras. Dl 5. ^' 

mg. C. 6. ^] corr. ex rjv D^ i6Xiv\ comp. B, -v eras. 

7. EE] corr.ex E^T C^, ^mg. C^ 9. EH] RE D. ~§ 1^ 
§Xri AC. 10. tov ano'] post ras. 6 litt. D, -v cc- e corr. 12i 
iotiv] comp. B, -v eras. D. 15. fX] corr. ex Tj A. 16. tov] 
corr. ex to D^, toiovtoov] corr. ex noiovvtmv D. sctCv] 
comp. B, -V eras. D. 17. X] corr. ex j A. xb oXov] oXov 
x6 D. 20. xovx£6XLv] comp. B, -v eras. D. 21. nQwxo)] 

cc BD. 



i 



MA0HMATIKH2 2TNTASESiS E'. 435 

esXcdLG) tov xavovog 9 iiocQag t6 7]^l6v 7C£Qis%eLV xcbv 

0,710 tOV A lltX tb Z/ [lOlQ&V Q7C. 

xccta ra avta ds^ xav trjv F^ TCEQKpiQEiav v7to- 
d^a^Ed^a t&v avtCbv |, r] ^sv F® 6EL%^Yi6EtaL tOLOv- 
tcov d Ay, OLCJV £6tlv rj EF ix tov xdvtQov £ le^ 7] 5 
ds E0 o^OLCjg /3 Irj^ Iol^c^ de r] Z0 tcbv avt cbv vt, 
K^' xal dLa ta avta rj ZF v7totELVOv6a vt, ky. a7tEQ 
dcpEXovtsg tcocXlv aTtb t&v tov 7tQG)tov oqov ^e le ta 
koL7td J li^ evQ7]0o^ev e^rjxoGtd ovta tov oAov dLacpo- 
Qov ^d o' d xal avtd ^taQad^r^^oiiev ev ta avrw 0e- 10 
hdiO) 7tQbg ta tcbv | «(^tO-ft^ dta ro xal tijv ABF 

TCeQLCpEQELaV ELVai ILOLQCbV ^. 

TtdkLV V7tOXEL^EVC0V tcbv aVtCJV 7tEQL(pEQELCbV VOEL- 

0d-G) t6 E xevtQov eTtl rot) TceQcyeLOv tov ixxevtQov^ 
xad"' rjv d^i^Lv te tQLtog ^Qog 7teQLi%etaL xal 6 ti- 15 
taQtog. iTtel ovv xatd trjv toLavtrjv d^iaLV Xoyog 
i6tlv tfjg ZE 7tQbg tijv EB 6 tcbv ^ 7tQbg td ^, xal 
oXcov ccQa rj BE yCvetaL TJ^ 6vva%%-ri6etaL xal exat i^a 
^EV tcbv BH xal FB Evd-Eiav^ otav xal ixatiQa tav 

AB Xal r^ 7tEQLCpEQELCbv | ^OLQ&V V7tOxirjtaL^ tOLOV- 20 



1. TjiiLav] mg. D^, t^ D, L ^^^ ^* saepius. nsQiixsL D, 
sed corr. r&v'] bis D, corr. D^ 2. J] cklcpu AC. Q7t] corr. 
expj^D*. 5. 6' Zy] B, corr. exX^D^"^ AC. 6. E0]corr. ex 
ES D^. b\ioC(og\ corr. ex D^. Ztj] corr. ex Jt] D^ v^'] 
corr. ex | Dl 7. ZF] Z- corr. ex T in scrib. C, TZ B. 

8. acpsXovxBg'] -Xo- e corr. D^ 11. iiQog] om. D. aqiQ^^m] 
ins. in ras. 1 litt. D^ 12. eIvccC] om. D. Post (jLOiQcbv 

ins. ry D^ Q7c] Q- ijis. D. 13. H mg. A. 14. to] ta> A. 

E] in ras. Dl 17. sotCv] comp. B, -v eras. D. 18. 

yivstcci] corr. ex / D^, ut saepius. 20. yiaC] om. D. vno- 
v,UtuL D, ante t ras. 

28* 



436 KAATAIOT nXOAEMAIOT 

rcov g vg, olcov ectlv rj ZE svd^sta J, iTcareQa de r&v 
EH %al E® rCbv avrcbv 8 O' a&ra jcat rijg iilv ZH 
yLvoaevrjg rcov avrCbv |d, rriq ds Z® o^OLCjg vlr, dLcc 
ra avra xal rrjv ^ev ZB v7tor£Lvov6av 6vvdy£6%-aL 
5 ^d xy^ rrjv ds ZF roLOvtcov vg Ttg^ olcov ierlv r] ^lv 
rov rQLrov oqov r] ZA evd^eta ^rj, r] ds roi) rov rQL- 
rov TCQog rbv rsraQrov dLacpoQov rj AA evd-sta Tg. 
say ^av aQa ra Jd %y dcpsXca^sv dith ratv |^, xara- 
X£Lq)d-7]6£raL r]^tv y kt,^ d7t£Q rcbv 7g roi) oAov dLacpo- 

10 Qov £^r]xo6rd yLvo^^va Ty ky 7taQad-r]6o^£v c36avtcog 
rc5 tcbv k dQL^^a iv tcj oydoG) ^eXLdCG). idv ds td 
vg zg d(p£kco^£v dno tcbv avtcbv Ji^, 7iatak£Lcp%-r]6£taL 
Td Ad, d xal avtd tcbv ZW tov oAov dLacpoQov i^r^xo^td 
yLv6pi£va Jiy xd 7taQad-7]6o^£v b^oCcog ta tcbv | dQLd^^a 

15 iv rc5 avtS dydoq) 6£XLdLG). 

td ^£v ovv did tr]v iv rc5 iTtLxvxXip yLvo^£vi]v 
^£tdpa6Lv tr]g 6£kr]vr]g 6vvay6pi£va dLacpoQa tovtov 
r]iitv tbv tQOTtov ixr^d^rJG^taL^ rd ds dtd rr]v avrov 
rov i7tLXVK?,ov Tcatd tbv £X%£VtQov TtaQodov ^^d^od^v- 

20 6o^£v ovtcog. 

£0tco ydQ 6 £XJC£vtQog trjg 6£Xr]vr]g KvxXog 6 ABFA 



1. ^] S 4 B. 2. EK xat] HE e corr. Dl E@] seq. ras. 1 

litt., E- e corr. D^. 3. ofioLcog] corr. ex iy\ D^, mg. ofiotcog D^. 

6. tov Tov] scripsi, rov ABCD. 8. ra] supra scr. D^ 

yiataXBLcpd"t]a£tai] -Ibl- corr. ex dhf D^. 9. tov] corr. ex 

t6 D^. 10. ly Xy] in ras. D^ 11. X aQiQ-^tp] supra scr. D^, 

infra est ras. 3 litt. 12. v?] corr. ex vc in scrib. A. 13. Ad]! 

corr. ex XX D^. 14. ofiotcoff] comp. D, corr. D^. f a^n-^-jLtaj]] 

corr. ex |? D^ 15. a-uTw] om. D. 18. avtov] om. D. 

19. tnLv.vv,Xov] post -i- del. tts^ov? D. 21. JBrj]] 

ABr C. 



MA0HMATIKHS STNTASES^S E' 



437 



TCSQL TiivTQOv xo E ocal did^sxQOv rijv AEF^ ecp ^q 

V0SL6d-C3 t6 TCBVtQOV XOV SlCC ^S6CJV XCbV t,(pdL(OV XVX- 

Xov xb Z, xal dLaxd^SLdrjg xfjg BZ^ vTCoxsL^d^G) TtdlLV 
sxaxsQa xav vTtb AZB xal FZ/J yovL&v xolovxcov 
?, 0LC3V sIgIv aC d oQd^al t|, oitSQ 0v^^aLVSL xfig cctco- 5 
Xfjg^ oxav ^sv sjtl xov B fj xb xsvxqov xov sjtLxvxXov^ 
A ^oLQcov v7taQX0v6rjg, oxav d' sitl xov ^, ^olqcov ^. 

Xal STtL^SVX^SL^&V x&v 

BE xal EJ xdd-sxog 
rJX^(o ditb xov E snl xijv 10 
BZ^ il EH. 

STtsl XOLVVV rj VTtb 

BZA yovCa xolovxcjv 
s6xlv 0%, OLOv at /3 6q- 
d^al t|, sl^rj dv xal rj 15 
^sv STtl xrjg EH TtsQLCps- 

QSLa XOLOVXCOV QX^ OLG)V 

s6xlv 6 TtsQl xb EZH 
oQd^oyavLOV xvxlog t|, 
r] d' sitl xfig ZH x&v loLTtov [Eucl. III, 31] sig 20 
t6 ri^LXvxXLOv |* xal x&v vit avxdg aQa svd^SL&v rj 




1. Std^srQov] corr. ex ^ D^, ut saepius. 2. Supra vo- 
eLod-co add. stXrjcp^ai D^ 4. AZB] corr. ex BZA Dl FZJ] 
corr. ex FZA D*. ywvL&v] corr. ex ycovLcc D^ 5. dgd^aL] 
supra scr. D*. 6. ^] corr. ex rjv D. 7. X] corr. ex a in scrib. C. 

9. %«/] om. D, comp. mg. D^. EJ] corr. ex EA D*. v.d&s- 
rog] corr. ex T'''^ Dl il. BZz/] in ras. A^ r] EH] add. A*. 

12. snsL] corr. ex sni A. 14. at] slalv at D. 18. 

sGrCv] corr. ex slaiv D*. 20. 8' snC] ds nsgC D, dl 

snC D^, 7] 8' inC mg. D^ 21. KaC] om. D (macula obscu- 

ratum?). 



438 KAATAIOT nTOAEMAIOT 

fi£v EH e0xaL toiovtcov gy ve^ olcov i6tlv rj EZ 
'V7toteLvov6a ^, rj ds HZ tcbv avt Giv |. &6t£ naC^ 

OLCDV E6tlv ri ^SV EZ ^Sta^V tCbV KSVtQCJV ~L tO", 
7] d' SK tOV XSVtQOV tOV SKKSVtQOV ^d' fttt, tOL- 

5 ovtcov s6taL xal i] ^sv EH svd-sta rj vg^ r] d\ ZH 
tcjv avtcbv s 7. Tcal sjcsl tb ccTtb tijg BE ksl^av 
t6 aiib trjg EH tiolsl tb anb tfjg BH [Eucl. I, 47], 
sataL xal sxatsQa [Eucl. III, 3] t&v BH Tcal JH t&v 
avtcjv ]irj 'vy' C36ts xa\ oXrj ^sv rj ZB tOLOvtcjv s6tlv 

10 vd j>, oZc3v i6tlv r} ^sv ZA t&v TtQatav oqov |, rj 
ds Zr tcbv dsvtsQCov oqcjv Xd' x^^ ii d' vtcsqox^ av- 
tG)V % kr]^ XoLTCrj de r] Z/i t&v avtcbv Jiy ]iy. ijtsl 
ovv ta I tcbv ^sv vd y v7tSQS%SL s v^, aTtSQ tcbv x h] 
Toi) oXov dLaq)6Q0V s^rjK06ta yCvstaL l^ Ttj^ t&v ds 

16 ]iy iiy totg T^ if, ccTtSQ xal avta tcov tc Xrj s^rjxoata 
yCvstaL ftj xa^ Ta ^sv l^ Trj drjXovotL TtaQad^yjao^sv iv 
ta ivdtto 6sXLdC(p ta t&v A aQLd-^a trjg djtoxfjg^ td 
ds ^5 XK tdo t&v QX^ tovts6tLV TtdkLV tdo tcbv | dLa 
tb TtQbg tatg 9 ovtog tov jtsQLysCov L6o8vva^stv xatd 

20 t6 aTtoatrj^a trjv tcov | dTto^riv tfj tcbv ^. 



1. ()y] in ras. C. EZ] -Z in reparat. D^. 3. i t^] 
corr. ex W§ D^ 4. 8' U] ^f|x A, 8E\iv. A.\ v,svtQov\ 

%bvtov C. 5. fdTat] BGtLv D, -V del. D^. 6. EE] EB D. 

8. EJf — 9. avta>v\ om. A, BH HJ mg. A*. 9. /Z^] corr. 

ex jl^ C. 0^7]] -X- e corr. A. 17] supra scr. D. iattvl 
comp. JB, ^"D. 10. Z^] ZHD. | — 20. px] mg. Dl 11. 
Zr] corr. ex !s;r A. Ante Xd- del. towvtcov D^ 12. ZJ] 
corr. ex Zz/H C^ ^ Z Dl 13. ovv] comp. ins. Cl 15. Jiy (alt.)] 
supra scr. C^. ansQ ticcl] supra scr. D^, ■nai etiam in textu. 

16. iv] ins. J)\ 17. ivditcp'] AC, -9^ BDl 18. tovtiativ] A, 
comp. BC, r/Tot D*, supra scr. yq. t^ D^. 19. tatg] j D^, i' supra 
scr. D*. ovtos] -tos supra scr. D^. 



MA0HMATIKHI1 STNTASEiiS E'. 439 

tbv avTOV dij tqotcov aal inl rcov alXcov nsQi- 
rpsQHwv ra yivo^eva i^rjKoGta t&v diatpoQGyv etcl- 
XoyL^diiSvoi Tcata tag ixtsd^si^svag tQstg vnsQOxag 
dia i^ t^rjiidtcov^ a yCvstai TtdXiv g t^^t^^ata iicl 
tcbv iv t(p xavovi aQid^^cov dicc ro ;«al tdg aTth tcov 5 
icTtoysiGiv ijcl td icsQiysia ^oiQag qtc TCQog tatg tov 
^avovog 9 ^oiQaig dicaQtils^d-ai^ icaQsd^ijxa^sv i(p* 
ixd6tov tcbv dsdsiy^svcov aQid^^&v oixsiog td 6vv- 
7]y^sva did tcbv yQa^^cov s^i]xo6td' tr^v ^svtoi t&v 
lista^i) t^rjy^dtcjv TCaQdd^sdv xad^' o^aXriv TtaQav^r}- 10 
6iv trlg tcov i^a^oiQcaicov vitSQOxfjg TtSTtonqiLSxta 
^rjds^iccg iv avtotg d^iol6yov yivo^svrjg dcacpOQag 
TcaQa td yQa^^ixd iisxql tcbv 8id to6ovtov Xa^- 
fiavo^svcov VTtSQOxcbv ^rjt inl t&v si,rixo6tG)v ^i^t 
iTt avtcbv tcbv TtaQalXd^scov. xaC iatLV 6 xavd>v 15 

TOtOUTO^' 



2. yLvoiisvcc] yt^" D, et similiter saepius. STCiXoyiad- 

ftfvot] -acc(i- corr. ex accifi D*. 4. zfiij^ccTa — 5. v.av6vL\ 

-fi^^ficcTcc — xa- mg. A^. 6. agi^fimvl corr. ex g D^. 6. 

fioLQag] comp. AC, corr. ex (iolq&v D^. Q7t] corr. ex qn D^ 
8. ccQL&fimv] e corr. D^. 9. (livTOLl corr. ex /LtfWoo D^ 

11. i^cc^iOLQiccLcov] s^ccfioLQ&v D , £- e corT. ; mg. yQ. s^afioi- 
QLaCcav D^. 12. yLVO(iivr]g Sc^LoXoyov D. 14. vTtSQOx&v] in 

-Q- inc. fol. 117^ B. (irjTS D. (iriTS D. 16. Post tol- 

ovTOs add. B fol. 117^: 

naQaXXd^SLg tjXlov %al csXT^VTjg sn\ t&v Sl' avTcav xal tov 
'KaTcc v.0QV(p7]v yQacpo(iivaiv (isyloTcov v.vv.X(OV : — 

a' . OL V.OLVOL dQL%^(L0l OL SV To5 d GsXLdCcp S7CL (l£V TOV B 

•Hal r J s g 6sXl8lov nsQLsxovOL Tccg svQL6v.o(isvag sv to5 B gsXl- 
6lco tov t&v ycovLcbv vavovog s%d6T0TS snl tov yiaTd KOQVcprjv snl 
rbv tJXlov t) tt/v ^sX^^vriv oiv.sCcog nsQLCpSQsCag Tcav dC amav yQa- 
(pO(Lsvcov (isyCoTcov vvvXcov : — 



440 KAATAIOT nTOAEMAIOT 

inl ds rov ^' xat r]' csXvdLOv tag ccno tov ccv,Qi^ovg 
ccnoysLov tov inv/,vv.Xov inl tb TiivtQOv tTJg 6EX7]vr]g i]aL6£Lag 
^OLQccg : — 

inl ds tov "d"' 6sXlSlov tag tfjg (ii6r}g &noxfig f^OLQCcg tfig 
esX-^vrig iqtOL &nb tov r]XCov i) tov Kcctcc dLciiistQOV avtov xara 
trjv iyyvtiQuv dLcceta^Lv : — 

JB. naQaXXd^sLg r^XCov inl tov Slcc tov yiatcc y.OQvcpr]v ■Kal 
tov tiivtQOv tov r]XLOv yQacpofiivov fisyL6tov y,vy.Xov : — 

r. tov inLKv-nXov tfjg ^sX^qvr^g v.atk tb anoysLotatov tov 
i%Y.ivtQOv ovtog v.a\ tf]g ^sXr^vr^g y.atcc tb icnoysLOv tov inLV.v-^.Xov 
o^6r]g naQaXXd^SLg inl tov Slcc tov yiata %OQvcpf]v 6r](iSL0v Kal 
tov TiivtQOv tfig 6sXr]vr]g yQacpo^iivov (isyL6tov v.vv.Xov : — 

/d. tov inL-Av-xXov tfjg 6sXr]vr]g inl tov icnoysCov tov i%v.ivtQOv 
ovtog, tfjg 6s ^sX^^vr^g inl (tov eras.) nsQLysiov tov inLV-vyiXov 
oii6r]g, t&v yLVO(iivoi)v tfjg 6sXi^vr]g naQaXXd^soav naQcc tccg nQ&tag 
ijtOL tccg anb tov ScnoysCov vnsQOxdg : — 

E. tov inL-nvyiXov tf]g 6sXijvr]g inl tov nsQiysCov tov iv.iiiv- 
tQOv ovtog, tfjg Ss ^sX^qvr^g inl tov ScnoysCov tov inLV.vv.Xov o^6r]g., 
naQaXXd^SLg 6sXr]vr]g : — 

?. tov inLvvvXov inl tov nsQLysCov tov ivvivtQOv 6vtog, 
tfjg Ss ^sX^^vr^g inl tov nsQLysCov tov inLvvvXov, t&v yLVO- 
(livoav naQaXXd^soov vnsQOxccg n^bg tccg tov tQCtov oqov naQ- 
aXXdi^SLg : — 

Z. tov inLvvvXov tfjg ^sX^^vr^g vatcc tov dnoysCov tov iv- 
vivtQOv ovtog, tfjg Ss 6sXi^vr]g (ista^v tov dnoysCov val nsQL- 
ysLOv tov inLvvvXov o^6r]g, diacpOQaL t&v toLovtcav dno6tr]- 
(idtoov tfjg esX^^vr^g n^bg tb (iiyL6tov an66tr](ia, ottov i^tlv 
i] tov (isyC6tov ccno6ti](iatog nQog tb iXdxL6tov vnsQOxi] | T X' 
ov6a : — 

H. tov inivvvXov tf]g 6sXr]vr]g vatcc tov nsQLysCov tov iv- 
vivtQOv o^6r]g, tfjg 6s 6sX-^vr]g inl tcc (ista^v tov dnoysCov val 
nsQLysCov tov inivvvXov o^6r]g, ^LacpOQal t&v inl tfjg toLavtr]g 
naQoSov tfjg 6sXr]vr]g dno6tr](idt(ov nQog tb inl tfjg tov nsQi- 
ysCov tov ivvsvtQOv ^iesojg tov inLVvvXov (iiyL6Tov dn66tr](ia, 
ol'(ov i6tlv ^ i] tov (isyC6tov dno6tr](iatog inl tf]g toLavtr^g 
&i6so}g tov inLVvvXov n^bg tb iXdxL6tov dn66tr](ia dLacpoQa ig 



MA0HMAT1KHS 2TNTASES>2 E'. 441 

@. zov BnLV.vv.Xov zf]g cTfiTjvrjs inl tav iieza^v nccgodmv ovros 
xov ccTioysiov v.al nBQiybCov xov 8v.v.ivTqov Siacpoqal xcbv yivo- 
fievayv ano6xriiidt(ov inl x&v etQJKisvcov fieta^v naQodoiv xov 
inLvvv.Xov nQOS xb xov ivvsvxQov vaxa xb anoysiov avxov [isyi- 
axov anoGXTj^a, oToiv icxlv | 17 vnsQOxr] tov (isyictov anoctri- 
\iatos tov iv.vivxQ0v nQog tb iXdxiGtov avtov dnoctrifia x Xrj' 
ovaa : — (des. fol. 117^). 



442 



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444 KAATAIOT nXOAEMAIOT 

id'\ TIsqI rrjg t&v TCccQaXXd^scov dLaKQiOscog. 

"Oxuv ovv TiQoaiQa^sd^a Xafipdvsiv^ tcoCov 7] esXtjvrj 
xa^' sxdaTrjv xCbv naQodcov 7taQaXXd66Si TtQ&xov iitl 
xov di' avxijg xal xov xaxd 7C0Qvg)rjv 6r]^Si0v yQacpo- 
5 ^svov ^syi^xov xvkXov^ STCi^KSipo^sd-a^ 7c66ag i6rj^sQi- 
vdg &Qag d7Cs%SL xov ^s6rj^PQivov xaxd xb VTCoxsi^svov 
TcXi^a^ %al xdg svQsd^si^ag sl^svsyxovtsg slg tbv t&v 
ycovioyv xavova tov oixsCov xli^atog xal tov oIksCov 
dcodsocaxrj^OQCov xdg TcaQaxsi^svag xfj coQa ^oCQag sv 

10 xm dsvxsQG) 6sXidC(p iq olag t) xdg S7Ci^alkov6ag Ta5 
^SQSi xrjg G)Qag s^o^sv^ dg aTCsysi xov xaxd xoQvq)rjv 
6rj^sCov rj ^sXrjvrj stcX xov di avxcbv yQag^o^svov ^s- 
yC6xov xvxlov^ dg Si6svsyx6vxsg slg xbv xcbv 7CaQaX- 
Xd^scov ^cavoVa 6xsi;6^sd-a^ xaxd 7tOi6v s6xi 6xCxov 

15 xov 7CQC3XOV 6sXidCov^ xal xd 7CaQaxsC^sva x(p dQid^^co 
sv xotg scps^flg ^sxd xb xCbv rjXiax&v 7CaQaXXd^sc3v 
xs66aQ6i 6skidCoig^ xovxs6xiv xa xs y' xal xa d' xal 
rc5 s' xal ta g', xcoQig sxa6tov aTCoyQatl^^^sd-a' STCSixa 
xbv xax^ sxsCvrjv xrjv cjQav diaxsxQi^svov xfjg dvco- 

20 iiaUag aQid^^bv 7CQbg xb dxQifisg dnbysiov Xa^6vxsg ri 
ax)xbv rj^ sdv vtcsqtcC^cxi] rdg QTt ^oCQag^ xbv ksC^tovxa 



1. 1-9''] C, 6JT B, om. AD. ^'tax^tafcog] SicccpOQ&g D. 2. 
TiQOcaQayiis&a^ corr. ex TtQoaiQOv^sd^a D^. Xcc(i^dv£LV^ ayio- 

nsLV D, yQ. Xccfi§dv" mg. D^. tcogov] bis D, corr. D^. 3. 
TtccQaX^dcGeL C. 4. ai^fitiov] supra scr. D*. 8. oUsCov (alt.)] 
-f- ins. A. 11. xfjg] corr. ex rdq C^ 12. Sl' avx&v'] corr. 
ex 8lu x&v D. 14. v,avivaq D, sed -g eras. 15. &.QLQ'ii(p\ 
g^i D, 0, D2, mg. icQLQ-iKo Dl 16. t6] add. Cl 17. xovt- 
S6XL D, comp. B. 18. STtELxa'] corr. ex snLxa in scrib. A. 

19. x6v] x&v C. 20. ccQLd-fiov] g^^ D, et similiter saepe. 

21. rag Qn] xcc Cfn C. Supra xov add. a D^ 



MA0HMATIKHS STNTASESiS E'. 445 

eig tccg t| t6 rj^iGv tcccvtots r&v ovtcjg silrj^iisvcjv 
liOLQcbv slosvsyKovtsg slg tovg avtovg aQid^^ovg 6ks- 
t^d^fO-a, %66a sirjxo^ta TtaQdKSitai ta dQid^^S xcjQlg 
sv ts t(p ^ Tcal ri 0shdLG)^ xal o6a [isv dv sv ttp t,' 
^skLdCcp svQsd-fi^ td to6avta s^7]xo6td la^ovtsg tov 5 
sv rc5 d' ^sXlSlg) diacpOQOv 7CQo6d'7]6o^sv aisl tfj tov 
tQitov 6sIl8lov TtaQakld^SL^ o6a d' dv sv rco ri' 6s- 
XlSlg) svQsd"}]^ td to6avta s^ri%o6td ka^ovtsg tov sv 
t(p g' 6slLdL(p dLacpoQOv 7tQo6^ri6oiisv aisl TtdlLv tfj 
tov s' ^sXlSlov TtaQaXld^SL xal tcov ovtog ysvo^svcjv lO 
dvo TtaQaXXd^sov sxd-rj^o^sd^a trjv vjtSQOxtjv s^flg ds 
ka^ovtsg^ 06ag dnsisi ^s6c3g rj 6sX7]vr] ^OLQag rjtOL tijg 
rjlLaxfjQ rj tfjg tavtrjv dLa^stQ0Tj6r}g xatd trjv syyvts- 
Qav bitotSQag avtcov 8Ld6ta6Lv^ sl6ol6o^sv ocal tavtag 
slg tovg sv t<p a 6sXl8lcp dQt^^ovg^ xal o6a idv 15 
7taQaxsr]taL Ttdltv s^r]xo6td sv t(p ^' xal tsksvtaCcp 
6sXLdC(p^ td to6avta sir]xo6td ka^ovtsg^ '^g s^sd^s^sd-a 
tav dvo TtaQalXd^scjv v7tSQ0xf]g, td ysvo^sva jtQo^d-T]- 
6o^sv alsl tf] sXd66ovL^ tovts6tLv tf] sx tov y' xal 
d' 6sIl8Cov diaxsxQL^svr]^ xal td 6vvax^svta s%o[isv^ 20 
d 7taQakkd66SL r] 66k7]vr] sitl tov dt avtf]g xal tov 
xatd xoQV(pr]v 6r]^sCov yQacpo^svov ^syC6tov xvxlov^ 
d^soQOv^svrjg avtodsv aTtlag xal tf]g r]kLaxf\g TtaQaX- 



1. ra?] corr. ex xd\ D*. r^] e corr. D^ Tidvtoxf[ -v- 

e corr. D^ 2. sl6E\vtyv.6vxEg A^, il6\svf:yv.6vxhq A. 4. xb\ 

supra scr. D^. 5. Xa^^dvovxsg D, corr. mg. D^. 6. atXi- 

8Cov B. 7. x()Lxov] 7 BD. GsXidCov'] supra scr. D. ?;'] 

6y86(o C. 8. ra] supra scr. D^ 10. ovx(m\ D. 12. r/Tot] 

om. B. 15. a \ nqcoxGii C. sdv\ dv BD. 16. naqd- 

%£ivxaL D. TtdlLv] supra scr. D^, ndXv C. osXLdCco tial 







xsXsvxaCa) D. 17. Xapcovxsg A. 18. yLv6(isva D, corr. D^ 
19. sXd.GOovL'] corr. ex g mg. Dl xovxsgxlv] comp. B, -v 
del. D. 21. TtuQaXd^SL D, corr. Dl 



446 KAATAIOT nTOAEMAIOT 

kd^scog xccta f^v o^oiav d^dciv evsxcc tcov rjXLaxav 
ixXecipBcov ix tcbv iv tc3 /3' aehdico TtaQaKSL^ivcjv 
^iOLQav tfj TCrjlLKotr^tL tfjg aTcb tov xata xoQvcpriv 

7tEQLCpBQ£Lag. 

5 Iva ovv xal ttjv TCQog tbv dLcc pii^cov tcov ^(pdicov 
toTS yLvofiivrjv TCaQakXa^Lv dLaxQLVco^sv xatd ts ^fjxog 
Tcal xatd nkdtog^ tdg avtdg itdXLV L0rj^SQLvdg ^Qag^ 
dg d7ci%SL tov ^sdrj^PQLVOv rj asXrjvrj^ SL6svsyx6vtsg 
ELg t6 avtb ^iQog tov t&v ycovLcov xavovog i7CL6xs- 

10 tl^d^s&a tdg jcaQaxEL^ivag ttp dQLd^^a tav cjqcov ^ol- 
Qag^ idv fisv TCQb tov ^sOrj^PQLvov 17 rj 0sX7]vr}, tdg 
iv tc5 y' 6slLdLG)^ idv ds ^std tbv ^sarj^^QLVov^ tdg 
iv t^ d\ Kav ^sv ivtbg t&v 9 ^olq&v cotjLV^ avtdg 
dTCoyQaiponsd-a^ idv d' vtceq tdg 9, tdg ksLTCov^ag slg 

15 tdg QtTC' to6ovtcov ydQ E6taL rj iXd66cov t&v tceql trjv 
ixKEL^ivrjv to^ijv ycovccbv^ olcov rj iiCa op-O^i) 9. tdg 
djcoysyQaii^ivag ovv ^iOLQag dL7cXco6avtsg sl6ol6o^ev 
ecg tb tcbv iv xvkXg) svd^SL&v xavovLOv avtdg ts Kal 
tdg XsL7Cov6ag slg tdg QTCy ocal bv dv E%ri koyov rj trjv 

20 tCbV dsdLTCXcO^ivCOV ^OLQCOV 7CSQlCpiQELaV V7C0tELV0V6a 

svd-Eta TtQbg trjv v7C0tSLV0v6av trjv kEL7Cov6av slg tb 
ri^iKVKkLov^ tovtov e%SL tbv loyov rj Katd 7cldtog 
7CaQdXkai,Lg 7CQbg trjv Katd ^rjKog^ i7tSLd7]7CEQ aC trjlL- 



1. %vBv.iv D. 2. bv'] s A. 5. fiieoov] corr. ex ^sao) D^. 

7. y.ccrd'] om. D. 9. ycovL&v'] corr. ex yavLm A^ 11. 7]] 
corr. ex ^r D^ 14. ccnsyQccipdfisd^a B. d'] ds D. vTtsg] -s- 
e o6rr. C. 15. Qn] Qn ^OLQag D, -ri e corr. D*. sXdaacav] 
l D, corr. D^ et in mg. 16. Post oYoav add. av D^, sed del. 

17. siaotaofisv dmXmaccvxsQ D. 18. v.vv.X(p] u" D. 19. dv 
ixvl corr. ex ccnsxij D^. 20. vnoxsCvovaccg sv&sCccg D, sed 

corr. 21. xdg Xsmovaug D. 22. ri{ii%vv.liov] o_ D, q D^, 
corr. mg. D*. 



MA0HMATIKHS 2TNTASEOS E'. 447 

Tcavrac tcbv kvxXcqv 7C£QL(peQeiaL adiaipoQOv^LV svd^stcjv. 
7tolv%ka6idt,ovx£g ovv tov aQid-^bv t&v 7taQax£i^£vcov 

£Vd^£iG)V £7Cl trjV £VQl6X0^£Vr}V Cjg £7ll tov dicc tov 

xata xoQvq)iiv 67j^£iov yQacpo^ivov xvxlov ^taQalXa^iv 
xal tk yiv6\i£va yi£Qi%ovt£g £lg tbv 'qx %a3()tg ta ix 5 
tov ^£Qi6^ov 0vvay6ii£va ^6Qia £%o^£v tfjg 0iX£iag 
7taQakXd^£cog. 

xad-6lov de £7tl ^£V t&v xatd TtXdtog 7taQaXXd^£G}v^ 
orai' ^£V tb xatd xoQvcpriv 6r}^£L0v £7tl tov ^£6r}^- 
^QiVOV ^0Q£i6x£Q0V y tov t6t£ ^£0ovQavovvtog tov 10 
did fi£6cov t&v ^(pdicov xvxXov^ rj 7taQdkka^ig £6tai 
7tQbg ^£6rj^PQiav avtov^ oxav d£ voxi(DX£Qov y xb xaxd 
xoQvcprjv xov ^£6ovQavovvxog^ TtQbg xdg ccQxxovg rj 
xaxd 7tXdtog £6tai 7taQdkka^ig^ £7tl de tdtv xatd (irixog^ 
i7t£idrj aC 7trjXix6tr}t£g tcov iv tkI xav6vi 7taQax£i^i- 15 
vcov yG)VLcbv triv aTt^ aQXtcov 7t£Qii%ov6i tav dvo tcbv 
r)7tb tov £7to^ivov t^ijfiatog tov did iii^cav £xaxiQCod^£v 
7C£Qi£xo^vcoVy xfjg ^£v xaxd 7tXdxog TtaQakkd^ecog 7tQbg 
aQxxovg yivo^ivrjg^ idv ^£v ^£i^cov r) OQd-rjg rj ixx£i- 
^ivrj ycovia^ ££g td 7tQor}yov^£va x&v ^codicov rj xaxd 20 
^rjxog £6xai TtaQaXXa^ig^ idv 8e iM66cov OQd^rlgy £ig 
xd £7t6^£va^ xrjg de xaxd 7tXdxog 7taQaXkd^£cog 7tQbg 
^£6ri^^Qiav yivofiivrjg dvdTtaliv^ idv ^ev ^£i^cov r) 
oQd^rjg r] ixx^iiiivrj ycovia^ £ig xd £7t6^£va xcbv ^Godicov 



4, ar}(iELov] D^, cotnp. D. 5. itat xa] supra scr. D. 10. 
^] corr, ex ^v D. tov (alt.)] tov\Tov D, corr. D^ IL Supra 
7} add. s D^, sed del. 12. vozsiotsqov D, sed corr. fj] corr. 
ex Tjv D. 13. rccg] om. D. 14. TclccTog] corr. ex Ttldtovg D^. 
^f'] supra ras. 3 litt, D^. •aatcc] v.ar- D, 15, ■Kavovioi D, 
16. TtSQLSXovGr] D, corr, D*. 17, syiatigcod^sv] -&sv corr, 

ex vs^i D^. 18, nXcitog] corr, ex nXdtovg D. 21. sXdoGcov] 
g D, sXdttoov D^. 24. OQ&fig] corr. ex oQ&fj D^. ycovia] 

comp. D, ut saepe. 



448 KAATAIOT nXOAEMAIOT 

rj 'naxa ^rlxog eCxai TtaQccXla^is^ sav de ikd60cov 6q- 
'9'iJ?, £ls xa 7CQOYiyov^£va. 

evvaxQYj^d^sd-a iiEvtOL rotg TCQoajtodsdsty^svoLg 
tcsqI xov rjliov wg ^rjdsv ai0%-ritov avtov 7CaQalld6- 
6 (Sovtog 0V7C ayvoovvtsg^ ort TCocijesi tiva tcsql avta 
diafpoQav rj icatavsvorj^svrj xal tcsqI avtbv sx t&v 
sg)s^rjg TCaQdlXa^ig^ dkX^ ijcsl ^rj ovtcog d^Ldloyov 
rjyov^sd-a tcsqI td cpaiv6^sva did tovto TCaQaKoXov&TJ- 
6siv d^aQtCav^ G)(5t dvayzatov sivai 7iivr]6ai rtm t&v 

10 avsv tfjg toiavtrjg ijCiOtdasog ^Qa%Siag ys ov6r]g tcqo- 
diSilrj^^svcov biioicog ds xal TCQbg xdg TCaQaXXd^scg 
tfjg 6sX7]vr]g rjQXs^d^rj^sv ratg TCQbg tbv did ^sdov tcbv 
icadicov Tivxkov yivo^isvaig vtco rov did rcov 7c6kcov 
rov oQi^ovtog yQaq)0(isvov ^syi6rov tcvkXov TCSQicps- 

15 QsCatg rs ;cal ycovCaig dvrl rcbv TCQbg rbv lo^bv rrjg 
0sX7]vr]g d^scDQOv^svcov ^ iTCsl rb [isv iv ratg ixksiTCri- 
xatg 6v^vyiaig ia^^svov TcaQd rovro didcpoQOV dvsic- 
aCa&rjrov rjv^ rb ds Tcal ravrag ixd^s^d^ai %oXviovv 
rs ratg dsi^s6iv %al iQycbdsg iv rotg i7Ciloyi0^otg (irj 

20 c3Qi6^svc3v xad-' SKa^trjv t&v iTcl tov ^cjdiaxov 7caQ6- 
dc3v tfjg esXijvrjg xal rcbv djcb rov 6vv8s6^ov dia6rd- 
6SCJV, dXXd otal rotg ^sysd^s^iv xal ratg %s0s6iv avtatg 
TCOiXilag ^sta^ddsig Xa^pavov6cbv. 

iva d' svxatavbrjtov ysvrjtai tb Isyb^isvov^ ixKSi- 



1. ft^xoff] supra (1- macula A. Ss] d' B. iXdeaoiv'] ^ D, 
•/) D^ 5. ccyvoovvtsg] Scy- in ras. 1 litt. Dl 6. avrwi' D. 

7. s^f)g D. 8. nBQL] supra scr. D^ rovto] corr. ex 

tovtov D^ 9. ojats D. rivcc] -v- mut. in fi» C^ 10. ye] 
AD^, ts BCD. 14. OQi^^tog D. neQLq^SQSLCcig rs] -SQSLccLg rs 
e corr. D^, TCSQLcpsQLcpsQSLaLg rs C. 18. Post rccvtug del. 

ccvtdg Dl 19. dsL^scL D. 22. ^sys^saL D. ^ mg. A. 

24. d'] ds D. 



MAeHMATIKHS STNTASESiS E' 



449 



^O-o t6 ^£v rov dia fi£0(av x&v t^cidCGJv xvxXov 
tfifjfia xo ABF^ xov de lo^ov xrjg ^sXi^vrjg xb A/l^ 
xal 6vvd£6^og ^iev v7tox£L0d^(D xb A 6rj^£tov, xfjg dh 

6£l7]vrjg xivxQov xb 
z/, xal yeyQacpd-G) 5 
dnb xov A £7tl xbv 
dia ^£0(DV xcbv ^oj- 
dt(x}V nvxXov OQd-r} i^ 
z/-B, £6x00 de Ttolog 
xov bQL^ovxog xb E lo 
6r}fi£Lov , xal y£- 
yQoiq^d-cj Sl avxov ^£- 
yCaxov xvxXov x^rjfia 
dta ^£v xov xivxQov xr^g 6£Xr]vrjg xb EzJ Z, dia d£ xov B 
xb EB^ 7taQaXla66£X(D X£ ri 6£kr]vrj xr^v /d H 7t£QL(p£Q£Lav^ 15 
xal y£yQd(p%'Gi6av 6l avxov TtQbg xdg B/i xa\ BZ OQd^al 
aC H@ xal HK^ g>6x£ x&v ^hv xaxd ^fjxog dTtoxcbv 
xov 6vvd£6^ov xijv ^£v dxQLpr} yCv^^d^aL xf^v AB^ xfjv 
d£ (paLVO^evr^v tf}v AK, xCbv dl xaxd 7tkdxog dTtb xov 
Scd fi£6(X)v xfiv fi£v dxQL^f] xfjv J5z/, tfjv dh (paLvoiie- 20 
vrjv tfiv KH^ xa\ tcov d^tb tf^g AH 7tQbg tbv ^ojdLaxbv 
^£C3Q0v^£V(x)v 7taQaXXd^£C3V xatd ^fixog y^lv tf^v L^rjv 
rfj &H^ xatd 7tXdtog d£ tf^v i'6rjv tfj z/0. 




1. t6 (ilv tov] rov fisv D. 2, tfiriiioc to] corr. ex r^i^aa- 
tos C^ 4. TievtQOv] x/ D, ^^ add. D^. 12. §l' avtov] corr. 
€x Sicc tov D^ 14. dta(pr.)] corr. ex ti D*. EJZ] corr. ex 

^ cc]\r 
EAZB^, mut in EJ"Z' Bl 15. tcsqlcpsqslocv] ^ B , -) D«, 

mg. 7t D^. 16. di' avtov] corr. ex dicc tov D^, Sl' ccvtov H 

Halma, fort. Slcc tov H. B^] corr. ex B^ D^ BZ] ZB J). 

17. )tat] om. D. 21. t&v] corr. ex fqv Dl 23. 0H] 

"H@ B. t6r]v] \ D, ^ add. Dl 

Ptolemaeua, ed. Heiberg. 29 



450 KAATAIOT nTOAEMAIOT 

iTtsl ovv 7] iiEV AH TtaQccXXa^Lg svQL^xstai, dtcc 
t&v jtQOSKtsd-ei^evcov tijg E^d TtsQLcpSQeiccg dod-eLerjgy 
ixatSQa de t&v z/@ xal SH jtaQaXXd^ecov trlg vnb 
rZE ycDVLag dod^eCarig^ r}^eLg d' ev totg e^JtQO^d^ev 
6 aTtedeL^a^ev tocg TtQog ta dod^evta tov icodLaocov 67}- 
fieta yLVO^evag tov dLcc tov xata xoQV(priv TteQLtpeQeCag 
te xal ycovCag^ ^idvov d' e^o^ev «Vrav-d-a dedo^evov 
toi) dia iie6c3v 6r]^etov tb 5, (paveQov^ otL t§ iiev 
EB TteQLcpeQeCa ^vyxQco^ed^a dvtl trjg Ezfy tfi de vTtb 

10 FBE ycjvCa dvtl tijg vjtb FZE. 

6 ^ev ovv "iTtTtaQxog e7te%eCQri6e ^ev xal tijv tot- 
avtr]v dLOQd^co^Lv 7tOLiJ6a6d^aL ^ itdvv d' dve7tL6tdtco$ 
xal JtaQa tbv Xoyov avtfi (paCvetai stQO^Pe^Xrjxmg. 
TtQcbtov fiev yaQ ^ta dLa6td6eL tfjg A/4 6vyxexQr}tao 

15 xal ovxl 7td6aLg -^ 7tXeCo6Lv^ OTteQ ^v dxoXovd-ov tc5 
xal TteQi t&v ^LXQ&v dxQL^oXoyet^d^aL 7tQoeXo}ievG)' 
eTteLta xal 7tXeCo6L totg dt07tc3teQ0Lg eXad^ev 7teQL7te6(x)v. 
eTtel yaQ xal avtbg tdg te 7teQL(peQeCag xal tdg yovCag 
tdg 7tQbg tbv dtd ^e6cov tcov ^codCcov d^ecoQov^eva^ 

20 etvyxccvev 7tQoa7todedeLX(og ^ xal otL trjg Ezi dod^eC^rjg 
rj ^H Xa^pdvetaL' tovto yccQ iv tco 7tQ(bt(p t&v 



3. ©Jf] corr. ex 01 B^. TtuQaXld^scov] pr. -a- eras. A. 

4. rZE] corr. ex IZE D«. 6. r. ^o^fW D, ut saepius. 

6r}(iEicc ytvofifVag] compp. in ras. D, corr. D^. 6. tov (pr.)] 

in ras. D. dia tov~\ bis A extr. et initio pag. 8. orjiisCoov 

c^ D, CH D^ 10. iTto-] ? D, « add. D«. TZE] corr. ex 
ZE D^ 11. iTeexsCQTjGs] seq. ras. 1 — 2 litt. D, corr. ex 

oi7tBX8LQr}6S B^ 14. A zJ] AB D. ovyASXQritai] -y- corr. ex 
V D^. 15. nlsCo^Lv'] -sC- in ras. A. 17. tiXslool'] corr. ex 

nXsL06LV D*, mut. in nXsLoet C^. xoLg\ om. C. axoncoxsQOLg] 
a- add. Cl UaQ-sv] -v del. D, sXaQ^s B. 20. hvyxcivs BD. 
nQoanodsdsLxCog'] -oa- corr. ex 3 litt. D. xfjg] A, anb xfjg 
BCD. 



«I 



MA0HMATIKHS STNTASESiS E'. 451 

jiaQaXXaKtiKcbv d7tod£ixvv6LV' 6vyxQfjtao Ttghg trjv trjg 
Ez/ 7t£QLq)£Q£tag 666 tv tfj t£ EZ 7i£Qi,(p£Q£ia xal tfj 
VTcb EZr ycovCa hg d^do^svatg' ovtcog yaQ iv toj 
d£vt£QC} trjv Zz/ £7nXoyL6d^£vog Kal koiTC^v trjv E/i 
v7ioti%£tai. 7taQ7]yay£v avtov ^iivtoi tb ^rj £7ti6tri6ai^ 5 
dioti t6 B xal ovxl tb Z 6rj^£i6v £6ti tov did ii£6cov 
tb d£do^£vov, xal did tovto tatv ts 7t£Qi(p£Q£iS)v rj 
EB didotac xal ovxl r] EZ xal t&v ycjvicjv rj V7tb 
EBF xal oi^xl rj V7tb EZF. £v^£v xal 7tgbg tb 7toi7]- 
6a6^aC tiva xav ^£Qi7crjv dibQd^co^iv 7C£xCvrjtai 7toX- lo 
Xaxr} yivo^ivrjg al^d-rjtfig 7tdvv diag)OQdg tG)v E^ 
7t£Qi(p£Q£iS)v 7tQbg tdg EZ did tb 7toXv ^dkkov £X£i- 
VG)v avtdg ^rj d^d^^d-at^ tfjg d£ BE trjg rcai ovti d£- 
do^ivrjg rj 7tQbg trjv Ezl diatpoQd tb 7tl£i6tov diOL6£i 
libvc) tcj tfjg BJ xad"' ixd^trjv t&v d^tb tov 6vv- 15 
di6^ov dia6td6£G)v ^£yi^£i. 

tb fiivtoi tfjg xatd tbv vytfj tQ67tov i6o^ivr]g 
diOQd^66£C3g dx^Xovd-ov yivoit dv rj^tv V7t' o-tpiv 
ovtcog. 

£6tco ydQ ^G)diaxbg 6 ABF xal 7tQbg dQd^dg avrw 20 
6 ^BJS^ rj dh 6£Xrivri ijtoi xatd t6 z/ t) xatd tb E 
d7tixov6a xatd 7tXdtog tov ABF did ^i6G)v tcov Jco- 



1. 7cccQaXav.tiv,&v D, corr. D^. cc7tod8iv.vv6L D. TCQog'] Ss 
TCQds B. 2. EzJ] corr. ex EA D^ nsQicpsgELa] corr. ex q"^ 
mg. D*. xort — 3. ycavLa] mg. C^ 3. EZF] E- corr. ex 
r in scrib. C, -F ins. Dl ' 4. ZJ]-Je corr. Dl 9. ovx !>• 
11. yLV0(isv7]s] s add, C^, corr. ex l'' D^ 12. tzoXv] -o- 

corr. ex v in scrib. C. 13. 8s] ds TE C et B (F- e corr. B^), 
corr. C^. 14. rj] corr. ex rfyi D. ti^v] rfj A. EJ] corr. 
ex EA D^. t6 TtXstGtov] tb tiXsl- in mg. transit D. 17. 
xara] -td supra scr. D*. 21. JBE] J- e corr. C. r/'] in 
ras. Dl 22. yiatd] bis D, corr. D*. ABT] AF D. t&v 
^cpSicov ■kvkXov] om. D. 

29* 



452 



KAATAIOT nXOAEMAIOT 



dt(ov xwcXov dsdo^evrjv TtEQicpiQELCcv ^ olov rrjv B^ 
xccl triv BE^ 6)6ts tccg ^hv Ttgbg tb B arj^elov tov 
^G)dtaxov 7tSQi(psQeCag aitb tov xata xoQvcprjv xal yco- 
vCag dsdoad^ai^ ^rjtst^d^at ds tag jCQbg tb /i ri tb E 
5 yivoiisvag. 

z 

J 



sav ^sv dri toiavtr]v s%ri d^s6iv 6 ^cydtaxog^ co6ts 
TtQbg OQd-ag yavCag slvai tS dia tov Z ^ri^sCov^ o 
v7toxsC6d^co TtdXog tov OQC^ovtog, xal dta tov B yQa- 
cpo^svm iisyC^tco xvxlcj^ oiov t(p ZB^ 6v^7CS6sttai, o^- 

10 tog dr]lov6tL trj ^E itSQicpSQsCa^ xal rj ^sv ycovCa rj 
TtQbg ra z/ xal E d^scoQoviisvrj ddttxcpoQog s6tai trjg 
TtQbg tb B vTtoxsi^svrjg' oQd-al yccQ xal at dicc tovtcov 
TtQbg tbv ^adiaxbv ytvo^svai' trjg ds ZB TtSQicpSQsCag 
i] ftfv ZJ sXd66cjv satai tfi BJ^ r} ds ZE ^isCt^ov 

Ih tfi BE dsdo^svatg xal avtatg. 

sdv ds 6v^jtC7ttr] b ABF t,G)8iaxbg tc5 8id tov 
xatd xoQvcpriv 6rj^sCov yQacpo^svc) ^syC^tco xvxIg)^ 

2. Supra itat add. r/ D*. 3. nBqicpBQsCcc$\ om. D, j supra 

scr. D^, crr mg. D^. 4. x6 (pr.)] corr. ex td C. 6. bxsi D. 

8. did'] supra scr. D^ yqcccpoiiivoi] -tp e corr. D^ 9. 

fifytcro)] corr. ex ^eyiGtog D*. xvx^oo] -w e corr. D^ ZB] 
BZ D.' GvvTtsGEttca ABC. 11. z/] corr. ex A D^ 14. 

Zz/] corr. ex ZA D*. sXccggoov] comp. D, sXdttoov mg. D*. 

15. BE] corr. ex KE D^. 16. Gv^TtLntrj] -v(i- e corr. D^ 

17. yQcc(poiisv(a] corr. ex I^"" D*. 



MA0HMATIKHS STNTASESiS E'. 



453 



xal vTtod^e^svoL JtoXov tov bQL^ovtog t6 ^ ijtt^sv^a^sv 
tag AA %a\ AE^ xal a\)taL dioi6ov6i tfjg AB iteQi- 
(peQBiag nal ai VTto BAA xal 
BAE ycovtat tijg ^rj ov^r^g 
TtQotSQOv. dCdovtaL de aC ^sv 5 
AA xal AE rov Xoyov ovtog 
cog i-jt^ sv&eLGtv dia tb ddLa- 
cpoQov ccTto ts tr]g AB xal tcbv 
BA xal BE dsdo^svcjv tk 
yaQ dit avtav 6vvts%^svta 10 
TtoLst td dTtb tG)v A/i xal 
AE [Eucl. I, 47]- dxoXovd^cog 
ds avtatg xal aC vTtb BA/1 
xal BAE ycovLaL. 
tfjg ds roi) ^adLaxov d^s^scog syxsxh^svrjg, sdv dnb 15 
tov Z TtoXov tov bQL^ovtog STtL^sv^co^sv tdg ZB xal 
ZHA xal ZE®^ dsdo^svrj ^sv s6taL i] ts ZB %sql- 
cpsQSLa xal rj 'bitb ABZ ycavia xal TtdkLV drjXovotL at 
BA xal BE. bcpSLXov6LV ds dod^fjvaL ai ts ZA xal 
ZE TtSQLCpSQSLaL xal aC vTtb AHZ xal vTtb A®Z 20 
ycovLaL^ dCdovtaL 6s xa\ avtaL xa^stcov dx^SL^&v S7t\ 
trjv ZB tcov AK xa\ EA. 

STtSLdrj yaQ r] vjtb ABZ ycovCa dsdotaL^ oQ^r] ds 




2. AJ y.al AE] e corr. D\ 3. ai] 17 BD. BAJ] corr. 
exAJ D^ Hat(alt.)] ytalvTto D. 4. yoaviaL] Fw"'' D, ycovCa D^ 

5. didovxai] supra scr. D^, mg. didovTaL Sa D^. 9. %al 

BE] §s D, §8 D\ 10. &7c'] corr. ex in D\ 11. zdtv] 

tfjg D. 13. at] 7] B. BAJ] B- postea ins. D. 14. yiai] 
om. D. 16. int^av^oafiev] -^- corr. ex | D. 19. xo:i(pr.)] om. D. 

ocpsCXovGi D, -at e corr. D^ 20. 'nal vtco] ■nal at vno C, 
om. D. 23. imidri] -Sri in ras. 1 litt. D^ ydo] supra 

scr. D^. 



454 



KAATAIOT nTOAEMAIOT 



jtdvtots 7] vTtb ABE^ dtdotai tcc BKzJ ytal BAE 6q- 
d^oycyvLa xal koyog trjg ZB TtQog rag jtSQi tr^v 6Qd"i]Vf 
BTtel xal TtQog tag AB xal BE vitotevvov^ag' m6t6 
xal at Z/l^ZE vitotUvov- 
5 6ai 8o%"Y\^ovtai dia tovto 
ts xal aC V7tb ZfZK Ttal 
'bjtb EZA ycovCai v7tSQ0%al 
ov6ac tG)v STtL^rjtov^evcjv' 
rj ^sv yocQ vnb AHZ iisi- 

10 Ig)v S6tlv tfig VTtb ABZ tfj 
'bitb JZB, ^ dh vTtb A®Z 
iXd66cov tijg vjtb ABZ tfi 
VTtb EZA [Eucl.I, 32]. (pa- 
vsQbv d\ ort ical nlsC^tri 

15 yCvstaL diafpoQO, tr]g av- 

trjg xatd itldtog ditoxrig vjtoxsi^svrjg tcbv ^sv ycjvL&Vj 
omi/ t6 B 6rj^stov avtb fj tb xatd xoQvcprjV ^rjdsnLccg 
ydQ JtQbg tb B yLvo^svrjg ycovCag ai STtl td A xal E 
aTtb tov Tcatd xoQVCprjv ^Qd^dg 7tOLOv6LV TtQbg t& t,(p- 

20 dLaxa ycovCag' tcbv ds JtsQLCpsQSLCJV , otav rj avti] d^s- 
6Lg ri' ^rjds^Lccg yaQ TtdUv yLVOfievrjg TtQbg tb B JteQL- 
cpBQeCag at TtQbg td A xa\ E trjhxavtaL s6ovtaL^ rjkC- 




1. Tidvxort] -To- e corr. D^ BKJ] BJKD. oq&o- 

a 

ymvia\ OQQ^oyiavi, D. 2. ZB] BZ D. 3. rag] supra scr. D*. 
zJB] mut. m BJ D\ 4. cct] i} B. Zz/] Zz/ xat D. 6. 
y.at (alt.)] kccI ai D. 7. EZA] corr. ex EZA A, ex ZA D*. 
^IO. lotCv'] comp. BD. 11. z^ZE]*z/- e corr. Dl di] 

8' D. 12. ABZ t^ vnb EZA] in ras. A^ 15. ytVerat] yCve- 
renouat. Cl 17. ^] corr. ex i]v D. 18. ydQ] comp. D, 

corr. D^ to\ D, rcS D^. xat] suprascr. Dl 20. 17] A, 
ccvtfiq 7] BC, avtfjg C^, ts D. 21. ■^] seq. ras. 1 litt. D. 

xo] mut. in tc5 D^. 



MA0HMATIKHS STNTAgESiS E'. 455 

xai ccv a)6LV koI ai Tijg xato^ Ttkdtog itaQodov tfjg 6s- 
Xnjvrjg' xal otav OQd^bg fj TtQog tbv Jcodtaxoi/ 6 dia 
rov xata KOQv^prlv' okri yccQ TcdXiv tfj xata nXdtog 
7taQ68(p dLOi6ov6L tijg ZB at Z/1 xal ZE TtsQtcpeQSLat' 
iv de tatg dXlaig d-e6s6LV syxkLvo^svrjg tijg /JE TtQog 5 
triv ZB av ts tav TtSQicpSQSiav xal aC tG}v ycovtcbv 
v7tSQ0%al STtl tb skattov 6vva%%"ri6ovtav. cct6ts xaC^ 
otav iisv s ^iOLQag ii ^sXt^vt] ^cara TtXdtog aTtsxii tov 
dva ^socov^ 1] 7tXsL6tr] dLacpoQcc t&v TtaQaXld^scjv s6taL 
dsxa syyL6ta s^rjxo6tG)v' al yccQ tov fisyL6tov dLatpo- 10 

^OV t&V 7tSQL(pSQSLG}V ^OLQaL S TO^aVTa 7tOLOV6LV S^rj- 

xo0td 7taQakld^SG)g STtl tcbv ^syL^tcov VTtSQOxav xal 
iXaxL6tG}v d7to6tr]^dtG)v' otav ds tijv sv tatg rikLa- 
xccis sxksL^s6LV ^syL6trjv 7tdQodov d^tsxr]' avtri de 
yCvstaL HLccg ^oCQag syyL6ta xal rj^C^ovg' td i'6a s^rj- 15 
xo6td d i' dLdcpOQOv s6taL trig 7taQaXkd^SG)g tov tOL- 
ovtov 67tavCog 6v^7tC7ttovtog. 

rj iiivtOL fiid^odog rj 7tQbg trjv tOLavtrjv dioQd^cj^LV 
tG)v ts ycovLcov xal tcbv 7tSQL(pSQSLG)v yivoLto dv 7tQ6- 
XSLQog totg ^ovXo^ivoLg G)g iv ovtoog fiLXQotg XbyoLg 20 
rbv tQ67tov tovtov. xad^^lov yaQ tbv tcov yovLcov 



1. mciv] -V eras. D. at] at Scno D. 2. f}] seq. ras. 1 
litt. D. 3. yccq] y^ D. 4. ZB] seq. ras. parua D. xat] 
oin. D. 6. Tf] corr. ex rt in scrib. A. nsQLcpSQSi&v] j D, 
Qj D*, et similiter saepius. 9. nXsLGtri] -X- corr. ex a in 

scrib. A. 10. 8sv.a\ corr. ex ds g' C*, T D. syyLGxcc] sr^ 
in ras. D^ sh,r\v,06t&v'\ |f renouat. D^ iisyCatov] e corr. D*. 
14. s-AlsCips^ D, -61 add. D^. 15. rnLCGovg] in ras. 1 litt. D*. 

G mg. A. 16. a /_'] in ras. D*. 19. t&v (alt.)] om. D. 

20. cbg iv] G)sv B. 21. tov (alt.)] corr. ex tcov C^. tatv] 

c 
corr. ex tcig D^. ycoviav] corr. ex yo) D^. 



456 KAATAIOT nTOAEMAIOT 

ccQid^^bv dtJtXcodavrsg xal £L0€vsyx6vtsg sig tb t&v sv 
xvxXg) sv^sicbv xavovLOv ta jtaQaxsi^sva avtm ts xal 
rm XsCTtovtL sig tag t&v dvo OQd^cbv ^oiQag QTt xcDQlg 
TtokvjtlafSLd^avtsg iitl tocg tov nXdtovg ^ocQag tb qx' 
6 ixatSQCov dnoyQa^oiisxta xal td ix trjg jtQcbtrjg ycovCag 
ysvofisva dcpsXoviisv [isv ditb trjg vjtoxsi^svrjg d%b 
Tov xatd xoQvcpriv TtSQicpSQsCag^ otav inl td avtk r^ 
ta xatd xoQVCprjv rj esXrjvrj^ 7tQ06d'rJ6o^sv ds^ ^otav 
inl td ivavtCa^ xal td ysvdiisva TtoiYi^avtsg icp savtd 

10 ^vvd^svtsg ts totg ix trjg XsL7tov6rjg ycovCag ysvo^svotg 
tstQaycovL0%^sl6i xal avtotg tcbv avvaxd^svtcov tijv 
nXsvQdv s%o^sv oixsCcog f^v ijtL^rjtov^svrjv TtSQLCpsQSLav. 
STtSLta td ix trjg ksL7tov6r]g ycovCag dxoysyQa^^sva 
sxatovtaxLxaLSixoedxL 7toLr]6avtsg xal ^SQC^avtsg x^^Q^S 

15 sig tdg si^Qrj^svag TtSQLcpSQsCag rcbv totg ysvo^svoig 
TtaQaxsi^ivcov "jtSQLCpSQSLcbv iv ta xavovL tcbv svd^SL&v 
rdg rj^L6sCag^ idv ^sv ^sC^cov tj rj dLcoQd^co^svrj itSQi- 
(piQSia rr}g jtQchrrig^ TtQO^d^rj^o^sv ralg rfjg jtQihrrjg 
ycovCag^ idv ds iXd66cov^ dcpslov^sv avt&v^ xal s%o^sv 

20 xal trjv ycovCav dLCOQd-co^ivrjv. 

vjtodsCy^atog ds svsxsv vjtoxsCad-co ijtl trjg jtQo- 
xsLiiivrjg xarayQacprig rj fisv ZB JtsQLCpiQSLa ^olqg)v JiSy 



1. &Qi&n6v'\ comp. in ras. D^. 2. yiuvov^^ov C. 3. tc5] 
x6 D, rw* D^ 4. tov'] in ras. D^. qv.''\ ^x A. 5. ycov/ag] 
bis C, corr. C^ 6. yLv6(isvcc D, corr. D^. 7. roi)] -ov in 
ras. D^ TtSQKpsQsiccg] comp. renouat. D^. ^] seq. ras. 1 
litt. D. 9. iavca] £- ins. D*. 11. tszQCiycovi6d-£LOi.v D, sed 

-V eras. 14. sv.cctovtav.iv.ccisiv.oad-ii mg. D^, 9 val x D. 17. 

THiiGsCag] in ras. 1 — 2 litt. D^_ idv'] v.al idv AB, vaC del. A^; 
S sdv C, corr. C^; av D. rf] con-. ex r^v D^ dioQ&oa[isvr} 
CD, corr. D^. 19. iXdttmv in ras. 1 litt. Dl 20. dLOQ&ca- 
^svriv CD, corr. D^ 21. ds svsvsv] corr. ex d' svsvsv D'. 



MA0HMATIKHS STNTASESiS E'. 457 

fj ds VTtb ABZ ycovia roLOvtcov A, otcov rj ^ta o^O-i) 
9, ixateQa dh tcbv ZlB zal BE to^ %Xdtovg ^olq&v s. 
ijcel toivvv tatg ^av SiTtXatg tcov A ilolqcov^ tovt- 
e6tiv talg J, jtaQccxeLtaL evd^eta t^rj^dtcov |, tatg de 
XeL7tov6aig elg tdg 8vo OQd^dg., tovte6tiv tatg qx^ 5 
TtaQdxeitai ev^eta t^rj^dtcov qS eyyiGta^ yCvetai Xoyog 
tfjg BA TtQog AE b tmv S JtQog td qS. 6 S' avtbg 
[Eucl. yi, 1] xal tijg BK TtQbg z/iT, oicov 7] 'bitotei- 
vov6a ^. 7toXv7tka6id6avteg ovv exdteQOv tcbv dgid-- 
li&v eitl tdg e ^OiQag tijg v7toteivov6rig zal tb qk 10 
avtcbv ka^ovteg e%o^ev exateQav [lev t&v KB xal BA 
tcbv avtG)v /3 A, ixateQav de tcov ^K Kal EA b^Oicog 
d X. td dri p X TtQcbtov^ edv ^ev xatd tb E 6r]^etov 
'^ eeXTJvrj 'iJTtoxerjtai^ dtpeXovteg tcbv trjg ZB iteQifpe- 
QeCag {lOiQcbv jie did tb eTtl td avtd t« xatd xoQvcprjv 15 
elvai tijv xatd TtXdtog ditoxiiv trjg ^eXrjvrjg^ tovte6tiv 
Sid tb d^cpoteQa rj votahteQa ri ^ogeioteQa eivat tov 
lcpdiaxov^ e^o^ev f^v ZA ^oiQcbv ^^ 1, idv de xatd 
tb ^ y rj eeXrjvrj, jtQoed^evteg avtatg did tb ivavtCov 



1. di^ d' D. ycovCa] supra scr. D. 2. JB] zJ- e 

corr. D^ 3. tovtscti, D, comp. B. 4. I (pr.)] in ras. A, 
corr. ex 1 D. | (alt.)] J- D. di] comp. ins. D^ 5. dvo] 
p BD. tovtieti D, comp. B. 7. BA] corr. ex Bzl D. 

TtQOs (pr.)] r^ D, ut saepe. ra] om. D. 8. JK] corr. 

ex AK D^. vnotLvovaa A, sed corr. in scrib. 9. sy,atiQ(ov D, 
corr. D^ tmv] ins. D^. aQiQ-iicbv] g D, ?g D^ 10. qy.'] 
9x AB. 11. ^at] om. D. 12. ^ X] pl BC, ut saepe. 

^ l — t&v] mg. A^ v.ai'] corr. ex x D^. 13. Post ic 

litt. (g?) ins. D^, sed del. E othlhov] corr. ex fa D^. 14. 
vn6v.eLtai D. 16. tovthti D, comp. B. 17. ^OQSiotSQa ?} 
votioatsQa (corr. ex votBio^a D*) D. slvai'] supra scr. D*. 

18. ^(o8Lav.ov] Sid ^ieov D, 8iu (isccov D^. 19. ^] corr. ex 
TiV D^ ' 



458 KAATAIOT nTOAEMAIOT 

£%ofiev rijv ZK ^OLQcbv ftj A. ^vvd^svtEg ovv tb ocnb 
STcatEQag tCbv ZA ncd ZK xciQlg ^eta tov ajtb ixa- 
t£Qag tG)v ^K ocal EA^ tovta6tiv tb aitb tcbv d x. 
fistd ts tov a%b tcbv ^p A xal fista tov ditb tcbv [nt, A, 
5 nal tcbv ^vvaxd^Evtcjv %(»(>t? Xapdvtsg trjv jclsvQav 
s%o^sv xal trjv ^sv ZE %SQL(pSQSLav ^OLQcbv ^^ Ji^ 
syyiata^ trjv ds Zz/ b^OLCjg ftg fid. koi%bv d\ td d 
X sxatovtaKLKaLSLKo6dxL 3tOL7]0avtsg xal 7taQa^aX6vtsg 
%G)Qlg TtaQci ts td fi^ fig Kal TtaQd td ^^ ^id s%o^sv 

10 tijv ^isv EA tOiovtcDV t/3 ij syyL^ta^ olcov s6tlv rj ZE 
V7totSLvov0a QK^ trjv ds ^K tOLOvtcov ~L L! y' syyi6ta^ 
OLcav i^tlv r] Zd v7totsLvov6a ^. JtaQaKSLtaL ds rj 
lisv tcbv L^ rj svd^SLa TtsQLcpsQSLa iiOLQcbv Td Kal y s\ 
tf] ds tcbv T C y' TiSQLcpsQSLa ^OLQcbv T y' syyL0ta, 

15 G)v td rj^i6rj ka^ovtsg td ^sv s Kal d s' tr\g vitb 
EZA ycovCag dtpsLlo^sv tcbv tfjg vitb ABZ yavCag 
yiOLQcbv X dLa tb Kal trjv ZE TtSQLcpSQSLav skd66ova 



1. Ante ovv del. avtatg dio. tb ivavtiov D. 2. ZA]^ -A 

in ras. J)\ xat'] om. D. ZK] -K in ras. Dl 3. xat] 

om. D. tovtiati D, comp. BC. 4. te\ supra scr. D^ ^ (pr.)] 

ins. D*. ihstd (alt.)] ^ D. tov (alt.)] ins. Dl 6. ZE] E Z D. 

jlg] vg D, /Li^ |u,y ty mg. D^ 7. jtt^] v8 D, [l^ [lav mg. D^ 

8. h%atovtav,iv.aL^' D, corr. D^. 9. ft?] #? B et, -s e corr., D; 

fi? supra scr. D^. /*^] r^ D. 10. toiovto) D. if\ l- e 
corr. Dl ^] corr. ex x D^ 11. ^^] om. BC. T /_' y'] 
in ras. D^ 12. Zz^] corr. ex ZA D^ 13. ^] e corr. D^ 

svd^scai 7CBQicpiq£Lai CD, corr. D^. io] -a e corr. D^. «'] 
i A, £ C, ^ BD. 14. /_'] in ras. D^ TtsQLqjiQeiai C. ^olq&v 
T y'] -V T y' in ras. 2 litt. D*. r(alt.)] postea ins. C. eyyLOta] 
in ras. D. 15. av td] in ras. D, oo- corr. ex o D^; ante av 
ras. B {mv corr. ex cav B^). ViiiGr}] in ras. minore D^. s'] 
J ABD^ s C. 16. tcbv] corr. ex tov CD^. 17. f] in ras. D^ 

ZE] corr. ex Z D^. iXdGCova] s" D, ^" Dl 



MA0HMATIKHS STNTASE^2 E'. 459 

^lvaL tfjg ZB xal saxo^ev riiv vjtb A®Z ycnvCav ^oi- 
QG)v xd s\ xa 8s s g' tfig vtco ^ZK ycovLag 7tQ06- 
d-evtsg totg avtotg X dta t6 xal ttjv ZA 7tsqi^)SQSiav 
\iisiC,ova slvai trjg ZB s6xoiisv xal tijv vtio AHZ 
yovCav ^OLQCJv Xs g'* ajtSQ jtQosxsito fisd^odsv^ai. 



1. A@Z] -@- e corr. D^. 2. F g'] s g C. ^ZX] 

^ X A, "^ I X D. 4. (isi^ova] f" D. AHZ] -H- in ras. D*. 
In fine: KXavdvov TLtoXsyLocCov ^ad^rjfiaziyimv f AC, KXavSCov 
IlToXsfiaCov (iad'r](iattv.f}g Gvvtd^soag I B, KXavdiov IltoXsfiiov 
(iad-7i(iatL7ioav F A D. 



5- 

Tccde eve6nv ev tco g' r(3v IltoXe^aLOv iia^iq- 

^atLKCJV' 

a\ Jtegl ^vvodcov xal 7Cav6ekriv(ov. 
5 /3'. TtQayiiateCa xavovCcov ^e6cov 6vt,vyiG3V. 
y\ exd^e^Lg tcbv xavovLcov. 
d\ (hg det tdg te JceQLodLxag xal tag dxQLpetg 6v^v~ 

yiag e7CL6xe7Cte6d-aL. 
e'. TCeqii tcbv eKXeLTCtLxcov o()cov yjXlov xal eeXtjvrjg. 
10 g\ steQl tijg dLa6td6ecog t&v exXeLTCtLXcbv firjvcov. 
5'. TCQay^ateia xavovCcov exXeLTCtLXcbv. 
ri'. exd^e6Lg tcbv exleLTCtLXcbv xavovCcov. 
^'. 6eXrivLaxG)v exXeCipeov dLdxQLOLg. 
l'. rihax&v exXeCipecov 8LdxQL0Lg. 
15 la. neQL tcbv ev tatg exXeCipe6L 7tQ06vev6ecov. 

lP'. exd^e^Lg tcsv TtQog tdg 7tQo6vev6eLg dLayQacp&v. 
cy'. 8LdxQL6Lg 7CQo6vev6ecov. 



2. tdS' D. t&v] tfis B, om. D. IlToXsfiaiov'] om. D. 

^ad^rKiccTLK&v] iiad"r]fiatLKfig Gwtd^sws B, om. D. 4. «'] etj 
ceteros numeros om. D. 5. Tcgayfiatia C. 6. y' — %aro- 

VLcov] om. D. 7. rag (alt.)] om. D. 9. iyiXriTttL-n&v D. tjXlov 
^al GtX^vrjs'] compp. BC. 11. ^'] in ras. A. v.av6v(ov D. 

12. T^' — Y.avovL(ov] v.aL comp. D. 13. did^QiOLS — 14. ^x- 
XsLipecov] om. D. 14. ^iax^tctg] in ras. D. 15. m'] ai B. 

Tieql tmv'] g nsQL td>v in ras. D. sv,XELipi6Lv D. 16. t^'] 
Pl B. t&v] om. D. TiQOVtvGSLg A. dLayqacp&v] g D. 

17. Ly'] Jl B. 



KAATA. nXOA. MAOHMATIKHS STNTASE.QS ?'. 461 

a. IIeqI 6vv6d(ov xal 7Cav6slrjva)v. 

'E(pe^rjg 8rj rvyxccvov6r}g trjg TtSQl tag ixlscntixag 
^v^vyCag r]Uov xal eskrivrig TCQay^atsCag^ '^g jtQorjyst- 
tat ndUv r} tcov dxQL^&g d-scoQov^svcov 6vv6dc)v xal 
7Cav6sXi]V(ov S7tC6xs^Lg^ djtaQxslv ^sv rjyov^sd^a TtQog 5 
trjv tG)v toiovtcov TtQCOtrjv xatdXrji(;i,v tdg aTtodsdsty- 
ILSvag xa%-^ sxdtsgov tav cpcotov TtsQiodtxdg ts xal 
dvco^dXovg XLvri6sig dvvatov did tovtcov ytvo^svov 
totg ^'fj xatoxvov6L tdg xatd ^SQog avt&v sjtoxdg 
sxd6tots 6vyxQCvsLV STtLXoyC^s^d^aL tovg ts t^Ttovg xal 10 
rovg %()dvovff tctv s6o^svcjv 6v^vyLcov tcbv ts TtQog 
td fis6a XLvri^ata ka^^avo^svcov xal tcbv ^std trjg 
dvcoiiakCag dxQL^cbv o^cog ds^ tva 7tQO%SLQ6tSQOv ^[itv 
xal avtaL iisd^odsvcovtaL^ TtQosxtsd^SL^svcov s^ stoC^ov 
tcbv ts xatd tdg TtSQLodLxdg 6vv6dovg xal 7tav6sX7]vovg 15 
Xq6vcov xal t67tcov xal tcbv xatd tovg ^s6ovg XQ^vovg 
S7toxG)v dvco^aXCag ts xal Jtldtovg tfjg 6slrjvrig^ dL 
cov 7] ts 7tQbg tdg dxQL^stg 6vt,vyCag dL^Qd^co^Lg yCvstaL 
xal d7tb tovtcov 7] 7tQbg tdg sxksLTttLxdg^ STtQayfiatsv- 
6d^sd-a 7tQbg trjv tOLavtrjv S7tC6xsilJLV xav6vLa 7tsQLSxovta 20 
tbv tQ67tOV tovtov. 



1. a'] om. AD. 2. Sr]] corr. ex av D^ syismtLyiccs A. 
3. xat'] Tf yiuL D. 4. GvvoScov] a- in ras. D. xat] ts 

v,ccL D. 5. STtLG-KSipLs] -Tt- corr. ex t D*. 6. yiutdXrjfiipLg D, 
sed n eras. 7. syidtSQOv] corr. ex stSQOv D*. 8. Slo] D, ts dLO, 
ABC. 9. xaToxvovffj D. snoxdq] -;f- corr. ex X D*. 10. %q6- 
vovg v,al tovg tonovq D. 14. (isb-oSsvovtccL CD, corr. in scrib. 
C et D*. 16. xQOvovs] XQ^v- in ras. D^ 18. yivstaL] supra 
scr. comp. et mg. D-. 



462 KAATAIOT nTOAEMAIOT 

p\ IlQccy^atEca xavovccov ^86cov ^vt^vyicbv, 

TIq&xov ^sv yccQj Xva Ttdkiv xal rag tav ^rjvcov 
STCoxdg^ co0jteQ xal rdg aXXag^ dito xov a sxovg Na^o- 
va66dQov 6v0xrj6(b^6d'a, xijv dTtodedsiy^avrjv iv xcp 
5 £X£L xovxco ®G)%' veo^7]VL^ xax' AtyvTCxiovg xfjg ^eer^^- 
pQtag eTtoviSCav djtoxrjg iiolqcov ov6av o kt, itaQa^a- 
Xdvxeg TtaQa xo rj^eQrj^LOv ^£0ov XLvrj^a trjg ditoxrig 
evQO^ev rj^£Qag i fij Xy^ G}g TtQO xo6ovxcov y£yov£vaL^ 
xrjv xfjg ev xfi veo^rjvLa xov ©cod- ^e^rj^PQLag TtQoye- 

10 yovvtav ^ie^rjv 6vvoSov. xal rj e^rjg ccQa yeyovev 
liexd rnieQag xy ^id Lt, eyyL6xa xrjg avxrjg ^e6rjfiPQLagy 
xovxeOxLV ^exd e^7]7co6xd ri^eQag ^Lccg ^d l^ xrjg ev xfj 
nd' ^e6rj^PQLag, iv de xatg Tty ^d l^ rj^eQaLg 6 ^ev 
ijXLog iie6cog ocLvetxaL ^OLQag %y xy v^ r] de 6eXr]vr] 

15 dvcoiiaXCag ^ev ^oC^ag xl rj Le^ jtXdxovg de ^oCQag^ 
XLd ^ Tcd. iitetxev de xal iv xf] xr]g veo^r]vCag ^e6r]^- 
PqCcc xov ©cod" iie6cog 6 iiev r]XLog 'Ixd^vcov ^oC^ag o 
ftf, dnb de xov djtoyeCov xov tdCov S^d xb evxQr]6xov 
fioCQag 6^e Te^ r] $e 6eXijvr] d^co^aXCag ^ev dnb xov 

20 dnoyeCov xov iTtLZVKXov ^oC^ag 6^r] ftO', TtXdxovg d' 

1. |3'] om. D. 3. hovs] post ^- ras. 2 litt. B, corr. ex 
inl Tovg C^, ex h D^ Na^ovaaaQOv D. 4. GvatrjaofiEd^cc C. 

z'qv'] corr. ex tirl D^. 6. stsl] corr. ex hr} D^. tovtaj 
-tco in ras. D^ vsofirjvLa] a in ras. D. 6. o] seq. ras. 1 
litt. D. TcaQa^dXXovtEg D, corr. D^ 9. V80fir}via] a D, 

yg. vovfirjVLa supra scr. D^ Gmd-] Qcbd' tfjg D. 10. ocQa] 
comp. C, ^^ D, yQ. aQa supra scr. D^ yiyovsv] -v eras. D. 

11. ^yLCta] sy- e corr. C. 12. tovtsctiv] comp. BC, -v 

eras. D. s^rjyioGtd] || B, comp. in ras. D^. 15. ti ^] B^D^, 
Ttrj ABC, T Irj D. 16. ^ xa] |3xa A. ineLXS D, -sl- in 

ras. D*. vsofirjvCag] -o- ins. C^; a D, corr. D^ fis6r][i§QL^ D, 
corr. Dl 17. tov Gcod-] om. D. fiOLQag] om. D. 19. c^sj 
6- corr. ex s A. 20. nXdtovg] corr. ex nXdtog J)\ 



MA0HMATIKHS STNTASESiS <5\ 463 

ccTtb tov pOQecov Tcegccrog tov Xo^ov xwcXov ^OLQccg 

tvd L€. TCal SV t(p TtQOXBL^ivCp aQCC XQOVG) tijg ^stcc 

tfjv vsofirjvtccv ^£6rjg 6vv6dov 6 ^sv i]Xtog Tcal 7] 6s- 
Xrjvrj ^s6cog a7tsl%ov d^cpotSQOt tov '^ltaTcov dicoystov^ 
tovts6ttv tcbv sv totg /Itdv^otg ^otQ&v s A, ^otQag 5 
67trj Xrj V, ri ds 6sXrjvri dvco^altag ^sv dito tov dico- . 
ystov ^otQag 6t^ v^ ts^ Ttkdtovg d' dno tov poQStov 
TtSQatog iiotQag irj tt, 7cd. 

td^o^sv ovv TtQ&tov xavovtov 6vvodt7cov 6tt%(0V 
^sv Ttdltv iis^ 6sXtdtc3v ds i, xal jtaQad^rj^o^sv sv totg 10 
TtQtototg 6tt%otg STtl ^sv tov jtQcotov 6sltdtov tb a 
stog Napova66dQOv ^ STtl ds tov dsvtSQOv tdg tov 
&G)d' rj^SQag Tcd ^d (f, STtstdrj td STtovta s^rjKO^td trjg- 
iv tri icd' s6tl ^s6r}^(iQtag, s%l 8s roi) tQttou tdg tfig 
^s6r]g STtoxrjg dnb tov aTtoystov tov rjXtov ^otQag 67tr] 15. 
Xrj v^ STtl ds tov tstdQtov tdg d%b tov ditoystov tflg 
6sXrjvtaxrjg dvca^altag ^otQag 6tr] i/J ts^ stcI ds tov 
Tts^Tttov tdg ditb tov ^oqsCov TtSQatog rov nXdtovg 
fiotQag trj tj xd. sjtstdr] ds Tcal sv ta r]^i6st tov ^s- 
60V ^r]vtatov xQovov rj^sQat ^sv 7tSQts%ovtat td ^ vs 20 
syyt6ta^ ^otQat 6s trjg ^sv r]Xtaxr]g S7to%fig td Xy ^/3, 
trjg ds 6skr]vtaxr]g dvcj^aUag ^9)3 vd A, rov ds TtXdtovg 
QfjS X g, dq)sX6vtsg tovtovg tovg dQtd^^ovg ditb tcbv 

2. I?] L- in ras. D^ 3. vovfir}VLCiv D. 5. tovtsgtlv'] 

comp. BC, -v eras. D. 6. dfj comp. supra scr. D*. 7. nXd- 
rovg] corr. ex nlccTog D^ 10. iv — 11. 6ZL%0Lq\ om. D. 12. 
frog] corr. ex |r>' D^. Na§ovcc6dQov D. dsvriQOv] -ti- e 
corr. in scrib. A. 14. ierLv D, -v eras.; comp. B. 17. 6£- 
Xr}VLayif^g'j corr. ex CfArjvrjg D^ le] corr. ex Ji D^ 19. 

fTrftdTj] corr. ex insL D^ r](iL6SL] -fi- e corr. A^. (irjvLaLOv 
fii6ov D. 20. rjfiiQUL] -dcl renouat. C^. nsQLixovtai] -ul 

renouat. C^. 21. iiolqul] -ccl renouat. C^. 22. d^ (pi")] 

ins. D2. 23. «91^11*0^5] gT^ D. 



464 KAATAIOT nXOAEMAIOT 

t7}g SKKSc^avrjg 6vv6dov tovg koi%ovg jCQOtcc^o^sv xal 
avtovg £v t» devtEQO) xal 6^0L(og E%ovtL xkvovlg)^ 
7tav6£XrjVLaxa ds fVoftfVoj, ;<aTa; tbv avtbv totg TtQOts- 
QOLg tQOTtov ocataX£L7tovtaL d£ ri^EQaL ^iev d' vrj x^, 
5 iioLQUL §£ aitb ^£v tov aitoyELOV tov rilLaxov dod £ 
Xri^ avca^alCag d' aitb tov ajtoyELOV trjg 0£Xr]vr}g z? 
/3 /i£, TtXdtovg d' d%b tov ^oqelov TtSQatog ql^ vt, H. 
£7t£l d£ Tcal £v x£ £t£6Lv AlyvTttLaxolg X£L7tov6Lv ^Lag 
rj^EQag eirjxo^tOLg dv6l /i^ £ oXol t£ ^fjv£g £yyL6ta 
10 aTtaQtL^ovtaL, xal £7tLXa^pdv£L ft£'9'' oXovg KvxXovg 
^£6(Dg 6 ^£v rjlLog ^OLQag tvy vfi Ad Ty^ r] de 6£lr]vrj 
dvco^aXLag ^£v ^ioLQag vt, xd fid a, TtXdtovg dh ^OLQag 
QL^ t/3 ^d" vd, td ^£v TtQCbta 6£XLdLa tcbv dvo xavo- 
VLOv 7taQav^r]6o^£v totg ke £t£6LV^ td df d£vt£Qa vTto- 

15 ^£Lcb60^£V tOtg O ^ JA^ £, tS>v d£ loL7tcbv td ^£V tQLta 

7taQav^r]6o^£v totg tvy v^ W Ty^ td df thaQta totg 
v^ Tcd ^d dy td dh 7t£fi7tta totg ql^ l^ ^d" vd. 

torjtOLg d' icpE^rlg td^o^Ev xavovLOV £VLav6L0V £7tL 
6tLxovg xd xal dlXo V7t avtb ^rjVLatov £7tl 6tL%ovg 
20 t/3, 6£XLdLG)v d£ £7cdt£Q0V tcov l'6c3v totg 7tQ(x)tOLg^ xal 
£7ti ^£v tov ^rjVLaiOv TtaQad^ivtEg iv totg 7tQd)tOLg 
6tC%0Lg i7tl ^£v tov 7tQC3tov ^eXlSCov tbv TtQcbtov ^rjva^ 
iTtl dh tov d£vt£Qov tdg toi) ^rjvbg rj^EQag xd" Xa v rj 

2. rc5] del. A\ om, D. 3. TCQcoTigoig A, TtQmtoLs CD. 5. 
^g'] ^' D. tjXlov D. 7. nldtovg] corr, ex TtXcctog A\ -X- e 
corr. in scrib. C. 8. ds xat] 8' D. ttt6iv\ comp. D, corr. D*. 

XsLTtOVGL D. 9. S^7l%06tOLg'] f^ B , 1« D. dv6LV B, B D. 

10. £7tLXa^^ccv£L'] -L ins. A. yivyiXovg] supra scr. D^ 14. toig 
— 16. nuQav^TJ6oii£v] bis A, corr. A^ 14. h£6Lv] comp. D, 
et£6L Dl v7tofiL6}60}i£v B et pr. loco A, corr. A*. 15. totg] 
-L- ins. D^ o (3] o|3 A utroque loco. 16. tstuQta] -ra supra 
scr, C^ 17. Post vd del, a D. 18. icps^fjg] -cps- e corr. in 
scrib. D. 20. di] d' D. 21. iv] ? B. 22. nQ&tov] corr. ex 
£va Dl 23. V Ti] C^D^ vri ABCD. 



MA0HMATIKHS STNTASESiS ?'. 465 

3c, STtl ds Toi) tQitov tag iv t<p toGovtco XQOvco 6vva- 
yo^£vag rov rjXiov ^ocQag xd" g Tty a^ STtl ds tov 
tstccQtov tag trjg dvcD^aXiag trjg ^slTJvrjg %£ /u-O" o ^, 
i%i ds tov Tts^Tttov tdg tov jtXdtovg ^oiQag 2, ]i td d" 
7taQav^7]6o^sv ds Tcal tavta totg avtoig aQid^fiotg Tcal 5 

STtl tCbV TtQCOtCJV <?Tt^G)l/ SKKSL^SVOLg. STtl ds TOV 

sviav^Cov TtaQad-svtsg sv totg TtQcStoig 6tC%oig STtl ^sv 
Tov TtQcbtov 6shdiov t6 jtQcotov stog^ STtl ds tov dsv- 
tSQOv tdg STtiXa^^avo^svag sv totg Ty ^rjolv rj^SQag 
Trj vy vp Jiirj^ STtl ds tov tQitov tdg sv t(p tocovtco 10 
XQOVG) trjg riXiaKfjg S7tov6iag ^oiQag Trj %p v^ Trjj sitl 
ds tov tstaQtov tdg trjg 6sXrjvia7cfjg dvco^aXCag ^iOiQag 
tXs X^ a vd^ STtl ds tov jts^Tttov tdg tov itXdtovg 
fioiQag Xr] ]iy y Im' TtaQav^ri^oiisv ds xal TOJiiTa jroT£ 
^sv tatg sKKSiiisvaig tQiGKaidsxa^Tjvoig S7tov6iaig^ 15 
3roT£ ds tatg dcodsKa^rjvoig^ aC 6vvdyov6iv rj^sQag ^sv 
tvd K^ d ji.^ iioCQag ds trjg ^sv rjliaKfig S7to%fig tfid' 
Tg Ag Zg, tfjg ds 6sXriviaKf]g dvco^alCag td" Jirj d ft)3, 
tov ds TtXdtovg rj j3 ^d' ft/3, TtQog t6 trjv TtQGytrjv s(p' 
oXoig Aiyv7ttiaK0Lg sts6iv 6v^vyCav rj^tv sKtC^sdd^ai' 20 
tdg lisvtoi ^taQad^s^sig dQKs6si ^s^Qi t&v dsvtSQcov 
s^rjK06t&v Ttoiri^a^d^ai. KaC s6tiv r} tcov KavovCcov Kat- 
aycoyr} toiavtri' 

1. x] corr. ex icf D^. 3. o tj] corr. ex ot\ D. 4. iioiQccQ] 
om. D. l vi id^ Ifiid corr. in Zft id A. -9-] del. D^. 5. ds] 
supra scr. D^. tccvta] corr. ex tavtccs D^. a^t-O-^otg] g D, 
ss^^ D^ 8. TtQoitov'] jJ). TtQ&tov] a BD. Btog] comp. D, 

corr. D^, ut saepius. 10. v§] va D. 14. fioiQag'] /xoi^" D, 

comp. C, ut saepe. di] supra scr. D^. 16. ai'] supra scr. D, 
renouat. Dl 17. a /Z] ofl AC et corr. ex Xy. D*. ^ 18. a] mut. 
in ;^ D-, a supra scr. D^. 20. stsaiv] -v del. D^, hsGi B. fjt- 
ts^^BLGd^aL D, corr. D^. 21. aQ^ichL] -f- alt. corr. ex l in scrib. A. 

t&v] corr. ex t D^. devtSQcov s^riy.oGt&v] -tSQcov s^iqyioGtcb 
in ras. D. 23. toLavtr]] des. fol. 136^ D, fol. 137^ uacat. 

Ptolemaeus, ed. Heiberg. 30 



466 



KAATAIOT nTOAEMAIOT 



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467 



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Ui Ui Ui 


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QQ. 


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III 




MA0HMATIKHS STNTASESiS S'. 



469 



l^.^r 


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CQ.QQ.QQ. 


SǤ 


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5=- ?r S- 


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S- 5=- S- 


P- p- s- 


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?=■ s=- s- 


jr«*J3Jo5 


8^ 8^8^ 


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470 



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MA0HMATIKHS 2TNTASE5iS 5'. 



471 



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472 KAATAIOT nXOAEMAIOT 

d\ 'Slg dst rdg xs TtSQiod iTcdcg xal tag aKQL^stg 
&vt,vyCag s%L6KS7Cxs6Q'ai. 

"Oxav ovv TtQoaLQcb^sd-a xaxd XLva x&v STtL^rixov- 

^svcov svLavxG)v xdg ^s6cog d^scjQov^svag Ovt.vyCag 

5 Xa^stv^ XoyuSd^svoL^ jco^xov s6xl xb vTtoxsC^svov sxog 

dno xov a sxovg Na^ova66dQov ^ xal axs^d^svoL^ 

notOL xov aQLd-iibv x&v sxav ^xC^ol jtSQLsxov6LV sk xs 

XCbV SV OTtOXSQG) XCQV TtQCOXCOV dvO XaVOvCcJV SLX06a- 

TtsvxasxrjQCdcjv xal sx xcbv xaxd xb xqCxov xavov lov 
10 svLav6Ccov^ xd TtaQaxsC^sva xotg 6xCxoLg d^g)oxsQOLg sv 
xotg siijg ^shdCoLg S7tL6vvd-t]6o^sv oixsCog sitl fisv x&v 
6vvodLXG)v 6v^vyLcbv xd sx xov TtQcjxov xavovog xal 
xd sx xov xqCxov^ sjtl ds xcbv 7tav6sXrjVLaxG)v xd sx 
xov dsvxsQov xal xd sx xov xqCxov biioCcjg' xal sx 
15 (isv XG)V xaxd xb dsvxsQOV 6skC8L0V ^vvxsd^SLfisvcjv 
s%o^sv xbv djtb xrig dQxr]g sxsCvov xov sxovg xrjg 6v^v- 
yCag XQOvov^ olov^ sdv 6vva%d-G)6LV r]^SQaL xd ^d^ 
^sxd ^id s^rjxo6xd Tr\g sv xfj xd' xov ©cod^ ^s^rj^^QCag^ 
xal Ttdhvy sdv Xd ftd, ^sxd xd l'6a s^i]xo6xd xrjg sv 
20 xfj d' xov 0ac3(pl ^s6rj^pQCag, sx ds xav xaxd xb xqC- 
xov xdg aTtb xov ditoysCov xov rjXCov ^oC^ag^ sx ds 
xcjv xaxd xb d' xdg ditb xov ditoysCov xrjg dvco^aXCag 
xfjg 6sXr]vr]gy sx ds xav xaxd xb Tts^nxov xdg ditb xov 



1. ^'] in ras. A, om. CD. oig] Tt&g D. 2. ev^vyiag'] -^- 

in ras. A, 4. ju-fccog] corr, ex fiecus D^ 5. nocov BC. 

6, a'] corr, ex d D^, Na^ovvaGaqov D. 8. -Aavovoiv D. 

ei-noGiTtsvtaetrjQLdcov D. 9. yialvLOv A, corr. A*. 12, avv- 

^vyL&v C, sed corr, TtQmtov'] a D*, d D. 15. yiaza] v.a D, 
-AoT' D^, ut saepius. 17. idv] corr. ex av D^ 18. e%r\-AO<itcc\ 
'll B, et similiter saepius, 19. yieta\ \zd A. 



MA0HMATIKHS STNTASEiiS ?'. 473 

^OQSiov TtSQatog roi) Jtldtovg. %al tag i^ps^rlg ds dxo- 
lovd^cjg^ idv ta Jtd6ag idv ts tuvag la^^dvsiv itQoai- 
Qafisd^a^ did t&v iv ta ^riVLaLG) xal tstaQtco xavoviG) 
xatd tb otxsiov iTtievvd-i^scov i^ stoi^ov 0vvs7tiXo- 
yiovfisd^a ^stag)SQO^ivG)v i(p sxd^tov tcbv %q6vg)V did 5 
ro svxQrj6tov tcov tfjg ri^sQag i^r^xodtcov sig coQag 
; i6rj^sQivdg. sCtai inivtoi ij ^vvrjy^ivrj tcov coqcov 
i7tov6ia (bg t&v vvx^-r^^iQG^v b^aXav ovtGJV {lii tavtr^g « 
ov6r}g alsl trjg xaiQiXcog xataXa^^avo^ivrjg ^ dlXd tr\g 
hg dvGoyidXGiv yivo^ivcjv t&v vvx^^rniiQcoV diOQd-G)- lO 
^oiisd^a ovv xal tb toiovtov i^std^ovtsg^ Sg VTtodi- 
dsiKtai^ t6 TtaQa tovto didcpoQov xai^ idv ^sv ftftjcoi/ 
^ r} TtQbg trjv dvm^aXov did6ta6iv ijtov6ia t&v XQO- 
vcov^ dtpaiQOvvtsg avtb ditb trjg b^aX&g 6vvrj'y^ivrjg, 
idv ds ikd66cov^ jtQo^tid^ivtsg avtfj. 15 

Xrjcpd^ivtog drj tbv tQOitov tovtov tov itQbg tdg 
^i6ag TtaQodovg d^scjQOv^ivov 6vvo8iKov rj 7tav6sXr]- 
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SKatiQov tG)v (p6tG)v sv^staxsiQi6tog s6tai xal 6 trjg 
dxQi^ovg 6vt,vyiag XQ^^^^? "^^ ^^^ tojtog xal sti r] 20 
Tiatd Ttldtog trjg 6sXr]vrjg jtdQodog ix trjg 6vyKQi6SG)g 
dficpotiQcov tcbv dvcj^aXiav. xad'' sxatiQav yaQ av- 
tcbv ijti^KSJl^d^svoi trjv iv t(p ixxsi^ivG) jtSQiodiXip 
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jtdQodov rjXiOV ts xal 6s?,r]vrjg xal jt^.dtovg., idv ^sv 25 
xal ovtcog i66^0iQOi i) did^stQOi svQi6xcovtai^ tbv av- 



8. 0)9] corr. ex 6g Cl 9. atft] corr. ex ccei D^ ccXXd] 
mut. in aXlr]s C^, dXXdXX7]g D. rj)s ag] supra scr. D^. 10. 
SiOQd-moo^sv D. 11. v7co8t8hv.xai D, sed corr. D et D^ 

15. iXdTtcav D. 16. tovtov tov tqotzov D. 21. rrjg ob- 

Xijvrig v.aTCi nXccTog D. 22. t&v'] om. C. 6[iaXid}V D, corr. D*. 

24. svQiaacoiihrjg A. 



474 KAATAIOT nTOAEMAIOT 

tbv £%o^sv xQOvov xal tijs axQL^ovg ^vivyCag^ iav d\ 
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6 L6ri^SQLvatg rj 6sl7]vr] tdg to6avtag ^OLQag tots dvcj- 
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TtlsLCJv^ dcpsXov^sv dit^ avtov. G)6avtc3g ds xal av- 

10 tdg tdg trjg dLa^tdascog avt&v ^OLQag fistd tov dco- 
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r]kLaxf]g^ jtQo^d^svtsg avtr]^ sdv 8s ^lsCov^ d(psl6vtsg 
dit avtfjg xatd ts tb ^rjxog xal TtXdtog t6v ts tfjg 

15 dxQL^ovg 6vt,vyLag %q6vov s%o^sv xal tf]v sjtl tov 

Xo^ov xvxXov tY]g 6sXY]VY]g dxQL^Y] TtdQodov syyt^ta. 

Xa^pdvstaL ^svtoL sxd6tots tb xatd tdg 6v^vyLag 

trjg 6sXY]VY]g aQLatov dvcofiaXov XLvr^fia tbv tQ^itov 

tovtov si6cpSQovtsg yaQ tbv xatd tbv vjtoxsL^svov 

20 %q6vov tG)v tfjg dvco^aXLag ^olqcov dQL^-^bv slg tb tfjg 
dvcD^aXCag tfjg 6sXr]vr]g xav6vL0v Ai^^dftfO-a sx tfjg tcbv 
TtaQaxsL^svcjv avta TtQo^d-acpaiQS^scov v7tSQ0%f]g tY]v 
S7tL^dklov6av dLacpOQdv tc3 svl tfjg dvcj^alCag tpnf]- 



1. %ai] om. D. 2. |li^] vno D, vno del. D*. SiccGtd- 
Giiog] post -f- ras. 1 litt. D, -oxaG- in ras. D^. 3. 8oi8£%urov\ 

i^ D. civxcbv] corr. ex avxov C. 7. iXdxxcov D. GsXLvrjg A. 
9. nXstov C. 10. dLaGxaGscog'] -Gxd- in ras. D*. dco- 

dsyidxov] l§ D. 11. iXdxxoov D. 12. ^^pdi^oi'] )^ D, ut 

saepius. 13. tiIsiov C. 14. rd] om. D. 15. £|o/ifv 

XQOVov D. xriv'] om. B. 18. dvco^alXov C. 20. xoiv'] 

x6v in ras. A, corr. A*. aQid-fiov] dqi D, -iiov add. D^ 

23. x^T](iaxi jtat] -t %- corr. ex iK A. 



MA0HMATIKHS STNTASESiS g'. 475 

liati xal 7toXv7tXa6icc6avt£g avtrjv btiI tb d)Qtatov trjg 
ccvco^alCag ^b6ov xtvri^a ta o X^ ji o ta ysvo^sva^ 
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tov Tcatd ^rjxog cjQiaCov ^£0ov Tctvrj^atog tcbv o A/3 5 
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6 ft£v ovv iv 'Al£l,avdQ£Ca yLv6^£vog %Q6vog t&v 
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Ttdkiv ^Cav dr]kov6ti Ttoiovvtcov coQav i6r]^£Qivr]v. 



2. fi o] fi o corr. ex fto A, jt D. 5. mQiaLov^ -i- corr. 

ex ci in scrib. C. 6. o] om. D. 8'^ mut. in 8e D. nqoa- 

d-T]60fiaL D. 9. y8v6fi£vog D. 11. Ttdcag D. 13. XQOVOV C, 
sed corr. 14. ysvo^svovg D. 15. nX^qd-ovgl -Q-- in ras. A. 

19. tov] corr. ex tov D^ 22. tEtT]QELad-aL B. $4] 8' D. 

24. a>Qav] corr. ex mQ(av D^. 



476 KAATMOT nXOAEMAIOT 

a. UeQl t&v enkeiTitiKQbv oqcov fiXiov xal 
^sXTJvrjg. 

Tovtcov d' ovtcjg icpcodsv^svcov dxoXovd^ov av sHrj 
jtQo^d-stvai ta (SvvtsCvovta JtQog tovg sxXsLTCtLTcovg 
5 OQovg tcbv ts tov yjXlov xal t&v tfjg 6sX7]vi]g stiltcqoC- 
%^Yi6scov^ Xva^ xav ^ij 7cd6ag tdg jtSQLodLOcdg Gvt^vyCag 
S7tLXoyCt,s6%'ai jtQoaLQco^sd^a^ ^ovag ds tdg dvva^svag 
sig tdg sxXsLJttLKdg S7tL0rj^a6Cag s^itsestv^ jtQoxsLQog 
vj^tv 7] toLavtr] yCvrjtaL dLaKQLGig sx trjg TtaQaxsL^svr^g 

10 sxd0tr} tGiv TtSQLodLKGjv 6v^vyLC3v ^s6r]g xatd Ttkdtog 
TtaQodov trjg asXTJvrjg. 

sv ^sv ovv Tw TtQO tovtov 6vvtdy^atL [V p. 421^ 3] 
dsdsC^a^sv^ otL tfjg asXyjvrjg rj dLd^stQog vTtotsCvsL 
TtSQLcpSQSLav tov Tcatd t6 ^syL6tov avtfjg d7t66tr]^a 

15 yQacpo^svov TtSQL t6 xsvtQOv tov ^a)dLaxov ^syC^tov 
TtvxXov ^Lctg ^oLQag s^rjxo^tcbv Xa sc, dLa dvo stcXsC- 
^SGov ysysvrj^svcjv 7tSQl t6 d^toysLov avtfjg tov S7tL- 
xvkXov t6 toLovtov S7tLXoyL6d^svoL. xal vvv d\ S7tsi 
tovg ^syC6tovg tcbv sxXsLTttLxav 6vt,vyLcbv oQOvg tcqo- 

20 aLQOv^sd^a Xapstv^ ovtoL d' sl61v oC yLvo^svoL tfjg 
6sX7]vr]g 7tsQl t6 ^tSQLysLOtatov ov6rjg tov S7tLxvKXov^ 
dsC^o^sv dLd dvo TtdXtv t&>v 7tsQL t6 7tSQCysLOV tstrjQrj- 
fisvcov skXsCxI^scov ^ STtSLdf] 8cd tcbv (pacvo^svcjv avt^v 
d6q)aks6tSQ0v dv sl'r] td tOLavta dsLKVvSLV, 7trjXCKr]v 



1. f'] om. D. 3. ecpodsv^^vcov C. 4. nqoG^^fivcci CD, 

corr. D. 5. ri}g] ins. D^ inLTiQoad-riGscov A. 8. ixTre- 

6£tv D. 9. yCvBxat C. 10. tyidGTrf\ corr. ex aKccGtaig D*, 

h-Adaxriq A. 13. otrt] o*' D, ut saepius. 15. ^co8tav,ov] 

^S^ D. 20. ^'] Si D. 22. x6] corr. ex xibv D. nsQt- 

ysiov'] corr. ex TtSQtysta D. 



MA0HMATIKH2 STNTASESiS S'. 477 

xal ivtavd-a 7tSQiq)8Q£i,av b^ioCcog r} trjg 6£X7jvr]g did- 
fietQog aTioXa^pdvsL. 

tGt toCvvv t,' £tSL 0LXo^7]tOQog^ £6tLv (po8' aTcb 
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xrj' djcb mQag rj' dQ%oii£vrig scsg l Xrjyov^rjg £v'AX£i,av- 5 

dQ£LCC, £^£k£L7t£V rj 0£kr}Vrj tb 7lX£L6tOV dii' aQXtCJV 

daxtvXovg ^. £7t£L ovv b fi£6og XQ^^^^S ysyov£v ^£td 
P [_' wQag TcaLQLKccg tov ^£6ovvKtCov^ aL ij^av L6r]ii£- 
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fiOLQag ^ d, xal 6vvdy£taL b d7tb tfjg £7to%rig %Q6vog 10 
^£%QL tov ^£6ov tfjg £xl£Cilj£C3g £tG)v A Lyv7tt LaxG)v (poy 
xal r]a£QG)v 6^ xal coqcqv L6rjU£QLVG)v d^tXag filv cd y' ^ 
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vov tb K£vtQov trig 6£Xr]vr]g ^£6(og [ihv £7t£L%£v Uxoq- 
ucCov ^oCQag J ^id^^ dxQLpcjg dl ^oCQag ? 7g, Kal d7tb 15 
(i£v tov d7toy£Cov rov £7tLxv7cXov fioCQag Q^y /I, d7tb 
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q)av£Q6v^ ort, btav r] % ^oCQag d(p£0tr]Kr] tcbv 6vvd£6^cov 
tb KsvtQov tfjg 6£lr]vr]g £7tl tov Xo^ov kvkXov TtSQL tb 
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Sl avtov TtQog OQd-dg tm Ao|« kvkXo) ^£yL6tov kvk- 
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avtf]g £ig tf]v 6KLdv £^7tC7tt€L tfjg dLa^stQOv. 

TtdXtv di] t(p Xt,' £t£L tf]g tgCtr^g Katd KdkL7t7tov 25 
7t£QL68ov^ 6 £6tLV %C,' d^tb Na^ova66dQOv^ Kax AiyvTt- 



3. Igxiv'] comp. B, ^gxl D. qpo^'] cpo8' exog D. 4. Na- 

^ovvccaaQov D. 5. aQxo^Bvrig'\ corr. ex aQxovarjg D. 6. 

gsXt] C, corr. Cl 7. y^yovs D. 13. (lovov B. 14. stcslxs D. 

21. avTfig D. 23. i§'] T ^' A, ip^ BCD. 25. KdXUTtnov 

ABCD. 26. Na^ovvaaaQov D. 



478 KAATAIOT nTOAEMAIOT 

tLovg Tvfi /3' sig tijv y' coQag e' aQxo^svrjg iv 'P6d(p 
^Q^ato eKXsLTtSLV rj aeXtjvrj xal ejteGKOtTJd-rj tb 7tkei6tov 
a%o votov daxtvXovg y. eTtel ovv TtdlLv Tcal ivtavd^a 
rj ^ev ccQxrj tfig eKleC^eGig yeyovev jtQO dvo Sqg)v xaL- 
5 QLX&v tov ^edovvxtLov^ aC r]6av L6rj^eQLval ev 'P6dc3 
te xal ev ^AXe^avdQeCa /3 y' Slcc th tbv tjXlov e7te%eLv 
cacQL^cbg 'TdQo%6ov ^oCQag e '^^ 6 de ^e6og XQ6vog^ ev 
G) tb nXet^tov eTte^Kotrjd^rj^ TtQb a /.' y' eyyL6ta coQag 
L6r]^eQLvfjg tov ^e6ovvKtCov, Kal 0vvdyetaL 6 djtb tYjg 

10 ejtoxfjg ne%QV tov ^e6ov trjg eKkeC^^eag XQ6vog itcbv 
AlyvTitLaKcbv %g Kal rnieQcbv QKa Kal coQcbv C^rjfieQLvav 
ditX&g te Kal TtQbg td biiala wx^riiiLeQa T Kal g', xaO'' 
ov XQOVOV t6 KevtQOV tfjg 6eX7]vrjg ^eocog ^ev inelxsv 
Aeovtog ^oCQag e 7g, aKQL^Cbg de e rj^ koI dnb iihv 

15 tov dnoyeCov tov ijtLKVKXov ^oC^ag Qorj jitg, ditb de 
tov ^OQeCov TteQatog inl tov lo^ov kvkXov fioCQag 67i 
Ag, (paveQov Kal ivtevd^ev^ oti^ otav T Xg ^oC^ag dq)e- 
6tr]Kr} tcbv 6vvde6^cov tb KevtQov tfjg 6eXr]vrjg iitl tov 
Xo^ov kvkXov TteQl tb avtb iXdxL6xov ov6r]g d7t66tr]^a 

20 tov KSvtQOV trjg 6KLag tr]v KOLvf]v to^f]v iTtexovtog 
tov te dtd ^e6cov koI tov dtd tov KevtQov tfjg 6eXfi- 
vr]g 7tQbg dQd-dg ta Ao|co yQacpofiivov ^eyC6tov kvkIov^ 
t6te tb tetaQtov ^sQog eCg tf]v 6KLdv i^7te6eLtaL tfjg 
6eXr]VLaKf]g dLa^itQov. 

1. y'] tqCt7]v C. 2. kv,Xi[LndvEiv D. 3. xat ndXLv BC. 

4. yiyove BD. 8vo\ |3 BD. 6. «V] om. D. y'] A, 

/.' y' BC, L; D. zo\ Tis C. 7. fi\ L' !>• »• Post y' supra 
scr. fn" C^ 13. sitELxt D. 15. (lOLQag — 16. yivyiXov] mg. D^ 

16. fjrt] om. D. iiOLQag 67i X?] corr. ex licnX^ D^, iLGn X<5 

mg. D*. 17. OTt] o D, D^. T] T v.ccC D. 18. rcov] anb 
T&v D. 19. avTov C, corr. C^ 23. tote'] bis C, sed corr. ; 
om. D. TETaQTov] ^^ BD. cyiLdv'] seq. ras. 2 litt. C. 



MA0HMATIKH2 STNTASESiS 5'. 479 

«AA' iccv ^£v rj xal y' ^otQag cc7CB%ri t&v 6vvdi6- 
licov STtl rov Xo^ov xvxXov t6 xbvtqov rfjg ^EXi^vrjgj 
]iy xal X i^rjxo6ta ^cag ^oiQag inl tov dia tcov 7i6- 
Xcov avtov yQatpo^ivov ^syl^tov xvxXov du6tatav 
tov dia ^iacov^ orav ds dixa [lOLQag xal y Tci^jcta 5 
tG)v 6vvdi6^c3v aTtixrj xata tbv Xo^bv xvxkov^ vd L! 
y' i^rjxo6ta ^iLag ^OLQag inl tov 8ia tcov ndXcov avtov 
yQa(po^ivov ^syc^tov xvxlov dU6tatai tov dia ^i^cov. 
ijtsl ovv rj ^sv tcbv dvo ixksCjjjscov vTtSQOxrj tb tQitov 
7t£Qii%su trig esXrjVLaxfjg dLa^itQov^ rj dh t&v ixxBi- 10 
liivcov tov xivtQov avtrjg inl tov avtov ^syL6tov 
xvxXov 8vo diaot descov ditb tov avtov 6rj^SL0v tov 
did iii^cov^ tovti6tLv tov xivtQOV tr]g ^XLccg^ s^r]xo6td 
^Lccg ^iOLQag La ^liJ, drjXov^ ort xal rj dLd^stQog oXrj 
tfjg 6sXr]vrjg vTtotsCvsL tov xatd tb iXdxL6tov avtfjg 15 
d7t66trj^a yQacpo^ivov tcsqI tb xivtQOv tov ^&dLaxov 
fi£yC6tov xvxXov 7tSQL(piQSLav s^r]xo6tG)v ^oCQag ^Ldg 
Xs y' £yyi6ta. i7t£l ds xal iv tfj d^vtiQcc tav ixl^C- 
tp£cov^ xad'' rjv tb d' ixX£XoC7C£L tfjg 6£Xr]VLaxfjg dLa- 
[iitQov^ dcp£6tr]X£L ro xivtQov tfjg 6£Xr]vr]g tov fi£v 20 
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xad'' ti^v£L tf]v tfjg 6xLdg 7t£QL(piQ£Lav rj i7tL^£vy- 
vvov6a avtcbv td xivtQa^ ro d' tfjg dLa^itQov tfjg 



1. cclXd A. aniiEi D, corr. D^. 2. x6 — 4, -avv.Xov] 

bis D. 2. v.ivxqov D. 3. %at] supra scr. D^ alt. loco. x'] 
mut. in y B, om. D. 4. fisyiaxov yivv.Xov'] om. D alt, loco. 

6. ^f'] supra scr. C*. nifinxa] 'ssB, s" D. 8. SLiGxavxat A. 

9. XQLXov] y' BD. 10. xov snyisi^svov C. 11. xov (pr.)] 

del. C*. 13. xovxicxL D, comp. B. 14. jLnaff ^iOLQag] om. D, 

Lo] corr. ex Ld D^. oX7]q D. 16. xo] supra scr. Dl ^co- 
dLaY.ov] ^wjT D. 17. tcsql^sl'^ D. fiOLqas fttag] om. D. 19. 

S^sXsXOLTtSL D. 



480 KAATAIOT nTOAEMAIOT 

esXrjviaxrjg^ o i^XLv i^rjKOGt&v rj /.' y\ (pavsQOV avto- 
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5 tQL6l 7t£[i7ttOLg ^£L^C3V tfjg ix tov TcivtQov tfjg a^Xi^vr^g 
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tov ijlLov {)7tot£LV£L 7t£QLCp£Q£Lav o^OLCjg tov ^tar' av- 
tbv yQacpo^ivov 7t£Ql tb nivtQov tov ^(pdLaTcov ^£yL- 
6tov xvxkov i^r]xo6tcbv Ti ji' L6dxLg yaQ id£Lx^r]6av 

10 [V, 14] xata^£tQovvt£g tovg IdCovg xvxXovg o t£ iqlLog 
xal 7] 6£X7]vr] xatd tb iv tatg 6vt,vyCaLg ^iyL6tov d7t6- 
6tr]^a. otav aQa tb cpaLvd^svov xivtQOv trjg 6£Xr]vr]g 
dcp£6tr]xr] tov xivtQOv tov r]kCov icp' ixdt£Qa tov dLa 
^i6c3V ^Lctg ^oCQag o ly x^ t6t£ 7tQcotov dvvatov 

16 £6taL ti]v cpaLVO^ivr]v d-i^LV tfjg 6£Xr]vr]g xatd tf]v 
i7ta(pf]v y^vi^d^aL tov r]Uov. 

olov^ idv vor]6G)ii£v tov ^£v dLa [ii6c3v tcbv t^codCcov 

XVXkoV 7t£QL(piQ£LaV tf]V AB^ tOV d£ Xo^OV tfjg 6£kY]- 

vr]g tf]v Fz/ 7taQaXlr]Xovg 7tQ6g at6^r]6LV yLvo^ivag 

20 ^ixQ'' Y^ '^03v xatd tovg ixk£L7ttLX0vg %Q6vovg 7taQ6dc3v^ 

xal dLa tcbv tov Xo^ov 7t6lG)v yQd^co^^v ^£yC6tov 

XVXXOV 7t£QLCpiQ£LaV tf]V A E F^ V07]6C3^£V 61 Xal 7t£Ql 

tb A 6r]^£tov t6 tov r]kCov f]y.LXvxhov^ 7t£Ql dh tb E 
t6 (paLv6^£vov tfjg 6£lr]vr]g^ &6t£ i^pdTtt^^d^at ^tQcotcog 

2. otC] om.C. 6. r^] U ABC, Fb D. Mg. ^ AC. 7. 

r - 

snirsivsi D. 8. Supra yQacpo^svov add. ft O D^. ^(pSLaTiov 

fisyiGTov y.v^iXov'] ^oo D. 12. Ante v,svtqov del. to Cl 14. 
/xmg iioLQDcq] om. D. tots] supra est ras. A, a sgtiv iy, t&v 
'KSVTQcov aiicpOT^QCov T&v cpcoTOiv TOTS B. TiQaiTOv] corr. ex a D^. 

15. sGTai] om. D. 16. ylvsGQ^ai D. 17. ^cpdLOiv] ^co D. 

20. sy.Isltit'] D. 22. nSQC] tcsql [liv D. 24. Tfjg] %-' Tfjg B. 



MAeHMATIKHS 2TNTASE5iS ?'. 481 

tov riXcaKOv xata xb Z arj^etov^ rj AE TCEQKpbQEia^ tJv 
d(p£6trjX£v to E (paivoiiEvov TcivtQOv rijg 6£X7]vrjg tov 
A riXiaxov^ dvvatat jtote yEviad^ai tcbv ixKEi^ivcDv o 
Xy x. aAA' iv totg anb MsQorjg tOTCotg^ otcov rj ^e- 

yCetri rj^iQa wQav iattv LarjfiEQi- 5 
vav Ty^ ^''^XQi' T^^v ix^okcbv Bo- 
Qv^d^ivovg^ 07C0V ij ^EyCatrj rj^iQa 
G}QG)v i6tLV L6rjfiEQLVG)v Zg, TCQbg 
^Ev aQKtovg t6 7Ck£L6tov rj aEXrjvrj 
icaQakXd06EL xatd tb tcov 6v^vyLcbv lo 
ild%L6tov aTCo^zrj^a vjcoXoyovfiivrjg 
trjg tov rjXLOv TcaQaXXd^Ecog o rj 
fyyL6ta^ TCQbg ^E^rj^^QLav d' byboCcDg 
tb 7cXEL6tov o Urj. 7CaQaXld66£L ds xal Tcatd iirjxog tb 
%k£L6tov^ orav ^Ev td orj 7CQbgtdg aQXtovg 7CaQaXld66rj^ 15 
tceqI tbv Aiovta xal tovg ALdv^ovg o X syyL^ta^ orav ds 
rd o vrj 7CQbg fiE^rj^^QCav ^ 7C£qI tbv UkoqtcCov xal 
tovg ^lxd^vag o Te £yyL6ta. idv aQa tb dxQLplg trjg 
6EXrjvrjg xivtQOv vTCo&th^Ed^a xatd tb z/, xal iTCL^Ev- 
^ca^Ev trjv AE tfjg oXrjg 7CaQaXXd^EG3g^ rj ^sv AFtrjg 20 
xatd ^rjxog £yyL6ta £6taL ^caQaXXd^Ecog^ rj dl FE tfjg 
xatd TcXdtog. co6t£^ 6r«i/ ^ev d^t' ccQXtcjv fj rj 6EXrjvrj 
tov rjXCov xal 7CaQaXXd66rj tb tcXel^xov 7CQbg ^£6- 
Tj^^QCav, ij iiEV AT £6taL tcov o T^, rj $£ AEF 




1. AE] A- e corr. D. 2. aqp^ffrr^xa D. 4. x] xa C. 

tOTCoig'} om. B. 10. TtccqaXXaGBi D. 6v^vyL&v\ corr. ex 

svtvyicav A^ 12. naqaXXak^ D. 13. 8'] e corr. D. 14. 
xo 7tX£L6Tov'\ om. D. 7taQaXld68L D. xat] supra scr. D*. 

Post y.atd del. to D^. 15. 7taQaXXd66'^] Halma, 7taQaXXd66si 

ABC, TtaQaXXd^rj D. 17, td] om. D. 19. vd-mfied^a D. 

22. otav'] ots C. i^ 6sXriv7\ 7] D. 23. TtaQaXXd^^fj] Halma, 
7taQaXXd66EL ABCD. 

Ptolemaeus, ed. Heiberg. 31 



482 KAATAIOT nTOAEMAIOT 

^ocQag a Xa syyiClta. Koi stcsI X6yog e6rlv rrjg djtb roi) 
6vv8b0^ov £7tl ro r 7C£QL(p£Q£iag TCQog rrjv FA xara rb 
^£ra^v rcbv ixXsLTcrLXcbv oqcjv dcdijrrjfia^ bv £%£l rd 
Td i! TCQog rb d' £vxarav6rjrov ydQ rj^tv rovro ytVf- 
5 tat dLa rcbv TCQoajcod^d^Ly^Evcov iicl rfjg £yxXL0£cog rov 
6£XrjVLaK0v xvxlov xal avrrj ^£v rj djcb rov ^vvdi^- 
fiov inl rb T £6raL fioLQ&v l^ jcg, ^srd dh rrjg F^ 
r&v avrGiv Lt, ^. orav S* dicb ^£6r]^PQLag ov6a rov 
riXCov rb 7ck£L6rov TCQog ccQxrovg naQaXkd66ri^ rj ^hv 

\0 jd r £6raL r&v o A, r] d£ AEF bXrj r&v o ^, xal 
dLa rd avrd r] ^£v djcb roi) 6vvd£6^ov iicl ro F ^ol- 
Qcbv J 2;/3, 'j^ ^^ ii^rd rrjg FA bXr] rcbv avrcbv rj xp. 
brav ccQa rb xivrQOv rfjg 6£lr]vr]g dxQL^cbg dicixr] bico- 
riQov ra)v 6vvdi6^c3v ijcl rov Xo^ov xvxlov iCQog fihv 

15 ccQxrovg ^OLQag Lt, Jid^ TCQog ^£6r]^pQLav dh ^OLQag ^ 
;c/3, r6r£ jCQcbxov iv rotg ixx£L^ivoLg r^icoLg rrjg xad"^ 
r]iiag olxov[iivr]g dvvarbv £6raL ri]v cpaLvo^ivr]v avrfjg 
d-i^Lv xard ri]v inacp^^v y^vi^d^aL rov rjUov. 

jcdhv^ iTC£l t6 ii£v rfjg r^kiaxfjg dvcD^aXCag 7Ck£t6rov 

20 dLaq^OQOV d7C£d£L%^r] [lolq&v /3 xy [III^ 4], rb df rfig 
6£Xr]Viaxfjg ro tc£qI rdg 6v^vyLag ^olq&v £ d [p. 337J, 
dvvarbv £6raL TCorh rf]v 6£Xr]vr]v dcp£6rdvaL tov r]lLOv 
xard rdg 7C£QLodLxdg ^v^vyCag dxQi^cbg ^oCQag J xd. 



1. iioLQag'] seq. littera macula obscurata A; dfioicog D, 
mg. II a Xa D^ sati D, comp. BC. 2. inL'] corr. ex 

iTtft C. TiEQLcpSQELccgl -£ postca ins. C. 4. /,'] X D. 5. cctio- 
dsSsLyfiivcov D. 6, 'hvtiXov'] C. avri]] avxr] B. 9. 

aQv,xovg'\ post jt del. 6 C. TtaQaXXccarj D. 11. ra avTa] 

xav D. 13. oxav] -av del. D^. 15. ds nEGrjfi^QLav D. 16. 

TiQmxcag D. 18. xam] corr. ex na D^ 21. TtSQL'] it D. 

23. a-AQL^iag] om. D. 



MA0HMATIKH2 STNTASEiiS ?'. 483 

d?,Xd^ sv 66ip diiQXBxai tavtag rj eeXrivri^ 6 iiev iqlLog 
TCQOOdiElEv^staL To ly' avtG)v eyyiQta^ tovtectiv o Ad, 
av 60(p 8e Tcdkiv yj aekTJvrj td o Id eTtixiveitaL^ Ttgoa- 
dielevaetaL xal 6 7]XLog tb Ly' avtSiv td o y eyyi^ta^ 
G)v ovxetL yCvetaL tb Ly' d^Lokoyov. edv aQa td enl 5 
t6 avtb o Ag, d yCvetaL tcbv ^| dQ%fig J xd {leQog l^\ 
TtQO^d^&^ev tatg tfjg rj2.Laxflg dvco^aXCag ^oCQaig /3 jc/, 
e%o^ev ^oCQag y^ alg tb nkeL6tov dLoC6ov6Lv tcbv ev 
talg TCeQLodLxatg 6vt,vyCaLg ^e^cjv jtaQodcov ^yjxovg te 
xal Ttkdtovg eyyL6ta aC dxQL^elg. xal 6tav ccQa rj lo 
^e6r] TtaQodog tov xevtQOv tf\g 6eX7]vrjg d(pe6t7]xy tcov 
6vvde6^c3v eitL tov Xo^ov xvxlov itQog ^ev ccQXtovg 
fioCQag X Jid^ TtQbg ^e^rj^^QCav de ^oCQag Td ;c/3, tote 
TtQcbtov ev totg exxei^evoLg tojtOLg dvvatbv e6taL tijv 
g)aLvo^evrjv avtfjg d^e^Lv xatd f^v enacpiiv yeve6d^aL 15 
xofj rjlCov. xal d^d td avtd^ 6tav 6 ditb irot) ^oqbCov 
xeQatog tov Xo^ov xvxkov tfjg 6e2,rjvrig 6 jtaQaxeC^evog 
[p. 471] tatg jteQLodLxatg 6vt,vyCaLg t&v ^olq&v dQLd'- 
libg rjtoL tatg ditb l-O* td' ii>e%QLg Qa xfi 7] tatg ditb 
6V7J Iri iiexQLg 6g Jid 6vve^7tC7ttr]^ Tore ^ovov ev totg 20 
exxeL^evoig toitOLg dvvatbv e6taL ^v^^fjvaL t6 tcqo- 
xeCuevov. 



1. ravTa B. 2. ty'] l r C, ut saepius; l f corr. ex fl D. 

3. Gsli^vr]^ ([ D, ut saepius. iTCLKLvsLtaL'] corr. ex stzl- 

KVELXUL A^ 4. ly'] t' y' D. 6. X^] corr. ex ;iA D*. t^'] 
corr. ex ty D*. 7. r}XLcc%jig'] i}- e corr. in scrib. C. 8. Sl- 
OL6OVGL D. 9. ratg] t?? D. 16. 6] om. C. 17. 6] om. D. 

18. tuLg] tgG D, ut saepe. ttbv ^olq&v] ft D. aQLd^l^iog A, 
aQL\&fi6g A^. 19. (lixQ'- D, corr. D^ r/'] seq. ras. 1 litt. D. 

20. 6vri] -7] e corr. D^ f^^XQ'' ^- cvvs^TiLTttSL C. 21. 
t6 ■jtQOv.sifisvov 6v^§rivaL D. 

31* 



484 KAATAIOT nTOAEMAIOT 

jtdUv xccl T&v rf}g 6ek7]vrig ixksLTCXiXGiv oqcdv 
evsxEv^ iTtEi ri ^ev ex tov ksvtqov trjg 0sX7]vr}g xatdc 
tb sld%L6tov avtrjg d%66tri^a v7COtsCvov6a sdsLxd^rj 
TtSQLcpsQSLav ^OLQG)v o L^ ^^ rj ds SK tov xsvtQov trjg 
5 6xLag dL%ka6LG)V ov6a xal HtL tolg tQL6l TtsfiTttOLg 
syyL6ta ^sl^ov trjg sx tov xsvtQOv trjg 6sl7Jvr]g 6vvd- 
ystaL tcbv avirwv o fli vg^ drjlov^ otL xaC^ otav tb 
xsvtQOV tfig 6sl7]vrjg dxQL^ag aTtsjri tov xsvtQOV trjg 
6xLag STtl ^sv tov Sl' avtcbv xal t&v jtoXcov tov 

10 Xo^ov yQa(po[isvov ^syC6tov xvxkov S(p sxdtSQa tov 
dLa (is6a)v fiotQav d y Xg^ STtl ds tov Xo^ov xvxXov 
trjg 6sX7]vrig dg)^ bTtotSQOv tav 6vvds6^c3v xatd tbv 
tov svbg TtQbg td Td C ^oyov ^oCQag t/3 Lp syyL6ta^ 
tdts JtQcotov dvvatbv s6taL tijv 6sl7]vrjv d7its6^aL trjg 

15 6xLdg. dLa td avtd ds totg xsqI trjv dvcj^aXCav djto- 
dsdsLy^svotg xaC^ otav tb xatd trjv ^s6rjv TtdQodov 
kaii^avo^svov xsvtQOv tfjg 6sk7Jvrjg dg)S6t7]xrj t&v 6vv- 
ds6^cov STtl tov Ao|ov xvxkov ^oCQag Ts t/3, G)6ts Ttdltv 
siLTtCTttSLV xatd tovg dnb tov ^oqsCov TtSQatog dQLd"- 

20 iioi^g slg ts tovg ditb od Ji^ i^^^XQf' Q^ ^/5 xal slg tovg 
dTtb 6vd JiTJ ^sxQL 6Jts i/3, tbts jtQcbtov dvvatbv s6taL 
tr]v 6sXr]vr]v djtt£6d-aL trjg 6xLag. JtaQad^Tj^Ofisv ovv 
totg TtQOXSL^svoLg tcDV 6vt,vyL&iv xavovCoLg xal tovg 



1. ([^ mg. C. 5. ns^Tttoig] 'fs B. 11. Xo^ov] ante | 

ras. 1 litt. A. 12. cccp'] corr. ex icp' D^ dTtozsQov D, 

corr. D^. rov] om. CD. 14. TtQ&tov] a D. %6tcci\ om. D. 

r^v] corr. ex ti)? D^ aeX^qvr^v] comp. D. aipaGd-cci D. 

15. t&v avoaiiaXicbv D. 16. ti]v] om, D. 17. acpsGtTJyirj 

— p. 485, 12. rrjv] fuit etiam in mg. sup. D, sed eras. 19. 
xara] corr. ex xa Dl 20. xai — 21. t|3] mg. D^ stg 

Tovg] sIg D. 22. aipa6&aL D. 



MA0HMATIKHS STNTASE^S 5'. 485 

XG)v re ijXLaxcav xal t&v 6eXrjvi,axcov oqcov tov TcXdrovg 
rfjg aeXTJvrjg aQLd^fiovg^ Xva xal rijv rmv dvvafievcov 
eig exXeiijJLv e^7ce6etv didxQLeLv e^ exoi^ov Ttoicj^ed-a, 

g'. UeQl rrjg dia0rd0eG)g rcbv exXemnxcbv firjv&v, 

Kal dta 7t60cov S* d}g ejtLTCav ^rjvav dvvarbv 5 
e6raL rag 0vt,vyCag exleLTCrixdg yCve^d-ai^ %Qri6iiiLov av 
etrj rovroig TtQo^d-etvaL TtQog ro Xa^dvrag fiCav eitox^v 
exXeLTtrLxfjg ^v^vyCag ^ij 7td6ag jtd^LV rdg icpe^rjg^ dXXd 
rdg dt' o^cav dv ev8e%6^evov fj ^rjv&v exXeLil^Lv yeve- 
ed^aL^ TtQog rijv rav oqcov ejtCdxeilJLV naQaXa^^dveLv. 10 

t6 ^ev ovv dC e^ ^rjv&v dvvarbv eivaL r6v re 
r]lLOv xal rrjv 6eXr]vrjv ixkeCiteLv avr6^ev dv elri drjXov^ 
eTteLdiJTteQ rj ^ev ^e6rj xard nldrog itdQodog rrjg 6elri- 
vrjg ev rotg g firj6LV 6vvdyeL ^oCQag Qitd d xe^ aC de 
ftfra|v rcov exXeLTtrLXcbv oqcov jteQLCpeQeLaL xal iitl tov 15 
ijXCov xal e%l rfjg ^eXtjvrjg aC ^ev evrbg rj^LxvxXCov 
eXdrrovag avrcbv ^oC^ag 7teQLexov6LV^ at (f vit^Q t6 
ri^LXvxkLOV TtXeCovag' rcbv re yaQ rjXLaxcbv oqcov TtQbg 
^ev rdg aQxrovg dTtoXa^^av^vrcov d(p OTtorsQov rcbv 
6vv8e6^G)V ejtl rov Xo^ov xvxXov rfjg 6eXr]vrjg rdg 20 
dTCodedeLy^Bvag [p. 483, 10] ^oC^ag x JLta, TtQbg 8e 
^e6ri^pQCav ^oCQag Td z/3, xal rj ^sv dic ccQxrcov dvex- 
XeLTCrog 7ceQL(peQeLa yCvevai ^olqcov qXi^ Xrj^ r} d' dicb 



1. xe] om. CD. %at] ts -aocC D. x&v (alt.)] om. D. 3. 

sfjLTtsoiv A. 4. ?'] BC, mg. A*, om. AD. 5. dvvarov] 

supra scr. D^, Svvat&v C. 6. yEvsa&ui BC. 7. nQOGd-fivca D, 
sed corr. 9. iyiXsLipSLg yCvsaQ^cci D. 10. nciqaXccyL^dv^ C. 

14. g] s^ BC. ii7]aC D. qnd'] QTt C. 17. «t] -l postea 
ins. C. 18. rjfiLyivKiLov'] i]- corr. ex N A. 22. iisariyb^QCav] 

ft D. xat] om. D. 



486 • KAATAIOT nXOAEMAIOT 

^£6r]^PQi!ag ^olqcjv qv^ Zs^, rav ts ^slriviaKcbv ccito- 
Xaii^avovtov eig ixdreQa ro; ^SQrj rov dia iie0(ov £7tl 
rov avrov tcvkXov ^OLQag aTcb rcbv 6vvd£6[icov i£ t/3, 
xal £xar£Qa rcbv dv£xX£L7CrG)v 7t£QLg)£Q£LG)v ^vvdy^raL 

5 ^OLQCbV Qfld' Ag. 

ort d£ xal d^d rovrcov rcbv V7to^£6£(ov dvvarbv 
£6raL 6£X7Jvr]g £Kk£Lil^LV d^tor^X^Od^rjvaL dta rrjg ^£yL6rr]g 
7t£vra^7Jvov^ rovrd^rtv ocad'^ tjv 6 [isv ijhog rrjv ^^yC- 
6rr]v 7tOL£LraL TtaQodov^ rj $£ 0£X'ijvr] rr]v £laxC6rr]v^ 

10 LdoL^£v dv ovrcog' 

£7t£Ldr] yaQ iv rf] ^£0r] 7t£vra^r]vG} rr]v ^£v xard 
^f]Kog ixar£QOv rav (pdyrov 7tdQodov £vqC6ko^£v £7tL- 
2.a^pdvov6av ^£6cog ^ioCQag q^£ Aj3, rr]v dh 6£Xr]vr]v 
dvco^aXCag £7tl rov i^tLKvxkov ^oCQag Qxd' i, rovrcov 

15 df aC iL£v Qii£ A/3 rov r]lCov ^otQaL xard ri]v icp' ixd- 
r£Qa rov 7t£QLy£Cov ^£yC6rr]v 7tdQo8ov i^ttXa^^dvov^L 
TtaQa rr]v ^£6r]v ^oC^ag d At^, aC d£ rov i^tLXvxXov 
rrjg 6£X7]vr]g Qxd" £ ^otQaL xard rr]v icp' ixdr£Qa rov 
d^toysCov iXaiC6rr]v TtdQodov d(paLQ0v6L rfjg ^£6r]g 

20 fioCQag r] fl, iv ra %()oVg3 aQa rfjg ^£6r]g Tt^vra^rjvov., 
orav 6 ii\v rjlLog rr]v ^£yC6rr]v 7tOLf]raL TtdQodov^ r] dl 
6£Xr]vr] rf]v ila%C6rr]v^ irt 7tQor]yov^£vrj £6raL rov 
r]XCov r] 6£lr]vr] ratg i^ d^cporiQcov rcbv dvco^aXL&v 
6vvayo^£vaLg [loCQaLg Ty Tf]. d)v TtdXLv rb Lp' ka^6vr£g 

25 dLa rd 7tQoa7tod£d£Ly^£va £%o^£V ^otQav d xal i^r]- 
xo6rd ^ £yyL6ra^ r]v 6 rjlLog i7tLXLvr]%"r]6£raL ^£%ql rov 



1. Lz\ corr. ex v^ D^. 6. dwutov] dwarcov A. 7. cs- 
XriVLan-^v D. 8. xovxb6xiv\ comp. B, -v eras. D. 15. Ss] 

d' D. 16. iniXafi^dvovGLV D, -v eras. 17. at] corr. ex 

Slcc D^. 18. fioLQag C, corr. C^. 21. noLfitaL] D, noiSLxaL 
ABC. 24. Xafi§dvovxsg D. 25. nQoSsdsiyfisva D. 26. 

Iisxql] ante % ^^^- 1 litt. A. 



MA0HMATIKHS STNTASESiS ?'. 487 

xataXrj(pd"f}vai, vtco tfjg ^sXTJvrjg. ijtSLdri ovv ix ^hv 
tfjg IdCag avco^aXCag iTt^LlricpeL (loCQag d xal s^rjKo^va 
Xri^ ix ds trjg ^i%Qt, tfjg ocnQi^ovg 0v^vyCag itBQLKata- 
Xrjiljecog aXXrjv ^otQav a xal s^rjK06ta g, £(3taL Tcal r] 
jisyC^trj Jtsvtd^rjvog itaQa f^v ^s0r]v iTtSLXrjcpvta xata 5 
{ifjKog ^oCQag 1 xal £^rjK06ta ^d. to6avtag aQU syyc- 
6ta Kal r} xata TtXdtog iitl tov lo^ox) tcvkXov itdQo- 
dog tf]g esXrjvrjg ijtSLXrjg^vta s6taL ^oCQag totg xatd 
tijv ^sijrjv Jtsvtd^rjvov 6vvayo^svoLg jtlatcKotg TfitJ- 
^a6LV Qvy xd syyL6ta' &6te xal rj aKQL^cog dscjQov- 10 
Hsvr] Katd itldtog TtaQodog iv t^ ^syCetj] Jtsvta^rjv(p 
6vvaxd^r]6staL ^olqcjv Qvd' xal s^r]xo6t&v s. a/lA' oC 
fisv itp^ sxdtsQa tov did ^sdcov ixksLJttLxol xatd t6 
p,s0ov djt66trjpa tfjg 6sXr]vr]g oqol JtSQLS%ov6LV ijtl psv 
tov dLd tav Jtolov tofj lo^ofj yQatpopsvov psyC6tov 15 
^vxXov potQav (iCav syyL6ta dt« t6 tr]v (isv xatd t6 
ikd%L6tov slvaL (lotQav d y Xg^ tr]v ds %atd t6 \isyL- 
6tov ^vvdys^d^aL o vg zd, ijtl ds tofj Xo^ofj tcvkXov 
djtb tcjv 6vvds6(icov t^irj^iata Td k^ r] ds (ista^i) av- 
tc3v xal dvsocXsLJttog jtSQLCpsQSLa d^d tovto 6vvdystaL 20 
fiOLQ&v Qv^ o, aCtLvsg iXdttovg sl6l tav xatd tr]v 
(iEyC6tr]v jtsvtd(ir]vov ijtLXa^iPavo^isvcjv tov Xo^ov kvk- 
kov (lOLQcbv Qvd" Tcal e s^r]Ko6t&v t(ir](ia6L dv6L Tcal 



1. £x] corr. ex a/* C. 2. fTrfdrjqpft] -X- corr. ex J A, 

post cp del. '9' C^. 4. v,al s^rj-noGTd s] <5 D, 6. [lOLQocg^ 

om. C. yiccl f^rjxoara] om. D, 7. 17] om. D. xara] -rd 
add. D^. ■kv-kIov^ ■kv-kXov t) D. 12. yial s^rj-nootcbv^ om. D. 

14. TCEQlixOVGLV^ 7tSQi£X0V6L XOV Xo^OV D, «JTt 15. TCOv] 

bis D, sed corr. 15. rov Xo^ov] om. D. 16. (iLav'] cc BJ). 

17. iXdxiOTOv] hinc inc. A^ fol. 175 (quatern. %y). a] fiiccv A^. 

21. 8l6l] mut. in £L6lv C, sed -v rursus del.; comp. B. 22. 
Xo^ovl -^o- in ras. A^ 23. qv^ v.a.1 s f|7jHO0Tc6v] Iqv %^b D. 

8v6LV B. 



488 KAATAIOT nTOAEMAIOT 

i^rjK06totg e. (paveQOv ovv ix rovtav^ otc dvvatbv 
£6taL tijv esXT^vrjv iv tfj iLeyC6tri 7t£vtaii7]va) aata ffjv 
nQfhtriv naveelrivov ixXeL7Cov6av Tcata tijv aq)' dicote- 
Qov tav 6vvde6^G)v d7tox6Qrj6LV xal iv tfj teXevtaCcii 
5 7cav6ekrivG} 7tdlLV ixXeCTceiv xar«; trjv i7cl tbv ivavtCov 
6vvde6n.ov 7CQ66odov d7cb t&v avt&v fieQcbv Toi) dcii 
^e6a)v iv d^q^oteQacg tatg ixXeCil^e^LV tfig i7CL6xotr]6e(og 
yLvonevrjg xal ovdeTCote dTcb tav ivavtCcov, 

otL ^ev ovv rj fieyC6trj Tcevtd^rjvog dvvatac dvo 

10 7C0Lri6aL 6elrjvLaxdg ixXeCtljeLg^ ovtcog rj^tv yeyove drjXov 
otL de Sl^ e7Ctd ^rjv&v ddvvatov e6taL tovto ^vfi- 
PijvaL^ xdv trjv iXaiC^trjv e7Ctd\irivov v7C0^G)\Le^ay tovt- 
e6tLV xad'' iji/ 6 \iev r]XLog trjv ika%C6triv TCOLiq^etaL 
7cdQodov, 'fj de ^eXtjvrj tijv \ieyC6trjVy l'doL\iev dv tbv 

15 avtbv tQo^cov i(po8evovteg totg ^CQoexted-ec^ievoLg. 

i^cecdii yaQ 7cdlLv iv tfj \ie6r] e7Cta\irjvG) r] \iev 
ixateQov tav <pcbtG)v xatd iifjxog \ie6rj 7cdQodog ijCL- 
ka^ipdveL [loCQag 6y ^Te^ r] S* iv ta iTCLXvxXca trjg 6e- 
Irivrig \ioCQag qtc Jiy^ tovtG)v d^ aC [lev 6y jie [lotQat 

20 rot) rjXCov xatd tijv i(p exdteQa tov dTCoyeCov iXa- 
xC6tr}v 7cdQodov d(paLQ0v6L trjg \ie6r]g XLvr]6eG)g \ioCQag 
d ft/3, aC de roi) i^CLXvxXov trjg 6eXr]vrig qtc ]iy iiotQac 
xatd ti]v i(p' exateQa tov TceQLyeCov \ieyC6tr]v TcdQodov 
7CQo6dyov6LV tf] fie67] [ioCQag &• vr]^ iv tm %q6vg) ccQa 

25 tfjg iie6r]g e7Cta\i7]vov , orav 6 \iev r]XLog ti]v iXa^C- 



3. 6c(p'] A^C^p^ icp' BCD. 5. zov] rcbv C. ivavticov C, 
sed corr." 6. Ttdgodov D. 7. i-aXsLipieL D. 11. ccdvvatov'] 
corr. ex dvvoctov B^C^. 12. tovtsGtt, D, comp. B. 17. 

«ara] corr. ex xa D^ 18. 3'] di D. 22. QTt JTy fiOLQai] 

fi, QTt Jvy B. 23. (isyiGt^\ C. 24. nQoedyovGi D. Q-] corr. 
ex o D*. 25. iisGT]?] A.\ iXaxtGtrjg BCD; cfr. p. 493, 14. 



MA0HMATIKHS STNTASES^S S'. 489 

<?Ti;i' TtotiltaL TCccQodov^ Yi de aslrjvr} xriv ^eyLatrjv^ 
TCccQsXrjXvd^vta e6tai tbv rjXcov r] es^rjvrj tatg s^ a^~ 
(potSQCJV tG)v avcoaaXccov ^vvayo^Bvaig ^OLgatg lS ]i. 
G)v dia ta avta tb i^' ka^ovtsg xal TtQO^d^svtsg tatg 
SK tfjg rjUaxrjg dvco^aXcag sXkskoiTtviaLg ^OLQaLg d ftjS 5 
tag evvayo^svag [lOLQag £ vs syyL^ta s%o^sv^ o6aLg ri 
ts xaxra ^fixog TCccQodog sv tf] slaxL6tri STttafirjvc) v6ts- 
QY16SL trjg sv tfl iLs6ri^ xal rj ocata TtXdtog d)6avtcog 
sXXsLipSL tcbv Kata tr^v fis6r]v sjttd^rjvov ^vvayo^svov 
t^rj^dtcov 6Ld ft/3* sv t^ sXaxL6tr] ccQa STttaarjvc) sjtSL- 10 
Xricpvta s6taL Katd nXdtog rj 6sXr]vr] sitl tov Xo^ov 
kvkIov tfirj^ata 6rj ft^ oXrjg tfjg (ista^v t&v SKlsLTttL- 
Kcbv Katd tb ^s6ov aTto^trj^a tcbv tf]g 6slrjvr]g oqcjv 
tofj ko^ofj kvkXov fisyL6tr}g nsQLCpsQsCag tov ts Katd 
tf]v 7tQ06ayG3yriv tov stSQOv tG)v 6vvds6^c3v koI tov 15 
Katd f^v d7to%(x)Qri6LV tov svavtCov 6vvds6^ov t^rj- 
^dtcov ov6rig 6y o. ovk ccQa dvvatbv s6taL trjv 6s- 
lfjvr]v ovd' sv tf] sXa%C6tr] S7tta^Y]V(p iKXsC7tov6av 
Katd tf]v 7tQ(6tr]v 7tav6skr]vov b7tco6dr]7tots Kal xatd 
tf]v tsXsvtaCav 7tav6sXr]vov stL SKksC^tSLV. 20 

dsLKtsov df] 7tdXLv^ otL Kal tbv iqlLOV dvvatbv 
s6taL 7taQd totg avtotg dlg SKksC^tSLv sv t§ ^syC^trj 
7tsvta^f]V(p Kal Katd Ttdvta td ^SQrj tfjg Kad'' r](iag 
OLKov^svr]g. 

s7tSLdf] yaQ sv t^ ^syC6tr] 7tsvta^7]V(p tf]v Katd 25 
7tkdtog 7tdQodov tfjg 6slr]vr]g d^tsdsC^a^sv [p. 487, 10] 
t^r]^dtc3v Qvd" s tfjg dvsKlsC^ttov 7tSQLcpsQsCag iTil tov 
r]XCov Katd tb fis6ov d7t66tr]iia tf]g 6sXr]vr]g tav av- 

1. noLBtrcii C. 7. tv t^] corr. ex Byyicru D^. 13. rcov] 
om. D. 18. ov8'^ ovds D.' 20. iyiXmuv D, corr. D^; item 
lin. 22. 26. osXsivrjg A^ 



490 KAATAIOT nTOAEMAIOT 

tcjv yLvo^Evrjg q^^ Ag dca t6 xccl rovg sxX£L7CtLX0vg 
OQOvg avtov tov dia ^s6(x)v aitsxsLV stcI ^sv tov dia 
tcjv TCokfDV avtov TtvTikov t^7]^ata o A/3 jc, stcI ds 
tov Xo^ov tTjg aslrivYig ^ocQag g i^ s'yyi6ta^ dfjXov^ 
6 ott ^rjSsv ^sv 7CaQaXXa06ov67]g tTjg 6sX7]vrjg advvatov 
s6taL t6 jcqoxsl^svov dca t6 [iSL^ova sivac trjv avsx- 
XsLJCtov 7CSQL(pSQSiav tf^g sv tfi ^syL^trj jcsvtafLTJvG) 
TCaQodov t[ir]^a<jLV sjcl ^sv tov Xo^ov xvkXov t] Aa, 
STcl ds tov TCQog OQd^ag tc5 dtd ^s^cjv o ^ syyL^ta^ 

10 07C0V d' av dvvrjtaL 7caQalkd66SLV ovtcog^ C36ts tag sv 
bjcotSQa tcDV axQcov Cvvodcov rj xal tag 6vva^q)otSQC3v 
ccfia 7CaQakXd^SLg ta o ^ls v7CSQ^dXlsLV , sxst dvvatbv 
€6taL xal tdg dxQag 6vv6dovg d^(potsQag sxXsL7CtLxdg 
yLvsed^aL. 

15 S7CSLdrj ovv sdsL%a^sv [p. 486, 20] iv t& XQOvfp trjg 
^syL6tr]g 7Csvta^r]vov , otojv rj ^sv 6sXr]vr] tf]V sXa%L- 
6tr]v 7C0Lf]taL 7cdQodov, 6 ds r]XLog tf]v ^syL6tr]v aTCO 

tCOV dvO ^SQCbV tfjg IlaQd^SVOV ^S%QL tCJV dvo ^SQCJV 

tov 'TdQOxoov^ 7CQor]yoviisvr]v stL tov r]XCov tf]v 6s- 
20 Xf]vr]v talg sx tf]g d^(potsQG)v t&v dvca^aXL&v ^OLQaLg 
Ty Tfj^ tavtag ds xal stL t6 l^' avtcjv r] 6sXf]vr] kl- 
vsLtai ^s6G)g sv r]^SQg: d xal ojQaLg /3 d\ cpavsQov^ 
otL tov XQOvov trjg ^s6r]g 7CSVta^f]vov tvy%dvovtog 
r]^SQCov Qfi^ xal Sq&v syyL6ta Ts i! d' 6 tf]g ^syL6tr]g 
25 7Csvta^7]vov ;updi/og s6taL r]^SQG)v Q^r] xa\ g)qg)v Trj. 
xal dLd tovto tfjg 7CQ(Dtr]g xal 7CsqI td dvo ^SQr] tf]g 



6. fiEv'] om. C, 10. naQCiXdaaELV A}. xdq\ om. D. 14. 
yaviaQ-ai D. 16. iLsyCavrig] -r]g in ras. A\ ^iar^g D. nevza- 
li^^vov] n- in ras. A}. 19. nQoriyov[iEV7\v'] -r]v comp. add. C^ 
20. rmv] om. D. avco(iaXCag D. (loCQag C. 21. t^'] 

l' §' A^ (" in ras.), C. 22. (iia\cog mut. in (is\acog A^ mQag C; 
comp. D, ut saepius. 



MA0HMATIKHS STNTASESiS <S'. 491 

IlaQd^svov yLvo^evrjg 6vv6dov 7} xeXevxaLa zal tvsqI 
xa dvo ii£Qri tov ^TSqoxoov yLVO^evri tcqotsqov £0taL 
taig slg okag rj^EQag XsL7tov6aLg cjQaLg g. ^rjtrjtsov 
(XQa^ jtov xal Ttots dvvataL 'fj 6slr]vrj 7taQalXd66SLV 
rjtOL sv ta stSQip tcov jtQOKSL^svmv dcodsxatrj^OQLCov 5 
rj sv d^(potsQOLg ^caro: trjv sv t(p ^TdQOiocp tr]g sv t^ 

IlaQd-SVC} JtQO ^ ^Q&V 6td6LV TtXslOV t&V SXKSL^SVCOV 

/la s^r}K06tS)V. 

TtQog ccQxtovg fisv ovv ovda^rj tfjg xa^ rj^ag ol- 
xovfisvrjg^ xad'' ov SLQrjxa^sv tQOTtov^ svQL^xstai to6- 10 
ovtov 7taQalXd(56ov6a rj 6slr]vrj' od^sv ddvvatov yC- 
vstaL t6 sv tfj iisyC^tri Ttsvta^rjvc) dlg sxksC%SLV tbv 
iqlLOV xatd trjv djtb ^s^rj^^QCag tov dta fis6c3v trjg 
0sXrivrig TtdQodov, tovts6tLV otav xatd ^sv trjv 7tQ(h- 
trjv Gvvodov dTtoxcoQT} tov xata^Lfid^ovtog OvvdsG^ov^ 15 
xatd ds tijv tslsvtaCav 7tQ06dyrj t(p dva^L^dt,ovtL' 
TtQog ^s^ri^L^QCav ds 0%sdbv ditb tCbv fistd tbv C6r]- 
^SQLvbv OLXOvvtcjv Sg TtQbg tdg aQxtovg dvi/atat tb 
to6ovtov sv d^KpotsQOLg tolg sxxsL^svoLg dcjdsxatrj^o- 
QCoLg xatd vrjv 7tQb s^ Sqcjv ^s6lv 7taQakXd66SLV^ 20 
otav td ^sv tfjg IlaQd-svov dvo ^sQr] xatd trjv 7tQ(D- 
trjv 6vvodov STtl tf\g xatadv6sc3g V7toxsr]taL^ td ds 
Toi) 'TdQoxoov xatd trjv dsvtSQav 6vvodov S7tL tov 
fis6r]^pQLVov ' xatd yaQ tdg toLavtag %'s6ELg £{)qC6xo- 
^sv tr]v 6slr]vr]v stcI tov ^e6ov d7to6tY]^atog 7tQbg 25 



Q Y 

1. TcciQ D, ut saepius. 2, v8qo D, ut saepius. 4. 17] 
in ras. A^. naQa'kl(x.66'^\ C. 6. vdQiqxoo) A^. 7. TtXsLcov C. 

10. toaovtov svQL6KEtaL D. 11. 17 asXijvr}] om. D. 12. 

sv.XELnsLv'] supra -IsC- add. v D^ 15. aTioxoiQ^] D, anoxcoQEv 
A^BC. %a^L§(ktovtO(s D, corr. D^ 22. vn6v,£Ltai D, corr, D^ 

25. Post nQog locus relictus ob naturam pergam. D. 



492 KAATAIOT nTOAEMAIOT 

^£6r}^PQLav 7caQaXMd6ov6av VTtoXoyov^svrjg tflg rjXta- 
xijg TtaQakld^ecog vito ^lv xov C6rj^£QLvbv iv ^lv t^ 
tfig IlaQ&evov %'£6£l ^OLQag o x^ £yyL6ta^ iv d£ tfj 
tov ^TdQoxdov o td, oitov 61 rj ^£yL6trj r}^£Qa cjq&v 
5 £6tlv Lp L\ Tcata ^£v tfjv tfjg IlaQd^dvov d^i^LV ^OLQag 
o Tc^y Tcatd d£ tfjv tov 'TSqoxoov ^OLQag o x/J, cog 
ivt^vd^^v ijdrj 6vvancpot£Qag tdg 7taQaXXd^£Lg i^rjTco^tolg 
d v7t£Q^dXk£Lv td 7tQ0K£L^£va o ^. 7tX£LOvog Sfj xatd 
tovg PoQ£Lot£QOvg d£l t67tovg tfjg 7tQbg ^£6rjy,^QLav 

10 7taQalXd^£G)g yLVO^ivrig (pav^QOv^ otL xal ^dXXov d^l 
dvvatbv £6taL tolg iv avtotg oixov6L 8lg iv tfj ^i^yC- 
6trj 7t£vta^7]VG) cpavfjvat tbv ^hov i7cX£L7tovta^ %atd 
^ovrjv ^ivtOL tfjv d7t ccQKtcav tov dta y,i6a)v tf]g 6£- 
Xrjvrjg 7tdQo8ov^ tovti6tLv otav i7tl ^£v tfjg ^tQcotrjg 

15 ixX£L^£cjg aTtoxcDQf} tov dva^L^dt,ovtog 6vvdi6^ov^ iTtl 
§£ tfjg d£vtiQag 7tQ06dyr] ta 7cata^L^dt,ovtL. 

Xiyco 8fi Ttdhv^ otL ocal iv trj ikaxC6tri £7tta^7]v<p 
dvvatbv £6taL dlg tbv ^Xlov 7taQd totg avtotg ixX^C- 
7t£Lv. i7t£Ldfi ydQ iv tfj ilaxC6tri £7tta^7]vG) tf]v xatd 

20 TtXdtog tfjg 6£Xr]vr]g 7tdQodov d7t£6£L%a^£v [p. 489, 10] 
t^r]n,dxG)v &^ |Lt^, fi£yC6tr]g d' dTtoXa^fiavo^ivrjg ^£ta^v 

tCbV ixX£L7ttLXG)V OQCJV 7t£QL(p£Q£Cag tOV Xo^OV XVXXOV 

tf]g dTtb to\) Tcatd tf]v 7tQ06ayG)yf]v toi) itiQOv 6vvdi6- 
^ov ^iixQt^ T^ox) xatd tf]v d7toxd)Qr]6Lv tov ivavtCov 



4. 5^] -8 in ras. D^ 5. i6TC D, comp. B. pLoCqag] 

om. D. 6. %^] corr. ex n^ D^ ^oLQag] om. D. 7. i]8r]] 
om. D. 8. d^'] corr. ex ds D*. 10. (i&XXov ccsl dvvarov'} -v 
asl S- euan. et eras. A^ {NA//J). 12. itiXsCnovta] -s- in 

ras. A^. 15. ccTtoxcog'^] D, a7to%o3QSi A^BC. 17. tiirivca D. 
18. xhv fjXiov SCg D. nagd roLg] post ras. 5 litt. corr. ex 

nag' D^ 19. Post slaxiGtrj del. r^ Cl 21. d'] Ss D. 23. 
Gvvdsc^ov'] 6- in ras. A^. 



MA0HMATIKHS STNTA^jEiiS g'. 493 

fSvvddo^ov 6vvdysxaL ocal aTcl tov rikCov rj xoiavxri 
did6xa6Lg STtl xov ^s6ov xfjg 6ek7]vrig d7to6x7]^axog 
x^rjiidxcov QCfp xd, dijAov, oxi, ^rjdsv ^sv TcdXiv TtaQuX- 
Xa66ov0r]g xfjg 6sXrjvr]g ddvvaxov s0xaL xb tcqoksC^svov 
did xb ^sC^ova slvav xijv xfjg sla%C(Sxrig STtxa^rjvov xov 5 
Ao|oi) kvkXov 7tSQL(psQSLav xrjg 'bitb x&v sxXsLTtXLxav 
OQcov xov rikCov ^syC^xrjg aTtoXa^Pavo^svrjg x^rj^a^LV 
STtl iisv xov Ao|ov xvkIov Ig jcy, STtl ds xov dLa x&v 
TtoXcov xov ^(pdLaocov d tcs^ onov d' dv dvvrjxaL TtaQaX- 
Xd66SLV ovxcag^ co6xs xdg iv ditoxsQa xcbv cckqov 6vv6- lo 
dcav rj xal xdg 6vva^(poxsQC0V dua TtaQakld^SLg vjtSQ- 
pdXXsLV xr]v d Tis ^olQaVj sksl dvvaxbv s6xaL xal xdg 
dxQag 6vv6dovg d^(poxsQag sxksLTtxLxdg yCvs^d^aL. STtSLdr] 
ovv sdsC^a^sv [p. 488, 24] sv xa XQ6v(p xfjg ^s6r]g 
STtxa^TJvov^ oxav r] ^sv 6sXr]vr] xf]v ^syC6xr]v 7toLf]xaL 15 
%dQo8oVj 8\ r]XLog xf]v sla%C6xr]v d%b xcbv s6xdxcjv 
xov ^TdQOxbov ^sxql xcbv ^s6cov xfjg UaQd^svov^ TtaQ- 
sXr^Xvd^VLav i]dr] xf]v 6slr]vr]v xbv iqkLOV dxQL^&g ^oC- 
QaLg Ld iLt, xdg ds xo6avxag fioCQag xal sxl xb l^' av- 
r&v r] 6sXr]vr] xLvstxaL ^s6cog sv rj^SQcc ^ia xal coQaLg 20 
Sy (pavsQbv, 6xL xov xQ^^^ov xf]g ^86r]g STtxa^irjvov 7ts- 
QLSXovxog f]^sQag '^g xal coQag l^ syyL6xa 6 xfjg ska- 
xC6xr]g S7txa^r]vov XQ^^^^S s6xaL f]^SQG)v 6s xal coqgjv 
t/3, xal dLa xovxo 6 xfjg xslsvxaCag xal 7tSQl xd ^s6a 



3. iiiv] supra scr. D^. 9. TcaQccldaEiv D, alt. X supra 

add. D*. 10. xdq\ xd D. 11. xat] om. D. itccQaX^d^sis D. 

13. yiyvEGQ^^ai D, ytyvfC-S-"'! ^^- ^^- V^^yCcxrivl corr. ex 

fisarjv D^. noiBtxcci A^C. 17. naQsXbXvd^vLav C, sed corr. 

18. ^oLQaiq^ A^CD, comp. B. 20. xr]v asXi^vrjv D, sed 

corr. 1^.^0005] om. C, a ty iieaoog B. ^lcc] d C. 21, xfjg] 
seq. ras. 3 litt. D. 22. xat] comp. postea ins. C. 24. 6] 
postea ins. D. 



494 KAATAIOT nTOAEMAIOT 

trjg UaQd^avov ijvvodov XQ^^^^S ^£ta l^ 6}Qag £6tat 
tov tfjg 7CQG)trjg xal tisqI ta f^^^arc»: tov 'TdQOxoov. 
^rjtrjteov aQa^ tcov xal jcdts dvvatai rj ^sXTjvrj utXstov 
tfjg a X6 iLOLQag 7CaQaXXd66eLv rjtOL iv t(p itSQG) t&v 
5 TCQOKSL^svcDV dcjdsxatrj^oQLCov ij iv d^tpotSQOLg Tiata 
tijv dtd Lp d}Q&v ^s6lv^ tovtsCtLV otav tb ^sv stSQOv 
dvvr]y tb ds stSQOv dvatsXXrj^ dLa tb ^r]da^cog dlXcjg 
dvva^d^aL tdg ixXsLtl^SLg d^(potsQag vtcsq yfjg yLVSOd^aL, 
TCQbg aQXtovg ^sv ovv TcdlLV ovda^f} tfjg xad'' rjiidg 

10 OLXOv^svrjg ^car' ovdsfiLav d^s^LV to6ovtov svQL6xstaL 
7CaQakXd66ov6a rj 6sX7]vrj iirjd' avtotg totg VTcb tbv 
L6rj^SQLvbv ^st^ov s^r]xo6t(x)v xy tfjg xatd tb ^syL6tov 
djc66tr]^a yLvo^svrjg xatd nkdtog TCaQakXdh^scjg' od^sv 
ddvvatov yCvstaL iv tf] iXa%L6tr] S7Cta^7]VG) dlg ixXsC- 

15 7CSLV tbv r]Uov xatd tf]v dicb ^s^rj^iPQLag tov dLa 
fis6c3v tfjg 6slr]vr]g TCaQodov^ tovts6tLV otav xatd fisv 
tf]v JCQotSQav 6vvodov 7CQo6dyr] tip dva^L^dt^ovtL 6vv- 
ds6^G)^ xatd ds tf]v tsXsvtaCav d7Co%G)Qf] tov xata^L- 
pd^ovtog' 7CQbg ^s6r]^pQLav ds tf]v to6avtr]v 7CaQdl- 

20 Xa^Lv svQL6xo^sv d7CotsXov^svr]v 6xsdbv d7cb tov dcd 
^Pddov 7caQaklrilov^ orav td ^sv s^^ata tov 'TdQOxoov 
dvatsXXf]^ td ds ^s6a tfjg IlaQ^svov dvvr]. TCaQak- 
ld66sL ydQ iv ^P68(p xal totg V7cb tbv avtbv 7CaQdk- 
Xr]kov t67COLg xad"' sxatsQav tovtcov tcov d^s^scov r] 6s- 



3. nov] supra scr. C^. 4. naQuXdGGsiv D. 7. a.vuxeXin D, 
corr. D*. 8. yCyvsGQ^ai D. 9. ovv'] om. C. 11. TCccQaiccG- 
Govaa D. 12. ^el^ov — fiEyLGtov'} supra scr. D*. 13. y,ar<x] 
A^D, xccToc t6 BC. Ante od^sv del. advvarov D. 14. 

yiyvhxai D. ivlsiiiuv'\ -%- supra scr. C, post l- del. y D, 

17. Gvvodov] coiT. ex gvvoXov D^. 18. aiioioiQhi B. 22. 
^ica T7)s] corr. ex (isGoyfig D. naQdsv C, " supra q add. C^, 
sed euan. naQaXXaGSL A^; TtaQaXdoGSL D, corr. D^ 23. toig] 
S supra scr. D^. 



MA0HMATIKHS STNTASESiS ?'. 495 

X7]vr} xara tb ^sdov d7t66trj^a rijg rjXiaxrjg TtaQaXXd- 
^scog vq^aiQOv^svrjg TtQog ^s^rj^^Qiav dvd o ]i^ syyi^ta^ 
cog tdg iv d^^potsQaig talg avvodoig TtaQalld^sig iv- 
tsvd^sv rjdrj ^st^ovg yCvsGd^aL trjg ^idg fiocQag Tcal tCbv 
its s^rjK06tG)v. TtlsCovog drj yvvo^svrig tfjg TtQog ^s6rj^- 5 
^QCav TcaQalld^scog iv totg sti tovtov tov TtaQalXrilov 
PoQSiotsQoig cpavsQov^ ort dvvatov s6tai totg Kat 
avtovg oCxov6l dlg iv tfj iXaxCatrj sjttafiijvG) sxXsLif^tv 
rjXCov cpavrivai^ jcatd ^ovrjv ^svtot TtdXiv tijv dit 
ccQXtcov tov did ^s6c3V tfjg dsXrjvrjg TtdQodov^ tovt- 10 
s6tcv otav iitl fisv tfjg TtQCJtrjg ixlsC^scag 7tQ06dyrj 
tc5 %ata^ipdt,ovti 6vvds6^G), inl ds tfjg dsvtSQag d%o- 
IGiQTi tov dva^i^at^ovtog. 

%ataXsC%oito d' dv ijtidst^ai xaC^ ort did ^rjvbg 
svbg ov dvvatbv s6tai dlg tbv rjXiov ixXsCjtsiv iv t^ 15 
^«0"' riiidg oCkov^svt} ovt iv ta avta xXC^ati ovt' 
iv diacpoQOig^ xdv itdvta ttg d^a vTtod^rjtai td fiij dv- 
vd^sva ^sv 6vvdQa^stv, 6vXXa^^av6^sva d' dXXGig rw 
dvvatbv 7toif}6ai tb TtQoxsC^svov ^ Xsyco df, xdv tijv 
^sv ^sXijvrjv Katd tb iXd%i6tov d7t60trj^a vjtod^co^sd^a^ 20 
iva TtXstov 7taQalkd<j0rj , tbv ds ^fjva ild%i6tov^ Iva 
06C0 dvvatbv sla%C6tcp ^sC^cov rj xatd TtXdtog ^rjViaCa 
TtdQodog yCvrjtai tfjg vitb tcbv ixXsiTttix&v oqcov tov 
rjXCov 7tSQiS%o^svr}g^ Tcdv ddiacp^QCog tatg ts wQaig xal 



2. 0] ins. D*. 3. rag iv'] ratg iv C, xcclgvv D (t mut. 

in c?). 4. yLVtcQ^aL] corr. ex y£VE6d-ca D^ 5. yiyvofiivrjg D. 

6. sxi] -X- in ras. A^ 8. iXa%i6X(o D. 11. TtQcotrig] bis D, 
sed corr. 14. ini8ugai\ -n- mut. in r C^, hi dstiaL D. ^ta] 
post ras. 2 litt. D. 16. o^x' iv (pr.)] 0- corr. ex x in scrib. C, 
o^xs D, o^xE iv D*. o^x' iv (alt.)] ovxs D, o^xs iv D^. 17. 
yiav'] g' C. rtg] corr. ex rrj D^ 18. 6vvXaijL^av6fisva A^BC. 

20. yiaxci rd] corr. ex yiax D. 21. 7caQaXd66rj D. 23. vnb 
xav] vnb x- in ras. A^ illsLnxL-Aibv D, corr. D^ 



496 KAATAIOT nTOAEMAIOT 

totg dodsKatrj^OQiOLg xat axQrj^co^sd^cc, xccd'' g)v tag 
lisyL6tag (paCvstaL TtaQakkd^SLg jcoLOV^svrj, 

STtsl tOLvvv sv t& iLS&G) ^Tjvl Tj fisv Tcatcc fifjxog 
sxatsQov tcbv (pcjtcov TtccQodog STCLla^pdvsL ^s6cog (iol- 
5 gag Kd' g, ri ds xatd tbv iTtLKVxXov tijg 6sX7]vr]g ^oC- 
gag xs ftO", tovtcov d' at ^av Tcd' g tov riXCov xatd 
tr^v S(p' sxdtSQa tov djtoysCov ska%C6triv Ttdgodov 
d(paLQ0v6Lv trig iis6rjg ^otQav ^Cav rj^ aC ds tov STti- 
Tcvxkov tfjg 6skrjvrig %s fid' ^otQaL xatd trjv scp" sxd- 

10 tsga tov TtSQLysCov fLsyC6trjv jtdQodov jtQo^tLd^sa^L t§ 
lis6rj ^oCQag /3 xrj^ sdv dKokovd^cjg totg TtQoanodsdsLy^s- 
voLg ^vvd^svtsg tdg i^ d^tpotSQCov tav dvcafialL&v 
7tQ06d-a(paLQS6SLg tcbv yLVO^svcov y kg tb l^' td o Trj 
jtQO^d^cb^sv^ olg 6 rjXLog ikXsXoCTtSLy 7toL7]6o^sv t^ri^ata 

15 « xg aal to6ovtOLg s%o^sv iXd66ova trjv tov iXa%C6tov 
^rjvbg TtdQodov trjg iv ta ^s6g) ^rjvl xatd ts ^rjxog 
Tcal xatd TtXdtog' co6t\ ijtSLdrjjtSQ r] tov ^s6ov ^irjvbg 
xatd Jtldtog TtdQodog ^olqcjv i6tLv X JLt, triv tov iXa%C- 
6tov TtdQodov yCvs^d^aL ^olq&v x& lS^ oCtLvsg 7tOLOv6Lv 

20 i^tl tov TtQog OQd^dg ta ^mdLaxa ^syC6tov xvxXov 
tariiiata /3 Xy syyL6ta. dXXd rj 7td6a tcov ixXsLTttLXov 
OQCov tov r]XCov 7tdQodog 6vvdystaL xatd tb iXdxL6tov 
d7t66tr]iia trjg 6sXr]vr]g ov6r]g t^rj^dtoov d ^, cyg ^sC^ova 

6. jLt^] corr. ex ^Ts D^ 8. cccpccLQOvoiv] -iv e corr. A^C, 

acpaiQovGL BD (-t in ras. D). 10. tov] supra scr. D*. 11. 

TtQoaTtodsdELy^svoLs] Tt- e corr, in scrib. C. 13. yLyvofisvcov D. 

14. 7toii]6o(isv] corr. ex noLiJGo)(isv D, noLi^aojfisv A^BC. 

r/xrj/n-ara] -tu supra scr. D. 15. a} fiLa D. s^co^sv D, 

sed corr. 16. Ante firjvog del. t D. xa D, ut saepius. 

17. wffr' — 18. TtaQoSog] mg. D^ (raffrf), naQoSog etiam in 

textu. 18. saTLv'] comp. B, -v eras. D. 21. T^-qiia D. 22. 
iXdx^TOv D, sed corr. 23. a] ^La D. 



MA0HMATIKH2 STNTASESiS <5'. 497 

yivs^d^ai rriv tov iXa%i6tov ^rjvbg naQoSov t^7]^a6cv 
a x^. deov ovv av sltj Tcdvtag^ eticsQ iv ta ivl ^rjvl 
dlg 6 ijXcog ixXsLTCOL^ rjtoc xata ^sv tr^v itsQav tG)v 
6vv6dcov ^rjdsv 7caQaXkd66SiV trjv 6sXr]vrjv^ xatd ds 
tr]v itSQav TcXstov tav d x^, 7) xad'' ixatSQav fisv 5 
TcdXiv t&v 6vv6d(ov ijcl td avtd 7CaQalXd00scv , tr]v 
d' v7CSQ0%riv tav TCaQaXkd^scov ^sc^ova slvai tmv d %J, 
r) 0vvau(potSQag tdg jcaQaXXd^sig TcXsCova tcav avt&v 
6vvdysiv tfirjfidtcDv^ orai^ rj ^sv tfjg itSQag 0vv6dov 
yivrjtai TCQog aQXtovg^ rj de trjg itSQag TCQog ^s^ri^^Qiav, 10 
«AA' ovda^fj trjg yijg iv tatg av^vyiaig ovds xatd tb 
iXdii6tov aTCo^trj^a TcXstov rj 6eXr]vrj xatd TcXdtog 
naQaXXd66ei tfjg riXiaKrjg TcaQaXXd^ecog vTCoXoyov^svrjg 
ILiag ^oiQag. ovk aQa s6tai dvvatbv iv tm iXaxC^tco 
lir]vl dlg iKXsiTCSiv tbv rjXiov^ otav ijtoi xatd ^sv tijv 15 
itsQav tcjv 6vv6dcov ^rjdsv r] 6sXr]VYi jcaQaXXd66rj rj 
Kat d^icpotsQag ijcl td avtd 7CaQaXXd66ri ^ trig v7CSQ0xf]g 
avtav ^rj 7cXsiovog yivo^svrjg trjg ^iccg ^oiQag dsov 
xal t&v d K^. ^6vcog dv ovv tb ^cqoksC^svov dvvaito 
6v^^aCvsiv^ Si i7Ci td ivavtCa yivo^evrjg iKatSQag tcbv 20 



1. sXax-tov D. 2. a] jttta D. av ovv D. 3. ^4] S^ 
supra scr. D. 6] om. D. Mg. 6 ^ Sig D^ 4. nccQ- 

uXXaGBLv D. 5. Ante a eras. ^ D. Bv.axiQav^ corr. ex 

iv.axBQa D^, exEQav A^. 6. ndXiv'] om. A\ corr. ex nccQodov D*. 

7taQaXXdGsi\ D. 7. d' vnEQOxriv'] corr. ex dvonsQoxriv D. 

8. nXBLOval D et post ras. 5 litt. A\ nXaiovaG BCDl 10. 

dQyiTOv D. 11. xaLg] rsc D. xara] X/: D. 12. Hara] 

corr. ex dh v.atd D, vatd x6 C. 14. Svvaxov] corr. ex dSvva- 

xov C^. 16. 6vv68(ov~\ Gv^vyL&v D. i} CEXrjvrj] rjo D, 17 c* D*. 

naQaXXaGGEL A^C. 17. naQaXXdGTj D. 19. a] ^iLa D. rd] 
ins. D^ dvvaixo] corr. ex dvvaLxov D; dvvaxai C, sed uide- 
tur corr. C^. 20, Gvfi^aivELv] x6 Gvii^aivsLv C. 

Ptolemaeus, ed. Heiberg. 32 



498 KAATAIOT nTOAEMAIOT 

^aQaXMl^scov i^ d^tpoteQcov TtXstova rcbv a x^ tfiTJ^ata 
^vvdyoito. tovto d' STtl diafpoQov ^sv oixov^svrjg iv- 
dsxo^svov s6tai did t6 dvva^d^ai TtaQa ^sv totg ^oqslo- 
tSQOtg tov i^rj^SQtvov t&v iv tfi xad'^ rj^ag otxov^svri 
6 nQog ^s6rj^PQLav 7taQaXld66stv f^v esXtjvrjv, TtaQa ds 
totg vottcotsQotg tov t^rj^SQtvov tcbv dvttx^6vG3v xa- 
2,ov^sv(ov TtQog aQXtovg 3taQaXXd06stv ^std tijv tov 
'^ktov TtaQdXka^tv ditb o xs iis%Qt ^otQag «, inl ds 
trjg a^r^g oixov^svrjg ovx. dv jtots ^v^^airj dtd tb 

10 7tXsi6tov trjv 6sl7]vrjv 7taQaXkd66stv c)6avtGig JtaQa 
^sv totg 'bTc' a^dtbv tbv i^rj^sQtvbv ov %kstov s^rj- 
xo6tG)v xs jtQbg ccQTttovg ts %al ^s^rjftpQtav ^ TtaQa ds 
totg fioQStotdtotg t) vottcjtdtotg avtcbv ^rj Ttlslov ijtl 
td dvttxsi^sva trjg TtQoxst^svrjg fitag fiotQag^ Sg xal 

15 ovtcjg ht ikd66ovag ^vvdys^d^at 6vva^(potSQag tdg 
TtaQaXXd^stg t&v d x^ t[irj^dtC3v' 7tokX& d\ iXd66ovog 
ijtl tcbv ^sta^i) tov ts i6rj^SQtvov xal tov stSQov 7ts- 
Qatog sxatSQag t&v dvttxst^svcov TtaQaXXd^scov dsl 
ytvo^svrjg TtQOxdittot dv stt ^aXXov TtaQ avtolg tb 

20 ddvvatov. naQa ^sv tolg avtolg aQa ovda^fj tfjg yfjg 
dlg iv ta svl ^rjvl dvvatbv s6tat tbv rjXtov ixXstTtstVy 
TtaQa ds dtacpoQotg ovda^ifj tfjg a^htfjg oixov^svrjg' djtSQ 
rjiilv TtQOSxstto dsl^at. 



t 



1. a\ fiia D. t(ir}iia D. 2. avvdyoi D, corr. D*. 6. 
voricarsQOLs] corr. ex votsioxEQOig D, et similiter saepius. i67\- 
liSQivov] l- ins. D', -Qi- e corr. D. avtix&ovi' D. 8. xs] 

X B. 9. d%ov[i8vrig D, sed corr. 12. }i£as[i§Qiag D, sed 

corr. 19. yiyvofiivrig D. 21. ^Xiov] et seqq. multis 

compp. C uersus finem fol. 188^. 



MA0HMATIKHS STNTASESiS ?'. 499 

^\ IlQccyiiatSLa xavovicov iKX£U7tti%&v. 

Ilotag ^lv ovv dLa6td6£tg t&v 6vt,vytG)v eig trjv 
£7tt6K£^LV tmv £7iX£t7l)£Cx)v 6(p£tXo^£v 7CaQaXa^^dv£tv^ 
dtd tovtcDv ri^LV y£yov£ driXov^ OTtcog dh tav t£ xat 
avtdg ^£6g}v xQOVov dLaxQL^£vtG)v xal tCov iv avtotg 5 
TtaQddcjv trjg 6£l7Jvr}g iTtLXoyL^d^^L^cbv £7tl ^£V t&v 
6vvodL7c&v 6vt,vyLG)v tcbv g)aLvo^£vcov ^ £7tl d£ tcbv 
7tav6£XrivLaKS)V tcov dxQLpav^ dLa t&v xatd 7tldtog 
£7toicav tfig 6£X7Jvrjg 7tQ0%£LQG)g i^tL^Tci^tt^^d^aL dvvd^^^d^a 
tdg t£ Ttdvtog £6o^£vag £xX£L7ttLxdg tcbv 6v^vyLcbv xal 10 
tovtcav td t£ ^£y£^ri xal tovg XQOvovg tcbv £7tL6xotri- 
6£cov^ £7tQayiiat£v6d^£d^a xavovLa 7tQbg tijv tOLavtrjv 
dLdxQL6Lv dvo ^£v tcbv rjlLax&v £xX£Lip£Ci3v £v£X£v, dvo 
d£ tav 6£lrivLaxG)v xatd t£ tb ^£yL6tov xal tb iXd^t- 
6tov trjg 6£?,7]vrjg d7t66trj^a^ v^tod^i^^vot tijv 7taQav^r}6tv 15 
t&v i7tt6xot7]6£cov did dcod£xdtov ^£QOvg tijg i7tt6xo- 
tov^ivrjg dta^itQov ixatiQOv tcov (patcov, 

tb ^£V ovv 7tQcbtov xavovtov tcbv rjXtaxcbv ix- 
X£Li(;£cov, 7t£Qti%£t toi)g xatd tb ^iyt6tov aTtd^trj^a 
tfjg 6£lrivrig ixX£t7tttxovg OQOvg^ td^ofi^v i7tl 6tt%ovg 20 
^£V xf, 6£ktdta de d. tovtcov dh td ^lv dvo td 7tQG)ta 
7t£Qti^£t trjv xatd 7tXdtog tfjg 6£X7]vrjg i7tl tov Xo^ov 
xvxXov (patvoiiivrjv 7tdQodov icp' £xd6trjg tcbv i7tt6xo- 

1. ^'] mg. BC, om. A^D. 7tgay(iaTSLa %avovCcov syiXELTtTL- 
xcoj^] cum superioribus coniuncta D sigAis 4: distincta, etiam 
mg. D^ 3. iyXsLipecov D, sed corr. 4. yiyovsv BC. 7. 
TcaqoSL-naiV D, mg. sTtox&v D^ av^vyL&v'] 6v- supra scr. C. 

8. Ante did del. s D. tcov (alt.)] corr. ex Tf]g D^. 9. 

sTtoxfjg D, corr. Dl 10. ^vyL&v C. 12. Ttgbg t^v] 7to6T^\ C. 

14. Tf] om. D. To (alt.)] om. D. 15. tt] 6sXr\v7] D. 16. 
TTig — 17. sv.aTiQov] om. D. 18. t6] t- ins. D*. s-nXsLtpscov] 
mg. Dl 19. t6] om. C. 21. d] corr. ex a D. dvo] b B. 

32* 



500 KAATAIOT nTOAEMAIOT 

t7]6s(ov' STtel yccQ rj ^ev tov riliov dLcc^EtQog £^rjxo6tG)v 
i6tLV Aa X, ri ds tr]g 6sXrjvrig kccI avtri xata tb ^s- 
yi0tov d7c66tr]fia sdsLxd^rj [p. 421, 3] rwv avtGiv la x, 
Tcal dLoc tavta^ orojv ro (paLvdfisvov xsvtQov trjg 6s- 
5 Xrivrig d(ps6tr]xri tov ^sv rjXLaKov KSvtQov snl tov dta 
tav KSVtQCov d^cpotSQCov ^syC^tov kvkIov s^rjKoetd Xa jc, 
tov 8\ 6vvds6^ov £jrl toi5 Ao|oi> kvkXov ^OLQag g 
Katd tbv TtQOSKtsd^SL^svov [p. 482, 1] Xoyov tbv t&v 
Td X TtQog t6 a, TOTf TtQ&tov Katd trjv STtacprjv s6tai 

10 Tov riXCov^ Katd ^sv tcov jtQcotov 6tC%Giv t&v 6sXl- 
dCcov td^o^sv tov ^sv TtQcbtov tdg Ttd fioCQag^ tov ds 
dsvtsQOv tdg (?og, Katd ds tav s6%dtG)v tov ^sv 
TtQcotov TcdXLv tdg gg, tov ds dsvtSQOv tdg 6^d. Kal 
STtsl tp dcodsKdtip tfjg ijXLaKrjg dLa^stQOv STtL^dXXsi 

15 tov Xo^ov kvkXov ^Lccg ^oC^ag s^rjK06td X syyL6ta^ 
totg to6ovxoLg av^o^SLa^o^sv td TtQOKsC^sva dvo 6s- 
lCdta dnb t&v aKQcov dQ^d^svoL ^s^ql tcov TtSQt tovg 
^s6ovg 6tCxovg' sitl ydQ t&v ^s6cov td^o^sv tdg ts g 
fioCQag Kal tdg '60. t6 ds tQCtov 6sXCdL0v tcsqls^sl td 

20 ^sysd^rj t&v S7tL6KOti]6scov sjtl ^sv tcbv cIkqcov 6tC%cov 
TtaQatLd^s^svcov tcov trjg sjtacprjg o o, STtl ds t&v scps^rjg 
avtcov tov svbg daKtvXov dvtl tov t/3' trjg dLa^stQov 
Kal ovtcog sitl tcov XoLitcbv ta svl daKtvX(p tfjg jtaQ- 
av^rj^scog yLvo^svrjg iis%ql tov pLs6ov 6TC%0Vy slg ov 6 



2. iatLv] comp. B, -v del. D^. 4. tccvtcc] corr. ex tcc 

avtcc D^, tavtd B. 7. (lOLQccg g] om. D. 8. rdv (alt.) — 

9. a] mg. D^. 9. cc] Iev ft s D. 10. t&v gsXlSlcov] corr. 

ex GtXCSoiv D^ 13. 9?] corr, ex tg D^ euan. 15. 1] e 

corr. D. 16. tOLOvtOLg D. ccv^OfisLmao^isv] D^, ccv^o^Lmao- 

ftfv A^BCD. nQO%£Lvcc B. 18. Ante ms del. t£ D. 22. 
Tov(alt.)] t6 C. l§']l§A^CI),l§B. 24:. yLyvo[iivrjgI>. 



MA0HMATIKHS 2TNTASES2S g'. 501 

t&v dadsxa daxxvk(ov ccQtd^^bg xatavt7]6sL. tb ds 
tstaQtov 6sU8lov tcsqis^sl tag yLVOfisvag tov xsvtQOv 
trig 6sk7]vrig TtaQodovg xad"^ ixd6tr]v i7tt6x6trj6i,v^ ag ^ri 
^vvsTttXoyt^oy.svcov ^svtot ^rjdsTtco ^rjts tobv iTttxtvT]- 
6SCDV tov riXCov ^7]ts tav iTttnaQaXkd^sov tf^g ^sXrjvrjg. 5 

t6 ds dsvtSQOv xavovtov tcov rjXtax&v ixXsttl^scjv^ 
o TtSQtsxst tovg xatd tb iXdxt6tov djt66tr}fia tTjg 6s- 
knjvrjg ixkst-jtttxovg oQOvg^ td^o^sv td ^sv ccXla g}6- 
avtcog r«5 7tQ(otG>^ inl 6ttxovg ds x^ xal 6sXt8ta d 
dtd t6 trjv ^sv ix tov xsvtQOv tfjg 6sl7]vr}g ijtl tov 10 
iXaxt6tov d7to6t7]^atog rotovroi/ dsdstx^at [p. 479, 14] 
t^ xal s^r]xo6tcbv ji, oIlcov i6tlv 7] ix roi) xsvtQOv tov 
r]ktov ts xal s^r]xo6tcbv ^, or«v 8s jtQmtcog xatd tr]v 
ina(pr]v ytvr]tat tov r]Xtov r] 6sXf]7^^ t6ts tb (patv6- 
lisvov xsvtQov avt f]g d(ps6tr]xsvat tov ^isv r]Xtaxov 15 
xsvtQOv TtdXiv ^otQug ^tag s^r]xo6td Xy xal SsvtSQa jc, 
tcbv ds 6vvds6^(ov ijtl roi) Xo^ov xvxXov ^otQag g xd' 
ytvovxat yaQ ot (isv iTtl tcov dxQcov 6ttxcov tov (patvo- 
^svov TtXdtovg dQtd-^ol o ts t&v %y Ag xaX 6 tcbv 
605 xd xal TtdXtv o ts tcbv 9^ xd xal 6 t&v 6^y Xg^ 20 
6 ^' iitl tov 11S60V tcbv daxtvXcov dtd tf]v o^otav 
v7tSQ0xr]v dcodsxa daxtvXcov xal stt tov svbg its^Tttr]- 
ILOQtcov d, xa%^ ov xal ^ovijg ytvstat JtdQodog. 

1. dmSsKcc] L§ B. 2. ritaQtov] 2 B. ytyvo(iivag D. 

4. 6vv\snLXoyL^o(i8vcov mut. in GvvslTtLXoyt^ofisvcov A^. 6. dtv- 
tSQOv'\ B B. 8. iyXsLTCtLv.ovg D, corr. D*. 9. di^ supra 

scr. D*. ^] corr. ex s D*. 12. 17] postea ins. D. 13. r]XLov'\ 
corr. ex riXia-Aov D^. 7CQmt(og\ corr. ex TCQ&tov D*. 14. yCyvri- 
tuL D. 16. fiL&g'] om. D. 17. tov] e corr. D, deinde del. 

cc-KQcov 6tC%0L tov (faLVOfiivov nXdtovg. 18. yCyvovtaL D. y«9] 
supra scr. D^ 6tL%0L D. 20. 6o^\ corr. ex olg D*. 0] 
ins. D*. 9?] supra scr. D^, rs D. 22. ?rt] corr. ex stL rt C^, 
ex S7CL D. 23. yCyvstaL D. 



502 KAATAIOT nTOAEMAIOT 

tav de 6elrjVLazG)v xccvovlov ixdtSQOv td^o^sv EJtl 
0tC%ov<s lisv [is^ GskCdia ds i, Kal tm ^sv TtQcbtc) tovg 
tov TtXdtovg aQLd^^ovg 7taQad'7]6o^sv Sg snl tov ^s- 
yCfStov d7to0t7]^atog ovarjg tfjg eslijvrjg. SJtsl yaQ rj 
5 iisv sx. tov xsvtQOv tfjg esl^tjvrjg sdsC%%^ri xatd tb 
[isyi6tov aTto^tri^a s^rjxo^tcjv Ts Jl^ rj d' sx tov xsv- 
tQOV trjg 6xLag t&v avtCbv ji /xd, &6tE^ orai/ TtQchtcjg 
ccTttrjtac tfjg 6xiag r] asXrjvrj^ tots tb xsvtQov avtrjg 
d(ps6tr]xsvaL tov ^sv xsvtQOv tfjg 6xiag STtl tov di,' 

to d^q)OtSQ(x}v tcav xsvtQcov fisyC0tov xvxlov s^rjxo6td 
vg xd^ tcbv ds 0vvds6^cjv sitl tov ko^ov xvxlov ^oC- 
Qag T xal s^r]xo6td ]iri, xatd ^sv t&v jtQatcov 6tCxcov 
td^o^isv tov ts tcbv oQ' t/3 dQtd^^ibv xal tbv tcjv ojr JTrj^ 
xatd ds tcav s6%dtGiv t6v ts tcbv q xal' s^r]xo6tcbv Jiri 

15 xal tcbv ^vd' L^' xal did td avtd totg jtQCJtOLg tf]v 
av^o^sCc36LV avtcbv TtOLr^^o^s&a totg siti^dXkov^L ta 
t/3' tfjg tots 6skr]VLaxf]g dLa^stQOv tQLdxovta s^r]xo6totg. 
t(p ds dsvtSQGj xavovCco tovg tov jtXdtovg dQtd^^ovg 
7taQad-r]6o^sv cjg sitl tov slaxC6tov d7to6tr]^atog ov6r]g 

20 tf]g 6sXr]vr]g^ xad'' b d7t66tr]^a r] [isv ix tov xsvtQOv 
avtf]g sdsCid-r] s^r]xo6tS}v l^ Ji^ r] d' ix tov xsvtQOv 
tfjg 6xLdg tcbv «vr«v ^ vg^ g)6xs^ otav TtQatcjg d7ttr]taL 
tfig 6xLdg r] 6skr]vr]^ t6ts tb xsvtqov avtfjg d(ps6tr]xsvaL 



2. JTs] -s e corr. D^ TtQooTco] a B. 4. Ante o^Giqq del. 
flTjHOff? D. ovflTTjff xfi? 6tXriv7]g\ -67]g Tfjg ([ in ras. A^ STtei] 
ex parte mg. A^. 7. t&v — 8. asXtjvr}] mg. D^ (17 6sXfjv7} 

etiam in textu D). 11. ??] corr. ex vS C. tov] supra 

scr. D^ 15. >ta/.'(pr.)] nal tov D. 6v&] corr. ex 6vs D* 

euan. tcc] -d del. D. 16. sni^dXlovGiv D. 22. ft¥] ^sv C, 

f 
del. C^, mg. fZg C*. jr^wTcog] tt^oj D, o mut. in co D'. 23. 
ro] om. D. 



MA0HMATIKHS STNTASESiS 5'. 503 

tov ^6V zevtQOv tfiq 6kldcs tcccXlv 6^0i(Dg ^ovQav iiCav 
xal £^rjxo0ta y Ag, tov dh 0vvda6fiov etcX tov ko^ov 
KvzXov iLOLQag tj3 %ai i^rj7co6ta i^. dca tovto drj xata 
^6v tcbv TCQ&tav 0tix(ov tcc^avtsg tov te tc3v oj ]i7J 
aQid-^bv xal tbv tav 0%^ fc^S, Ttatcc de tcov e6%dtG3v 5 
tov te t&v Q^ L^ zal tbv tav 0v^ Jirj^ TtdXiv trjv 
av^oy,£L(D6LV avtcjv JtoLrj^d^ed^a totg e7tL^dkkov6L ta 
Lp' tfjg tote ^elrjVLaTcrjg dLa^etQov Xd e^rjKoetoig. ta 
de t(5v daTitvlov tQLta CeXCdLa tbv avtbv tQ^TCov 
TCeQLe^eL tolg rjlLaxotg Tial b^oCcog ra ecpe^fjg Kal tceql- lo 
eyjovta tag TCaQodovg tfjg ^ekTJvrjg zad'' eKd6trjv tcbv 
e7CL6xotr]6ec3V tdg te exateQag tfjg te e^7Ct(X)6ecog xal 
tfjg dva7cXr]Qco6ecog xal etL tdg tov r]^C6ovg tf]g ^ovfjg, 
eTceXoyc^d^ed^a de xa&^ exd6triv t&v e7CL6xot7j6eG)v 
tdg eKxeL^evag ^caQodovg tfjg ^elrjvrjg yQa^fiLxag^ 6vy- 15 
XQrj6d^evoL ^ievtOL tatg deC^e6Lv ag e(p' evbg e7CL7Cedov 
xal Sg eic ev^^ei&v d^d tb tdg ^e%QL tov trjlLTcovtov 
^eyed^ovg TceQLcpeQeCag ddLa(poQetv TCQbg af^d-rj^LV tcbv 
V7C avtdg ev^eLav ;cat etc cog ^rjdevl jcdhv d^LoXoyc) 
8La(peQov6rjg tfjg e7tl tov Xo^ov xvxlov 7CaQ6dov tfjg 20 
^eX^ijvrjg TcaQa tfiv TCQog tbv dLa ^e6cjv tcbv ^adCcjv 
d^ecjQOvnevrjv. ^f] yaQ V7CoXd^ tLg rj^ag riyvorjxevaLy 
dLOtL xal xad^oXov 7CQbg tfjv xatd ^fjxog TcdQodov tfjg 
6e^rjvrjg yCvetaC tLg dLa(poQd TCaQa tb 6vyxQa6%^aL tatg 
tofj Ao|ot) xvkXov 7CeQL(peQeCaLg dvtl tcbv tov dLa ^e6cjv^ 25 
xal etL tovg tcbv 6vt,vyLcbv xQOvovg ovx e^axoXovd^et 



1. (iCav] a B. 5. 07r|3] -^ e corr. D. 7. inL^dXXova D. 

10. nsQLExsL BC. nsQLBXovroc] Tiixovtcc D. 11. sxt D. 

15. 6vvxQr}od(i8voL D, sed corr. 16. inLTisdov] -i- e corr. C. 
21. Tt^r] -rj- e corr. D. tov'] -6v e corr. D^. 24. GvvxQccad^ccL D, 
sed corr. 25. t&v] tcov dLoc D. 




504 KAATAIOT nTOAEMAIOT 

tovg avrovg ccTtaQaXXdxtcjg slvat totg ^i^oig t&v stc- 
Xstifjscov. 

iav yctQ aTtoXdpco^sv aTcb tov A 6vvde6^ov dvo 
tav JCQOxst^Evcov xvxXcov l'6ag nsQKpsQsCag t7]v ts AB 
5 ^a\ tijv AF xal STCt^sv^avtsg tijv BF OQd^riv aTcb 
tov B JCQbg triv AF yQcc- 
xl^cj^sv tijv 5z/, (pavsQov 
ai)t6^sv s6tai trjg fisv 0s- 
Xrjvrjg iicl tov B VTCoti^s- 

10 fisvrjg^ oti tfj AF tov dia 
^sffcjv nsQLcpsQsCcc 6vyx9V~ 
6a^svc3V rj^av dvtl tfjg A^ did tb TCQbg tovg dca 
tcbv jcoXcov tov ^adLaxov kvkIov tdg TCQbg avtbv icaQ- 
odovg d'sc3Qst6d'aL t^ FA 8ioC6si tb icaQa triv syKh^LV 

15 tov 6slr]VLaxov icvxlov dcdcpoQOV. tov ds rjkCov JcdkLV 
r] tov xsvtQOv tfjg 6mag stcl tov B vorjd^svtog 6 ^sv 
tfjg 6v^vyCag XQOvog s6taL ocatd tb ddtdcpoQov tCbv 
xvxXcDv^ otav xal rj ^sXrjvr] xatd tb F ysvrjtaL., 6 ds 
^s6og tfjg sxXsCtl^scog^ otav xatd tb z/, dta t6 Tcdhv 

20 toijg fid6ovg XQOvovg t&v s7CL6xotrj6SG)v TCQbg tovg dvd 
t&v TCokcav tov 6sKr]VLaxov xvxkov d^scjQst^d^aL' xal 
SloC^sl 6 tfjg 6vt,vyCag XQO^^og tov ^s6ov tfjg sxXsCi{;scog 

tfj Pz/ TCSQLCpSQsCa. 

dkXd altLov tov ^f] xal tavtag rj^dg 6vvs7CLloyC- 



1, 6LnaQttXdv,xoig D, corr. D^; 6tnttXXdv,x(og C. 9. vnoxC- 
d-stisv D, corr. D*. 11. avvxQrjattfiivcov D, corr. D'. 12. 

AJ] A- e corr. D. 14. ByAX7]6iv B. 15. iiXCov'] r]^ D. 

17. didcpOQOv D, corr. D^ 19. Post oxttv del. xb (iCa D*. 

23. xy] X D. nsQLtpsQeia D, t add. D^ 24. v.ttl xttvxtts] 
-ttl X- corr. ex ar C. xttvxttg] xava D, a eras. 



MA0HMATIKHS STNTAgESiS S'. 505 

^s6d'ai, rag %aQL(p£Q8Cag iv tatg %axa [iSQog Ttgay^a- 
TsCaig t6 ^iTCQccg sivai xal dv£7tat6 d^TJtovg avtGiv tag 
dcaipoQdg^ xal oti tb ^lv dyvofi6aC xi t&v toiovtcov 
atOTtov^ ro d' evsocev trig iv tatg TCaQ exaeta ^sd^odoLg 
Kata6x£kECag ixovta xata(pQ0V7}6aC tivog tcbv tiqXLxov- 5 
TtDv, rilCxa xal TtaQd tdg vTtod^i^^Lg xal TtaQd tdg 
tr}Q7]6£Lg avtdg ivdi%£taL TtaQad-EcoQ^t^d^aL j tov ^£v 
xatd t6 d7tXov6t£QOV xq7]6C^ov 7tX£C6trjv aL6d"r]6LV i^- 
7tOL£l^ tov d£ 7t£Ql td q)aLv6^£va dLa^iaQtavo^ivov 7) 
ovds^Cav rj 7tavtd7ta6L PQa%£tav. tijv yovv bfioCav t§ 10 
r^ 7t£QL(p£Q£Ca xad-oXov ^£V ov ^£C^ova £VqC6X0^£V 
£^rjxo6tcbv £ ^Lccg ^oCQag' d^CxvvtaL ydQ tovto d^d tov 
avtov d^EcoQij^atog ^ Sl' ov xal tdg dLatpOQdg i^CEloyL- 
6d^£d-a tcav tov C6rj^£QLVov 7t£QL(p£Q£Lcbv TtQog tdg 
tov 8La ^i6cov xcbv t^cadCcov hg i7ti xcbv d^d xcbv 7t6- 15 
Xcjv xov L6rjy.£QLvov yQa(pofiivcov xvxXcov i^tl dh xcbv 
ixlEC^l^Eov ov ^Eviova Stjo i^rjxo^xcbv^ i7t£Ldri7t£Q^ oXcov 
liiv i6XLV ixaxiQa xcbv AB xal AF 7t£QL(p£Q£Lcbv l^' 
6%£dov ydQ ^ixQL xrjXLXOvxcov cpd^dvov^Lv aC xaxd xdg 
ixX£Lip£Lg xijg 6£X7]vr}g 7tdQodoL' xolovxov i6xlv rj BzJ 20 
ivbg £yyL6xa' did xovxo dl xal rj Az/ xcov avxav Td vrj 
£yyL6xa^ xal xaxal£C7t£xaL r] F/l XoL7tr} dvo i^r}xo6xcbv^ 
d7t£Q ovd£ ixxaidixatov 7tOL£t fiLdg &Qag i6rjfi£QLvrjg' 
TtEQL dl tb to6ovtov dxQL^£V£6d-aL x£vod6^ov yiaXkov 



1. v,utu\ xa D, " add. D^, ut saepius. 3. oxi] ox- in 

ras. A*. ju.^v] corr. ex ft? D^. xoiovxcav] supra scr. D*. 

4. h'\ corr. ex F D*. 5. Ixof D, " add. D^ 6. iraff (pr.) 
— 18. icxiv «%-] in ras. D. 8. Evnoiuv D, sed corr. 11. 
ivQtG-AcoiLsv D, sed corr., supra bv- add. tj. 12. yap] y^ C. 

13. STtsXoyrjGoc^Ed-cc A^D, corr. D. 15. x&v (sec.)] xov B. 

16. dil d- in ras. A^ 20. xolovxcov D. ' 23. iGrniSQLvfig] 
-g add. D^ 24. Post xocovxov ras. 2 litt. C. 




506 KAATAIOT nTOAEMAIOT 

7j (piXaXyjd-ovg ccv sHrj. dca ^sv dri ravta xal tag ix- 
xsL^evag tcov S7tL6xot7]6£cov TCaQodovg tY^g (SslTJvrjg d)g 
adcacpoQOvvtcov TCQog atad^rjaLV tcov tcvkXov TtSTCQay^a- 
tsv^sd^a^ ysyovsv d' rj^tv 6 totovtog S7tLloyL6^bg ag 
5 sg/ svog ij dvo tcccXlv VTCodsLy^dtcov tcsqls%g)v ovtcog. 
s6tco yccQ tb ^sv tov rjlLOv ri ro 
tfjg 6xLag xsvtgov tb A^ rj d' dvtl 
trjg TCSQLcpSQsCag tov 6sXrjvLaxov xv- 
xXav svd^sta rj BF^^ xa\ v7Coxsl6%^co 

10 t6 ftW B xsvtQov trjg 6sXrjvrig^ otav 
7CQ06dyov6a 7CQd)tcog a^ctrjtac tov 
rjXLov 7] tfjg 0XLag^ tb ds z/, orai/ 
d7Cox(OQOv6a' xal s^CL^svxd^SL^cov tcov 
AB xal AA rii%co dTcb tov A stcX tf\v B^ xd^stog r\ AT. 

15 or^ ^sv ovv^ otav ;cctjra ro T ysvrjtaL ro xsvtQOv 
trjg 6sX7]vrjg^ o ts ^s6og XQOvog yCvstac tfjg sxlsC^scog 
xal i^ liLsyC6tri S7CL6x6tr]6Lg^ cpavsQbv §x ts tov trjv 
^sv AB tfi AA L6rjv slvaL^ dLa tovto ds xal tfjv BF 
TCaQodov r?5 JTz/, xal sx rov tfjv AF 7Ca6cov sld66ova 

20 sivac tav S7cl tfjg BA td dvo xsvtQa s7CL^svyvvov6cov. 
dfjXov d', ort xal sxatSQa ^sv tcov AB xal AA 6vv- 
a^cpotSQag 7Csqlsx£l tdg sx tcov xsvtQcov tfjg 6sX7]vrjg 
xal tov fjXCov r) tfjg 6xLag^ tj ds AF skdttcov s6tlv 
sxatsQag avtcov ta V7cb tfjg S7CL6xotr]6scog dTCola^^avo- 

25 ^svGi iisQSL tfjg tov sxXsC7Covtog dLa^stQOv. 

3. ScSicccpOQOvvroov^l ante -r- ras. 1 litt. D. 4. ysyovs A^. 

5. Ttixcov D, et similiter saepius. ovt D. 6. r}XCov'] 

7]^ D. 7. d'] e corr. D^ 9. rj] corr. ex v D^. 10. B] 

seq. ras. 2 litt. D. 13. inE^svx^SLG&v D, corr. D^. 16. trig 

ctX7]vr]s] om, C. 19. nccQSov A^. 20. ini^svyvvova&v] -o- 
in ras. C. 23. t]] ins. D^. 



MA0HMATIKH2 STNTASE^S <5'. 507 

tovtcjv ovv ovtcog ixovtcjv yivi^d^co TCaQadsLy^cctog 
evExsv 7] STtt^Kotrj^ig daxtvXcjv y^ xal vTtoxsi^d^co tcqco- 

tOV tO A TO tOV ^XioV XSVtQOV. STtl ^sv ovv ccQa 
tov iisyC^tov a7to6triiiatog ov6r}g trjg dsXrjvrjg rj ^sv 
AB yCvstai s^rjzo^tcbv Xa % [p. 500, 4] 'nal tb aii 5 
avtr\g %%a fij, rj ds AF t&v avtcbv xy A* iXd66c3v 
yccQ s6tLV trjg AB totg y t/3' trjg 'fjXLaxrjg dia^stQOv^ 
tovts6ttv totg ^ V' tb d' aTt' avtrjg cpvp Is' C36ts %al 
tb ^sv ccTtb trjg BF s6tai [Eucl. I, 47] t&v avtav 
vx^ A/S, avtrj ds rj BF fi7]xst % ]iy syyi6ta^ a xal lo 
TtaQad^rj^o^sv sv t^ JtQcotG) xavovCoj t&v r^Xiaxcbv totg 
tQi6i daxtvkoig xata tov d' 6skidCov' sjtl ds tov 
sXaxC6tov ccTto^f^^atog tfjg ^sXtjvrjg rj ^sv AB jtdXiv 
yCvstai s^r}xo6tav Xy x [p. 501, 13] xal tb dTt' avtfjg 
OQid 5, rj ds AF tcbv avtcbv xs l xal tb dit avtrjg 15 
XV LS^ XoiTtbv ds tb djtb trjg BF s^rjxo6tG)v v^ v^' 
xal ^7]xsi ccQa rj BF s6tai tcov avtcbv xd xrj^ d xal 
avtd TtaQad-yj^o^sv sv rc5 /3' xavovCco tcbv rjXiaxav 
totg y daxtvXoig xatd tov d' 6sXidCov. 

jtdXiv vjtoxsC^d^co tb A xsvtQOv tfjg 6xiag xal r] 20 
i7ti6x6trj6ig tov avtov d' tfjg 6sXrjViaxf]g dia^itQov. 
ijtl ^sv aQa tov ^syC6tov d7to6t7]^atog tfjg 6sX7]vr]g 
r] iisv AB yCvstai s^r]xo6tS)v 'vg xd [p. 502, 8] xal tb 



1. yLyvsGd-co D. 2. 17] om. C, del. D*. iniGyiotriG ig] corr. 
ex in^y.orrjGLg D', et similiter saepius. 3. ovv] om. D. 6. 
avtfig] -g in ras. A^ S^^rta] C^D*, -^na BC et 7» in ras. A\ 
5r5ra? D. 7. iotiv] comp. BD. i^'] t^^' AiBCjD. 8. tovt- 
sativ'] comp. B, -v eras. D. ^ v] D, ^v A^BC. 11. 7ra(>a- 
^7]60fiaL D, corr. D^ iv] addidi, om. A^BCD. 14. yiyvs- 
tcci D. 19. totg] corr. ex ri^g D^ d'] supra est ras. A^ 

20. 7}] seq. ras. 1 litt. D. 21. d'] supra est ras. A^ 23. 
yiyvztoti D. i%'r\Y.06tGiv] -\- in ras. A^. 



508 KAATAIOT nTOAEMAIOT 

«jr' avtrig yQ% vrjj i] de AF t&v avtCbv ]irj Xd' iXcc6- 
6g)V yocQ i6tiv trjg AB t^ d' trjg ^eXrjvtazrjg dia^i- 
tQOv^ tovtietiv totg iitl tov ^syi^tov d7to6t7]^atog 
i^rjKO€totg ^ v' tb d' an avtr^g ^Prvrj ]jiy' cj0ts xal 
5 t6 luv aTCo trjg BT xatalsi(pd'r]6€tai, cox^ Ts^ avtrj ds 
ri BF s6tai ^TJKSi t&v avtav icrj Jicc^ a xal jcaQa- 
d-rj^ofisv iv ta jtQmtG) t&v 6sXr}viax&v ocavovicov totg 
tQi6l daxtvXoig xata rov d' esXidiov TtsQiixovta tr^v 
trjg i^7ttco6scog JtaQodov trjv «vti^v ov€av itQog af^d^rj- 

10 6iv tfi trjg ava7t2.rjQC30sc3g, ijtl ds tov iXaji^tov aito- 
dtri^xatog r\ \tsv AB yivstat s^r}xo6t&v ^y Ag [p. 503^ 1] 
xal tb «Jt' avtrjg d[id vrj^ r] ds AF tcbv avtiov vd fTg* 
ra yccQ rijg V7tSQ0xr]g rj v tstaQtov i6tiv TtdXiv trjg 
xatd tb ild%i6tov aTto^trj^a ^sXrjviaxrjg dia^stQOV tb 

15 d' aTt' avtrjg ^p%9^ xy' co6ts xal tb ^sv ditb tfjg BF 
xataXsiTtstai a^s Af, avtr] ds r] BF ^rjxsi t&v avtcbv 
A/3 3C, ct xal avtd TtaQad^rjeo^sv d)6avtcjg tolg tQi6l 
daxtvloig xatd tov d' 6sXidiov tov iv ta /3' t&v 
6sXr]ViaxG)v xavovicov. 

20 TtdXiv svsxsv tmv xal ^ovrjg %q6vov i%ov6S}V 6sXr]- 
Viaxcbv i7ti6xot7]6scov s6tco tb ^sv xivtQov tr]g 6xiag 
t6 A 6r]^siOV^ r] d' dvtl trjg ^tSQiCpSQsCag tov Aolot) 



1. ,yQTt\ corr. ex gxti D*. 2. bgxlv] -v eras. D, comp. B. 

8''] supra est ras. A^ ([yta^t^g D. 3. xovxBGtLv'] comp. B, 

-V eras. D. 4. Post uvxfiq eras. diTil . . . D. ^^tvtj] D, 

\xv7i A^ (b renouat.) BC. 7. nQcoxai] d B. 8. xov] -o- 

corr. ex co C. 8'] supra est ras. A^ 10. t^] xfjv e corr. B. 

12. fts] vf C. il3. Ante ?) eras. o D. sgxiv'] comp. B, 

-V eras. D. 14. &no6xriiLaxoq mut. in anoGxriyLU xfiq D. x6 (alt.)] 

ins. D*. 15. ^^^9^] -^9 -e corr. D, \%^ A^BC. 16. a^s 

D, a e corr. 17. x] D, ^ABC. 18. ^'] f A^C, 8svx8qco BD. 
20. xat] comp. supra scr. D^ 22. nsQLcpsQSiaccpeQSLagl), sed corr. 



MA0HMATIKHS STNTASESiS g' 



509 




rrig 6£k7]vrjs kvxXov svd^sla yj BF/iEZ^ xal ro ^sv B 
VTtoxst^d^cj ^ Kccd-' ov ro KBVTQOV s6tai rrjg eeXijvr^g^ 
otccv 7CQOddyov6a :tQ(bta)g s^cod-ev cc7ttr}tai trjg ^Kiag^ 
t6 ds jT, Kaxt^ ov £6tai ro JC£Vr()oi/ trjg Oslrjvrjg^ btav 
TCQcbtcog blrj ixXeL7tov6a edcjd-ev aTttrjtac rov tcvxIov 5 
tfjg 6Kiag\ ro de E^ Ka%'' ov 
TCockiv e0tat ro xevtQov tfjg 6e- 
Xrjvrjg^ btav djtoxcoQOv^a jtQG)- 
tcjg e^cjd^ev ccTttrjtaL tov xvxlov 
tfjg 0xiag^ ro de Z, xad'' ov 10 
ro xevtQOv e0tac tfjg 6eXr]vrjg, 
btav ex^aCvov6a tb e6%atov 
aTCtrjtac e^cod^ev tfjg 6xiag' xal 
r]x^(o Tcdliv djcb tov A ijtl 
trjv BZ xdd^etog r] Azl. ^e- 15 
vovtcav drj xal ivd^dde t&v 
7CQoa7Codedeiy(ievc3V eti xal tovto cpaveQov^ bti xal 
exatBQa tcbv AF xal AE evd^ei&v 7ceQiexei trjv 
v7CeQ0XYiv^ 7} v7CeQe%ei trjv ix rov xevtQOv tfjg 6eXr]vr]g 
rj ix rov xevtQov tfjg 6xidg^ &6te xal trjv ^ev JTz/ 20 
7cdQo8ov !!6rjv tfj AE yive^d^at^ xal 7CeQie%eiv exateQav 
ro r]^i6v tfjg ^ovij^, loi7cf]v de ti]v BF tfjg i^7Ct(b- 
6eG)g loi7Cf] tf] EZ tfjg dva7Ckr]Qd)6ecog i6r]v elvac. 

v^coxei^d-co ovv exXeiipig^ xa%'' iqv 7CaQdxeivtai Te 
ddxtvXoi tfjg 6eXr]vr]g^ tovte6tiv xad'^ r]v ro z/ xevtQov 25 

1. 6i:Xrivr\q'] -g e corr. seq. ras. 2 litt. D. 17] corr. ex 

r D'. B Fz^E Zl |3y5 ij BC. 3. orf D. TtQoadyovGcci BC. 

Post s^ood^Ev relicta lac. 6 litt., deinde del. novaa sccod^sv D. 

rr^g — 5. a7CXT]xai\ om. D. 13. '^h^coQ^av anxrixaL D. 6v.Lag\ 
6- e corr. A^ 15. BZ] corr. ex XZ A*. AJ] a J' D. 

19. vTtSQSXfi'] corr. ex vnsQoxri D'. 21. yiyvs^Q-aL D. 23. 
tlvaL'] ins. A, supra scr. Dl 25. xovxiexLv'] comp. BC, -v 

eras. D. z/] corr. ex ^ D* euan. 



510 KAATAIOT nTOAEMAIOT 

avtijg ivdot£QG) ycvstaL tov xata tovg ixXsLTCtLTcovg 
OQOvg JtSQatog ima 6sk'rjvcaKf] dta^stQG} xal stt tstaQtG) 
fiSQSL avtrjg^ tovts6tiv otav ri A/1 ikd&6(DV ri sxatsQag 
^sv tG)v AB xal AZ trj TCQOxsL^svf] fita 6slr]VLaxfj 
5 diaiistQG) xal stt tstaQtco avtfjg ilsqsi^ sxatSQag ds 
tG)v AF xal AE tstccQtG) ^sqsv ^tag diaiistQOv 6sXri- 
VLaxrjg. iTtl ^sv aQa tov ^isyC^tov aTto^tTj^iatag ov6r]g 
tfjg 6sXr]vrig ^ ^sv AB yCvstai tCbv 7tQ0XSLiiLSVG)v s^rj- 
xo6tG)v vg xd xal tb djt' avtfjg /yQ% v^^ rj ds AF 

10 tG)v avtG)v xs d' ri yaQ tfjg 6sX7]V7]g dLd^stQog i%l 
rov fisyC6tov d7to6t7]}iatog s^r]xo6tG)v i6tLV ka x' xal 
to dit avtfjg ptrj sc, r] ds AA 6^oCG)g l^ Ld xal tb 
djt^ avtfjg 6gg v%" G)6ts xal tb fisv dnb tfjg B^ 
xataksL(p%-r]6staL [Eucl. I, 47] ^pG)7ty vd'^ xal avti] 

15 iiir]xsL s6taL tcbv avtobv vy [ip^ tb ds ditb tfjg F^ 
xataksLfpd^r^^staL tXa xd^ xal avtf] ^fjxsL s6tai t&v 
avtCbv Ttj ^/?, XoLTtf] ds xal r] BF tcbv avtcbv Xs X. 
7taQa%r]6o^sv ovv ta tc5v Ts daxtvXcov dQLd^^cb rov 
7tQG)tov xavovCov tG)v 6sXr]VLaxG)v ixXsCipscov xatd ^sv 

20 tov tstaQtov 6sXLdCov td tfjg i^7ttG)6sG)g s^r]xo6td 
Xs X L'6a ovra totg tf]g dva7tXr]QG)6sG)g^ xatd 8s tov s' 
td Tov r]^C6ovg j^qovov tfjg ^ovfjg Tr] l^. irtl ds to\> 



1. Ev8oxiq(OL BC. 2. 0Q0V(s] corr. ex %q6vovg C^ Post 
•KaC ras. 2 litt. D. tEtdqtail 'j B, item lin. 5 et 6. 3. ^] 
ins. D^ 4. AK\ -B eras. B. GsXrjVTjaKy C, sed corr. 7. 
Ante o^6rig del. s^riyioGtmv iotiv Xa X' D. 8. yCyv^tai D. 

B^7]yL0Gtcbv'] om. D. 9. m^] -d 8 corr. C. j^qn D. 11. 
eGtiv] comp, BD. x] Z D. 12. x, 17] xi^ D, 14. ^^any'] 
^B^y A^BC, Boo^ D, %Eny Dl 15. Ss] 8' D. 19. tt^w- 
Tov] d B. 20, tBtdqtov'] Jr B. 21. toig] ins. D^. 22. ta] D, 
tdg A^BC. xQOVovg BC. 



MAOHMATIKHS STNTASESiS S'. 511 

iXaxi6tov d7to6t7]^aTos ov6rjg tfjg ^sXi^vrjg 7] ^sv AB 
yivetai TcdXtv tcbv tiqotisl^bvcov |y Ig xal tb di^ av- 
trjg ^d^d vrj^ rj ds AF t&v avtCbv tc^ Tg' rj yaQ trjg 
esXijvrjg did^stQog STtl tov £la%C6tov d7to6trj^atog 
idsLxd^rj [p. 479, 14] £^rj7co6tc3v Xs %' xal tb djc^ avtrjg 5 
^gd" o, ri ds A^ o^OLcog Ld" xg xal tb d% avtrjg to^ 
AO" a6ts Tcal tb fisv dnb tfjg B^ TcataXsLcpd^TJ^stac 
,7%a tO", Ttal avtij rj B^ ^7]xsl s6taL tcbv avrSv | Ad, 
ro d' ditb trjg F^ TtataXsLcpd^T^astaL vza icd^ xal avtij 
^TJxsL s0taL tcbv avtcbv % A)3, XoLTcfi ds xal rj BF tcbv 10 
ai)t cbv ji p. TtaQad^rj^o^sv ccQa xal sv ta /3' TcavovCcp tcov 
6sXrjVLaKG)v skXsCiI^scov ta tcbv ls daxtvXcov dQLd^^a xatd 
^sv tov tstaQtov aslLdCov td trjg s^7ttc36sc3g i^rjxo6td 
ji ^ i'6a Ttdhv bvta totg tfjg dva7iXrjQ(h6scog^ xatd ds 
tov s' 6sXLdCov td tov rj^C6ovg tfjg novfjg x A/3. 15 

iva ds xa\ S7tl tcbv ^sta^v tov ts ^isyC^tov xal 
tov skaiC6tov d7to6trj^atog tfjg 6slr]vrig S7tl tov S7tL- 
xvxkov 7taQ6dc3y tdg S7tL^aXlov6ag sxd6taLg v7tSQ0%dg 
tov olov dLatpoQov dLa tfjg t^v s^r]xo6tcbv ^sd^odov 
7tQ0%sCQC!)g la^pdvcj^sv^ vTtstd^aiisv totg 7tQOXSL^svoLg 20 
xavovCoig dkko xavovLOV ^Qa^v 7tsQLS%ov tovg ts tfjg 
TtaQodov tfjg xatd tbv STtCxvxXov dQid^^ovg xal td s^ti- 



1. AB] corr. ex ABFB. 2._yL'yvsTat, D. 3. diid] 

AJZ^A^ A^d B, I^ C, Afi$ C, A|^ D. AF] ay D.' 6. 
tp<j&] e corr. D, f q0 BC. o] e corr. D^ Ante lQ' eras. 
o D. xg] X C. ' 8. J^] Srilf A^BC, rSf D, ^rSfD^ 

BzJ] corr. ex JB C. 9. vxcc] supra add. ^ A\ rx S C. 

12. Kcctd] corr. ex g' td D*. 13. xBtdqtov] j B. f|rj- 

-AOGtd] om. D, l^" supra scr. D*. 14. /Z f] JIp AifiCD. 

18. nciQodaiv] -68- ins. D*. vTtsqox D, v7ceQo'xD^. 21. nBQi- 
£X^t,v D, sed corr. tovg] corr. ex rf/s C'. 



512 KAATAIOT nTOAEMAIOT 

PccXXovta i^rjxo6ta £Kcc6trj tc5v g)cavo^evcjv v7teQ0%^v 
ix tc5v TtQcbtcov xal dsvteQcov xavovtcov tcov mlECipBcov 
TCSTtQay^dtavtai d' rj^tv rj tovrov tav £^r]K06tC3V ito- 
eotrjg £7tl Tov JtaQalXaxtiKOv trjg 6£2.7]vrjg xavovog ix- 
5 tsd^Eviiivri xata tb J' 6£kC8L0v cog tov iTCinvTiXov xata 
tb ccTtoyELOv tov izTcivtQov dLa tag 6vt,vyCag vitoxEL- 
^ivov. 

iTtel dh OL %l£L6tOL tav trjgovvtov tag ixXeLTttL- 
xag i7tL6r]^a6Cag ov tatg dLa^itQOLg tcbv xvkXcjv Ttaga- 

10 ^£tQov6Lv ta ^Byid-rj tcov i7tL6K0t7]6£C3v^ aAA' cog iitCTtav 
totg oXoLg avtcbv ijtLitidoLg trjg oifjscog Kata tb aitXovv 
trjg jtQo^^okrjg tb (paLvo^Evov avtb Ttdv tm iirj cpaLVO- 
liivco ^vyKQLVOV^rjg^ 7tQ06£%"ifiKayb£v tovtoLg Kal akko 
^Qa%v KavovLOv inl 6tC%ovg ^ev i/3, 6£XCdLa d£ y, 

15 tovtcov d' iv ii£v Tc5 TtQcotco tovg L^ daKtvXovg itd^a- 
yL£v cog £Kd6tov SaKtvXov 7t£QLi%ovtog^ Kad^ditEQ Kal iv 
avtotg totg iKl£L7ttLKotg KavovCoLg^ t6 t/3' tfjg dLa^itQov 
EKatiQOv t&v <p6tcov^ iv dh totg i^fjg td iTtL^dllovta 
avtotg TtdkLV dcodiKata tcov oXcov i^^ad&v^ iv ii£v ta 

20 dEvtiQGo td Toi) rikLaKov^ iv ds tc5 T^tTOJ td tov 6£Xri- 
VLaKOv. iitEXoyL^diLE^^a de xal tdg tOLaiitag inL^oXdg 
ijtl ^ovcov t&v yLvo^ivcov ^Eysd^cbv Katd t6 ^i6ov 
d7t66trj^a trlg 6£X7]vr}g ov6rjg' 6 yaQ avtbg £yyL6ta 
Xoyog iTtC y£ trjg trjXLKavtrjg tcbv d^a^itQcov av^o^SLa- 

25 6£cog 6vvC6tataL Kal ag tov koyov tS)v 7t£QL^itQC0V 



1. ty.dara) D, corr. D^. vnsQOx&v] -%(bv e corr. D^. 9. 
8TtLar}iia6L6ov D, sed corr. 7caQcc(isrQov6Lv^ -v eras. D, naQa- 
HsrQov6L B. 10. aXld D, 13. 6vvKQLV0v6r]g D, corr. D^ 

14. y] rQia BD. 15. rc5] supra scr. D^ nQmrco] d B. 

17. t^'] B, t'j3' A^CD. ^1%. Post avroLgJiOi. x- D». £>" 

^oXmv C. 20. dsvriQOi] B B. XQLrco] r B. 22. yLyvo- 

(isvcov D. 



MA0HMATIKHS STNTASEiiS ^' 



513 



jtQog tag dia^stQOvg ovtog^ ov exsv ta y rj k TtQog 
tb £v' ovtog yaQ 6 Xdyog ^ista^v B6tLv syyc^ta tov 
ts tQLTCladiov TtQog t(p 5 ft£p^t xccl tov tQi%ka6Cov 
TtQog tolg dsxa i^do^r}xo0to^6voLg, olg 6 '^Qj(^c^7Jdrjg 
xara tb aTtXov6teQOv 6vvexQ7]6ato. 

edtG) drj TtQcatov evexev tcov rihaxcov exlecil^ecjv 6 
^ev tov rjXcov xvxlog 6 ABr/l jteQl xevtQOv tb E^ 
6 de xata tb ^e6ov djtodtrj^a trjg ^elijvrjg 6 AZFH 




TtBQi xevtQov t6 @ te^vov tbv tov r]XCov xvxXov xatd 
td A %al r drj^eta' xal eTtL^evx^eC^rjg trjg BE®H 10 
V7tOKeC6d'C3 tb d' exkeXocTtevaL tfjg dia^etQov trjg rikia- 
xrjg^ G)6te tijv ^ev Z,/! toiovtcov eivai y^ olcov e6t\v 
rj B^ did^etQog t^, f^v dh ZH tfjg eeXt^vrjg dtd^etQOv 
tcbv avTwv fc/3 3c eyyc^ta xatd tbv tcov Te Ji TtQbg td 
Ig Jl koyov^ dcd tovto de xal trjv E® Cvvdye^d^ai 15 



3. rc5 ^'] rcb i^ A^D. 4. £^8o(ir}'ii06to(i6voig] CD et cum 
ras. post -ato- B, 8^8ofir}yi06too}i6voLg A^ {-co- e corr.), s^do- 
(iriK06toLS (i^ovoLg A*?B^. 5. Mara] -a e corr. A^ Hq^H- 

6ato C. 8. AZFH] corr. ex AZFH D^, AZHF A^BC. 

9. tov] in ras. D^ kvkXov'] supra scr. D. 10. td] t6 C. 

BE@H] BEGN D, corr. D^ euan. 11. vno-KSL^-Q-g D, 

" add. D^. toSE-nXsXoinivca C. 12. 7] tQicbv e corr. D^ 

14. x] supra scr. A^ 

Ptolemaeus, ed. Heiberg. 33 



514 KAATAIOT nTOAEMAIOT 

XGiV avrcbv ^ T. xal x&v TCSQt^etQcov ccQa xata xov 
tov ivbg JtQog ta y rj X Xoyov ri }isv tov rjXtaKov 
xvkXov yCvatai t^rjfidtcjv X^ ft/3, rj ds tov eskrjvtaKOv 
tmv avtcbv Xrj ^. d^occog ds Tcal t&v oXg)v iiipadcov^ 
6 iTtsidrjTtsQ rj ix. tov ocsvtQOv iitl trjv TtSQi^stQov itolXa- 
TtXaeLadd^sl^a dvo i^fiada tov xvxXov Ttoist^ tb ^sv 
tov r]XLaxov xvxXov 6vva%%-ri6staL ^olqcov 'Qiy g, tb 
ds tov trjg dsXijvrig tcov avtcov Qid' A/3. 

tovtcov drj ovtcog ixovtcov TtQOXSi^d^co svqsIv^ Ttodcov 

10 i6tlv tb 7tsQLS%6^svov V7tb tcov AzirZ i^padov, olcov 
i6t\v ro okov tov riXLaxov xvkXov i^^adbv l^. 

iTts^svxd^codav dr] at AE xal A® xal FE xal FS 
Tcal stL r] AKF Kccd^stog. 

iTtsl ovv^ oZcov i0tlv '^ E@ sv^sla %• t, tOLOvtoov 

15 sxatSQa ^sv tcbv AE nal EF hTtoxsLtaL g, sxatSQa ds 
tcbv A® xal @r tcbv avtcbv g 7, xal oQd^TJ i6tLV r] 
jtQog t^ K ycovLa^ iav tijv vTtSQOxrjv^ f] vtcsqsxsl tb 
aTtb ®A tov aTtb tfjg AE, tovts6tLV ra /3 xal s^rj- 
xoatoc /3, TtaQapdXco^sv TtaQcc tijv E@^ s%o^sv tijv 

20 tcbv EK xal K@ {jTtSQOxriv t&v avtcbv s^r]xo6ta)V Ty y' 
&6ts xal f^v fisv EK 6vvdys0^aL d xrj^ trjv ds K0 
tcbv avtcbv d ftj3, dta tovto ds xal sxatsQav tcbv AK 
xal Kr^ iitsl t'6aL sl6lv^ t&v avtav d syyL6ta. tov- 

3. yLyvstcci, D. 4. ifi^aXcov C. 5. ■nQi^iBxqov D, -ql- e 
corr. D^ 6. Trotft — 7. yi,vY.Xov] bis A^, corr. A. 7. /liot^mi'] 
corr. ex ^olql&v D^. 10. icxCv'] comp. B, -v eras. D. 11. sctlv] 
comp. BC, -V eras. D. 12. ^tj'] -r^' e corr. A^ AE] corr. 
ex z/E J)\ 13. AKF] -KF e corr. A^. 14. oacov D. 18. 
SA] ifiq 0A CD. AE] cc Jl D. zovrictLv'} A\ comp. BC, 
lac. 4 — 5 litt. D. ta ^ — 19. ^] supra scr. D^ euan. 20. 
ccvt&v~\ supra scr. D*. iy y] supra scr. D^; deinde add. 

avt&v J (i^ Slcc tovto ds yiaL sv.atiQav tav AK Ir T D, del. 
D* praeter ir f. 23. sleiv] comp. B, -v del. D. 



MA0HMATIKHS STNTAtEjESiS S'. 515 

toLg 6' axoXovd^(og xal t6 ^sv tov AEF tQiyavov 
i^Padbv €%0fL6v t^ v/3, t6 de tov A®r tCbv avt&v 
Tri ]i7J. Ttdliv ijtsc^ oi(ov i6tlv r^ fisv BA did^stQog 
ip^ rj ds ZH b^oicog ip %, toiovtcov xal tj AF 6vv- 
dystai ri^ xal olcjv ^sv i6tiv ri B/i did^stQog qk^ 5 
toiovtcov ri AF s6tai ui, oicov ds ri ZH did^stQog qx^ 
toiovtcov o^ i/, xal tcov in avtrjg ccQa itSQicpsQSicbv r] 
ILSv AAT toiovtcov i6tlv %y AJ, otW 6 ABTA 
'xvxXog t|, rj ds AZT toiovtcov jr i/j3, otW 6 AZTH 
KvxXog t|. &6t ijtsl 6 avtbg l6yog i6tlv t&v kvxXcjv lo 
JtQog tdg TtSQicpSQSiag xal tcbv i^pad&v avtcov TtQbg 
td t&iv V7tb tdg TtsQifpsQsCag to^scov^ xal t6 ^sv tov 
AET/d toiiscog i^^adbv s%o^sv toiovtcov xg tg, otcov 
idsi%^r] t6 tov ABTA xvkXov ^iy g, t6 ds tov A&TZ 
to^scog tCbv avtGiv xg vd^ i%sl xal t6 tov AZTH 15 
xvxXov tcbv avtcbv rjv Qid' Xp. idsdsixto ds xal t6 
^sv tov AET tQiycovov i^^adbv tcbv avtcbv i^ v/3, 
t6 ds tov A®T b^oicog Trj ]irj' xal Xoiitbv ccQa t6 ^sv 
tov AATK t fiTj^at og i^padbv s^o^sv ^ xd^ t6 ds tov 
AZTK tcbv avt&v r^ y. xal oXov ccQa t6 vitb tcbv 20 
AZTA itSQisyoyisvov ifipadbv toiovtcov i6tlv Tg x^^ 
dicov t6 Toi> ABTzJ xvxkov vjtoxsitai Qiy g. c)6ts 
xai^ oicov i6tlv t6 tov rjXiaxov xvxXov i^^adbv i^^ 
toiovtcov t6 7tSQis%6iisvov vjtb Tov ixlsi7tovt6g i6tiv 

7. avtfiq'] mut. in avtdg (comp.) C^ euan., avtdg D. 8. 
Post Xt add. ^ supra scr. C^ 9. xrxAoff t^, i] Se AZT'] supra 
scr. C*. 10. BatCv] comp. B, -v eras. D. 12. TOftfcoi;] corr. 
ex To fi mv D. 13. Tq] corr. ex x D. 14. A&FZ] A et T 
e corr. D. 15. to] td D. AZFH] AHTZ D. 16. riv] 
supra scr. D^ X^] corr. ex J^ D. 17. AEr] corr. ex 

z/Er D^ euan. 18. Ante T^ ras. 1 litt. D. 21. htCv] 

comp. B, -V eras. D. 23. sGtCv'] comp. B, -v eras. D. 24. 
xoiovtov D, sed corr. 

33* 



516 KAATAIOT nTOAEMAIOT 

cc C d' eyyiOta^ a xccl Jta^cc^tj^o^ev iv ra SLQrj^Evc) 
KavovLG) tm dtLX^ "^^^ y ^axtvXcjv iv rco /3' rSiv 
6eXidLGiv. 

'jtdlLv vTtoxEL^d^G) xal tmv dekrjVLax&v ixXsLif^ecjv 
5 evexev iTcl tfig avtfjg xatayQatprjg 6 ^ev tfjg ^eXr^vYig 
xvxXog 6 ABF^^ 6 de trjg xata tb ^e6ov ccTtoatr^^a 
GXLOcg 6 AZm^ xal ixXeLTtetG) tb d' S^avtcog trjg 
6eXrivLaxrjg dLa^etQov^ w6te^ olcov i6tlv rj B^ dLcc- 
^ietQog t/3, tOLOvtcav tijv ^ev 2.A trjg ixleCipecog eivat y, 

10 tiiv de ZH tr]g ^XLag dLa^etQOv %ata tbv tov evbg 
jtQog ra p Ag Xoyov tcbv avtcbv Xa £./3, Slcc tovto de 
%al trjv EK@ 6vvccye0%^aL Trj kg. xal tcbv ^iev TteQL- 
HetQcov ccQa JtdXLv rj ^ev rov 6eXrjVLaxov kvxXov yCvetaL 
t^rj^dtcov AJ ftj3, rj de tov trjg 6}iLag tcov avtcbv 9^ a, 

15 tS)v d' i^pad&v tb ^ev tov 6eXrjVLaK0v xvzXov QLy g, 
t6 de tov trjg 6xLdg tcbv avtcbv ifj^d A/3. iTtel toCvvv 
xal ivtavd^a^ olcov i6tlv ri E@ evd^eta Trj Ag, tOLovtcov 
eTcateQa fiev tcbv AE xal EF VTtoxeLtaL g, exateQa de 
tcbv A® zal @r t&v avTwv Te Ag, idv co6avtcog trjv 

20 vTteQOxrjv^ i] v7teQe%eL tb dnb trjg 0A tov ditb tfjg 
AE^ TtaQa^dkcoiiev TtaQa trjv E@^ e%o^ev trjv robv 
EK xal K@ vTteQoxijv tcov avrcbv Td ^, co6re %al rrjv 



1. iyyiaTa a] corr. ex hyyiOTu D^. nagaQ^iqGO^ iv corr. 
ex 7taQccQ"^oo^£v D^. 2. rm |3 corr. ex rm t^ D^ 4. xat] 
comp. supra scr. D*. 5. (liv] seq. ras. 1 litt. D. 7. om&g] 
seq. ras. 3 litt. D. 8. BJ] B- in ras. A\ e corr. D. 9. 

y] corr. ex cct y C^. 11. Xcc] corr. ex Xd D, Xoc supra scr. D^. 
13. ylyvhxui D. 14. X^ fi^] postea ab extrema linea ad 

initium sequentis translatum D {X- corr. ex a D^). 15. xov\ 
om. C. 17. OLmv] seq. ras. 2 litt. D. Ante i7\ ras. 1 

Htt. D. _18. g] corr. ex Tq CD. 8b\ postea add. D. 2 
^] ^t B, M^ C, ^ D, riv A^ 



MA0HMATIKHS STNTA^ESiS 5'. 517 

fisv EK ^vvdysGd^cii y ^d, triv ds K& rc5v avtcov 
id v/3, diu tovto dh xccl ixatEQav tcov AK xal KF 
tcbv avtcjv d fi^. dxoXovd^cDg ds tovtOLg xal ro fihv 
tov AEF tQiycovov ifi^adbv £%o^€v t^ Ay, ro ds tov 
A®r t^v avtcov ^d" v/3. jtdXcv ejcsi^ oIlcov ietlv 7] 5 
ILSv Bz/ did^stQog t/3, rj ds ZH 6^0icog Xa i)3, toi- 
ovtcov xal 7] AF 6vvdyetai d^ xd, tcal oXcov (isv i6tiv 
rj BA did^stQog qx^ toiovtcov rj AF s6tai gd^ oXcov 
ds 7] ZH did^sxQog qx^ toiovtcov Ag '9', Tcal tcov iit 
a^vtfjg ccQa itSQnpsQSi&v ri nsv A^F toiovtcov iatlv lo 
Qy -^, oicov 6 ABFA TtvxXog t|, rj ds AZF toiovtcov 
Is dj oicov 6 AZFH xvxXog t|. G36ts dtd td jcqo- 
eiQriiieva xal tb ^isv tov AEFA to^scog i^fiadbv toi- 
ovt cov s%o^sv Aj3 xd, oicov idsix^rj tb tov ABFA 
KvxXov iQiy g, tb ds roi) Ar@Z to^scog tcov avtcov 15 
od xrj^ insl «at t6 tov AZFH xvxXov tcov avtav 
ijv if^d Yp. idsdsixto ds xal tb ^sv tov AEF tQi- 
ymvov i^^adbv tcov avtcov tf Ay, tb ds tov A&F 
hiioicog ^d' v/3* xal XoiTtbv ccQa t6 ^sv tov AAFK 
t^rjfiatog i^^adbv s%oiisv id vd^ tb ds tov AZFK 20 
tav avT(5v d Ag. xal dXov ccQa t6 ijTtb tav AZ^ F^ 
7tSQis%6n,svov i^padbv toiovtcov i6tlv i^ xj, olcov t6 



2. 8icc — 3. d iif\ mg. D^. 2. xai (alt.)] seq. ras. 1—2 
litt. C. _ 3. &mo).ov¥J), ^ add. D*. 5. vj] v- in ras. A\ 

9. X<5 -9"] ^S® B, deinde add. ty supra scriptum C^ 10. 
avtfjg] avr D. 11. Qy] D, corr. ex Qoy A^C, ipty B. 12. d] 
corr. ex X D* euan. 14. X^] supra scr. D*, yi§ D. ABTJ] 
-B- corr. ex F in scrib. D. 16. avr&v] om. C. 17. ds] 

comp. postea ins. D. AEF] A- corr. ex J D. 18. A@r] A- 
corr. ex J D. 19. AJFK] -K postea ins. D, -J- corr. ex 
@ D'. 20. va] corr. ex v8 D. 21. Xg] corr. ex I9 D. 

r^] corr. ex TA C*. 22. hxCv] comp. B, -v eras. D. 



518 KAATAIOT nTOAEMAIOT 

tOV ABFzl XVKIoV VTCOKSttCCL Qiy ^. S6t£ KCCL, OiCOV 

i6tlv tb tov 6£Xr]VLaxov kvxIov i^padbv i^^ tOLOvtcjv 
tb jt£QC£x6^£vov 'bicb tov ixl£i7tovtog avtrjg t^tj^atog 
£6taL /3 xal £ti i£ ii£QOvg ^yycdta^ a xal TtaQad^y^^o^^v 
5 iitl tov aittov xavovCov t(p 6tC%m t&v y daxtvkcav 
iv rc5 y' xal 6£Xi]VLaxm 6£XLdCGi. xaC i6tLv r] t&v 
oiavovCov ^xd^^^Lg tOLavtr}' 



2. sGTLv] comp. B, -V del. D^ 3. to] e corr. D. 4. ^CTai] 
e corr. D seq. ras. 1 litt. le'] i' e' A*CD, Tb B. a\ ins. D^. 

7. 'KOCVOV D, TiOCVOVt, D^ 



MAOHMATIKHS STNTASEiiS ?' 



519 



7j\ KCCVOVLOV rjXiOV ixlBLll^ECOV. 
ILEyiGTOV ccTtoGriqfiaTog 



jj?.iou iy.Xsiipsoov 

slaxiGxov a.no6tiqybCixog 



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xavdviov yjXiov^l 


1. ixXsiipstUiov C. 


axio 


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^Xiax&v D. ixXfiWei 


ov] -Xsixpstov in 


om. D, u. supra). 3. a ' — 
4. TtAdroy?] BC, dQi^/uot 


■6'-\ om. D. 


Taa. D. Inter lin. 


l, quae utrius- 


A\ om. D. 


que tabulae commun] 


8 est, et lin. 2 


uQiS-/uoi'] TtXdtovgB. 6dx^ 


wXot} dqiS- 


ins. roti Xo^ov yvxXov 


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Ttaqodo!; D. 3. a' — 


6"\ om. D. 6. 


/LioiD. s/xTttcoostjg jUOQta'] 


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t.)] e corr. B». 


D. lO.vt^^faC. lS.Xg]X-e 


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corr. ex xg D. 14. jus] /ug " 


3C. 16. ra] 


17. ;i] a D. vrf] cor 


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19. x6-\ -6 e 


;ia] corr. ex Xd D. 
ras. Ai. 22. A(pr.)] cc 
0^C] -? e corr. C. 28. c 
31. (T^d] a^a D. 


21. 9a] -a in 
)rr. ex a D. 24. 
f^«] a- e corr. C. 


corr.D. 20. tS 6^] t^un rai 
C, //^D. x(io-\x(ioA^BG 
xg D. 26. alC] a^tj D. 28. 


as.B», <,^a'^ 

x^ corr. ex 

oi^g] aggD. 




29.x6{vT.)}x^C. 31.Q«]cc 


)rr. ex g6 D. 








' 


v^l mut 


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10 



15 



30 



520 



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521 






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29. (yx|3] in ras. D. 30. 


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MA0HMATIKH2 STNTAgEiiS ?', 523 

'&•'. UslrjVLaxav sxXsliI^scov ScdxQL0cg. 

Tovrov drj TCQOSxtEd^st^evov rrjv fisv rcbv ^sXrjvta- 
xav ixXeitl^scjv STtC^KS^LV Ttoirjeo^sd^a rbv rQOTtov rov- 
rov sxd^s^svoL yccQ rfjg STCL^rjrov^svrjg 7tav6sXr]vov 
rbv 6vvay6^svov ccQLd-^bv xara rrjv sv 'AXs^avdQsCcf 5 
xov ^s0ov xQovov rfig 6vt,vyCag coQav rcbv rs ditb rov 
aTtoysCov rov s%ixvxXov rfjg xaXov^svrjg dvcj^akCag 
fiOLQcbv xal r&v ditb rov ^oqsCov TtSQarog rov TtXdrovg 
lisrd rrjv sx rrjg jtQo^d^acpaLQs^scog dLdxQL6LV rbv rov 
%Xdrovg itQcbrov si6oC6oiisv sCg rd r&v 6sXrjviaxG)v 10 
sxXsC^scav xavovLa, xdv 6vvs^7tC7trrj rotg rcbv jtQcarcov 
dvo ^skLdCcov dQLd^^otg^ rd itaQaxsC^sva ra rov TtXd- 
rovg aQLd^^m xaO*' sxdrsQov rcov xavovCcov sv rs rotg 
r&v JtaQodcjv ^sXidCotg xal sv rotg rav daxrvXcjv dito- 
yQaifjOfisd-a xoQlg sxa6ra' sjtSLra xal rbv rfjg dvca^a- 15 
XCag dQLd^^bv Si6svsyx6vrsg slg rb rfjg diOQd-c36scog 
xav6vLov^ o6a sdv rj rd TtaQaxsC^sva avrw s^rjxo6rd^ 
ro6avra la^ovrsg rrjg vTtSQOxfjg rcbv xa^' sxdrsQov 
xav6vLov d7toysyQa^^svG)v daxrvXov rs xal s^rjxo^rov 
TtQo^d-rj^o^sv rotg sx rov itQorov xavovCov xarsLkrj^- 20 
^svoLg. sdv asvroL 6v^paCvr] rbv rov itldrovg dQL%-- 
fibv sig rb dsvrsQOv ^6vov xav6vLov TtCitrsiv^ rcbv sv 



1. %■'] om. A^D. 4, &v,%'Bii£voi] -01 e corr. D. 5. h~\ 
ins. D^ 6. t&v^ mut. in tov C*, corr. ex tov D. 10. ticr- 
oiaa^sv A^ 11. iyXsiipsav D, sed corr. 12. 6sXr}di(ov A^ 

14. ccTtoyQaipdiisd-a post ras. 1 litt. D, -0- pr. et -ipdfiE&a in 
ras. 15. ^foj^tg] in ras. D. 17. sdv] i- postea ins. A\ 

i- del. D. avtoig D. 18. tocavta] td toaavta D. T7)i 

vneQOxfiL B. iv.dtEqov] corr. ex snaatov D^ 19. yiavoviov] 
corr. ex iv tm xavovtoo D'. dnoysyQaiiiiivov C, sed corr. 

21. 6v}i§aLVSL C. 



524 KAATAIOT nTOAEMAIOT 

avTc3 ^ovG) TtaQaKSL^EVov daxtvXcov xal ^oqlcov ta 
£VQi6K6^£va i^rjxo^ta ixd^rj^o^sd^a^ ocal o6ovg ^sv iav 
evQCO^sv ix tfjg toiavtrjg diOQd^aaacog ix^sprjxotag 
daxtvXovg^ to6avta dcodixata TtEQii^Eiv (pr]6oy.€v trjv 
5 i7CL6x6trj6iv trjg 6£XrjVLaxfjg dLa^itQov xata tbv ^i6ov 
Xq6vov trjg ixX£Lx(j£Cjg. totg d' i^rjxo^tolg totg yLVO- 
liivoig xairct: triv avtijv dL^Qd^cj^Lv TCQo^d^ivt^g 7cdvtot£ 
tb L^' avtcbv^ dvd'^ cov 6 rjlLog i7CLXLV£ttaL ^ xal ^eql- 
6avt£g £Lg ro t6t£ trjg 6£Xr]vr]g dvm^aXov SQLatov 

10 XLvrma^ b6dxLg idv ix7ci67] 6 n£QL6^6g^ to6avtag L6rj- 
fi£QLvdg G)Qag £%o^£v £xd6tov t&v 7CaQodLxS}v xq6vc3v 
trjg ixX^LipEcog^ tdg ^lv ix tov d' 6£XLdL0v 6vvayo^ivag 
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6£C3g XQOVov^ tdg d' ix tov Tci^Tttov tfjg r}^L6£Lag tov 

15 tfjg ^ovfjg ^^dvov, (pav£Qcbv oivrd-O-^v yLvo^ivcov tcov 
t£ xatd tdg dQxdg xat td tilrj t&v i^pd6£C3v xal 
dvaxad^dQ^ECjv G)QLaLcjv iTCoxcov ix tfjg TCQog tbv ftf- 
ta^v tfjg ^ovfjg^ tovti6tLv tbv tf]g dxQL^ovg ^yyL6ta 
7Cav6£Xr]vov xq6vov^ £xd6tov tc5v xatd ^iQog £vql6xo- 

20 ^ivcDv 7CQo6d-a(paLQi6£cog' avt^d^^v dh xal tcov tfjg d^a- 
fiitQov dcod£xdtc3v £L6£V£x^ivtcov £lg tb iTcl 7Ca6L ^Qaxv 
xav6vLov xal td t/3' tcov oXcov i^fiadav £VQr]6o^£v ix tcov 
7taQax£L^ivcov iv tm y' 6£XLdCcp^ b^OLCog df xal td tcov 
r]XLaxcbv ix t<Jov iv ta d£vtiQ(p 6£XLdLG) 7CaQax£L^ivcov. 



1, nccQccnsLvcav D. 2. idv] o av D, o (ovv) del. D^. 8. 
t^'] l' §' A^ (" in ras.) C, doadsKcctov BD. avd'' oiv^l corr. 

ex CCV& D*. BTiLv.ivstxai'] -i- sec. in ras. 2 liit. D. 9. t6xi\ 

om. D. 10. b6dv,Lg\ 06%' D. 14. xq6vov\ )^V D. 15. 

XQovov'] inter duas ras. D. 17. dvavaQQ^d^ecov D. 18. xovx- 
i6xiv'\ comp. B, -V eras. D. 22. svQi^ofisv C. 24. dsvxiQa\ 

^ B et supra scr. D. 



MAeHMATIKHS STNTAgESiS ?'. 525 

6 ^£v ovv koyog aiQEi ^rj Tcdvrors tbv djtb rfjg 
KQXVS T^VS ix^£^i^£G}S XQOVov inixQ^ '^^^ iiioov i'6ov 
yive^d^ccL ra ocTtb rov ^s^ov iisxQi rov rfjg rsXsvrrjg 
dtd rriv TceQL rs rbv ijXiov xal rr^v ^skTJvrjv dvcj^aXtav 
rcjv l'6c3V TCaQodcov did rb roiovrov iv dvCcoig %q6- 5 
voig dTCorsXov^EvcDv^ rrjg ds aL6d'7]6scjg svsxsv ovdsv 
dv d^LoXoyov dTCSQyaGairo TCobg rd (pacvo^sva dia^dQ- 
rrj^a ro fti) dvtdovg rovg xQovovg rovrovg vTCorCd^s^d^ai 
r«l, Ttdv JCSQi rovg ^E6ovg dQOfiovg c)6iv^ otcov ^sC^ovg 
Si6iv at r&v 7CaQav^rj0scov v7CSQ0%aC^ rtjv ys \is%Qi rd3v lo 
ro6ovrGiv wqcov TCaQodov^ o6cov s6zlv 6 %ag rijg rs- 
IsCag EKXsC^fjscog %Q6vog^ ^rjds^Cav TCavraTCaacv aCad^rjrriv 
TtOiSiv rriv rfig v7CSQ0%fig dia^poQav. 

ori ds xal Six6rcog dirjnaQrrj^svrjv svQC6oio^sv rrjv 
VTcb rov 'l7C7cdQ%ov dsdsiy^Evrjv rov icldrovg rf]g 6skri- 15 
vrig tceqCoSov ;car' SKsCvrjv ^sv rijv 'b7c6d's6iv sXdrrovog 
q)avsC6rjg rfjg ^sra^v rcbv sxrs^Si^Evcov sxXsC^scov stc- 
ov6Cag,^ ^cXsCovog ds rijg xard roi)g rj^srEQOvg STCi- 
loyi6^ovg xarsiXrj^^Evrjg^ d7cb rav avrcbv dv 7cdkiv 
£7Ci6riJ6avrEg xaravorj^ai^sv. 20 

Xa^cov yaQ slg rrjv roiavrrjv d7c6dsi^iv s%ksCilfSig 
dvo 6EXr]Via7tdg did ^rjvcov ^J()| yEyEvrj^Evag^ iv alg 
d^cporiQaig ro riraQrov rfjg ^EkrjViaxfjg dia^irQov 



2. (isxQi "1:01} IIB60V xfiq iv^XsLipscog %q6vov D. Laov] corr. 

ex 060V D. 3. yLVB6%-aL\ A^, ysvsed-ai BC, yCyvs^d-UL D. 5. 
TOiovTov'] corr. ex tolovt D. sv] -v ins. C^. uvL60Lg] -l6- 

e corr. D. 7. av] supra scr. D. 8. nsQLTLd^sed^uL D, sed 

corr. 9. v,dv'] vav st BD, corr. D^ 10. vnsQoxdv A^. 12. 
uieQ^iiTriv] £6d-gT D, supra i- add. at D*. 13. ttji;] supra est 
ras. A^; fort. delendum. 19. yiaTSLXr^^iiEVTig] -tj- alt. e corr. D. 
av ndXiv] corr. ex avdnaUv D. 22. ^] ^^A^BC, 

^^ D. 23. TSTUQTOV] J B. 



526 KAATAIOT nTOAEMAIOT 

xata f^v wbtriv ano tov ava^i^dt,ovrog 6vv8b6iiov 
TCaQodov ixXeXoLTcbg itvyiavBv^ hv TCQatrjv ^lv f^v 
£v rc5 /3' £t£L MaQdoxB^Ttddov t£trjQi]^£vrjv^ d£vt£Qav 
dh tijv £v tS AJ' £t£L trjg tQttrjg ocatd KdXiTtTCov 
5 7C£ql68ov^ 6vy%QfitaL ^lv t<p trjv avtrjv xatd TcXdtog 

SCdQOdov £V £Xat£Q^ taV ixX£Li^£COV f'! b^aXoV 7C£QL- 

£X£6d^aL TCQbg triv trjg djcoxata6td6£cog djcod^L^LV ix 
tov trjv iilv 7CQ0t£Qav £xX£liIjlv y£yov£vaL xatd tb djco- 
y^Lotatov tov £7ClxvkXov trjg 6£X7]vrjg ov6r]g^ trjv dh 
10 d£vt£Qav %atd tb 7C£QLy£L6tatov^ xal d^d tovto ^rjdiv^ 
cag y£ «^ro, ^v^^^^rjxBvaL dLatpoQov £k tfjg dvo^aXCag^ 

dLa}iaQtdv£L d£ Xal %at avtb tOVtO TCQCJtOV^ £7C£Ld7]7C£Q 

xal £x tfjg dvco^aXLag £yLV£t6 tLg d^L^loyog dLatpoQd 
7CaQd tb [lij ta l'6a) ii£Lt,ova tr]v b^aXijv TcdQodov 
15 ^VQL^x^^d^aL tijg dxQL^ovg ;cair' d^(pot£Qag tdg £xk£LiJj£Lgy 
dXX' £7cl ^£v trjg 7CQ0t£Qag ^ca iloCqcc £yyL6ta^ iTcl d£ 
trjg d£Vt£Qag byd6(p ^Lccg [loCQag, mg xatd y£ tovto 

£lk£L7C£LV tijV tOV TCXdtOVg 7C£QCodoV £Lg oXag dTCO- 

xata6td6£Lg ri^C6£L xal d' xal rj' ^Lccg yboCQag^ oXcav 
20 i6tlv 6 Xo^bg trjg 6£X7]vr]g xvxlog t|. £7C£Lta ovdh 
tijv dLa td trjg 6£Xf]vr]g d7C06tr]^ata 6v^^aCvov6av 
7C£QL td ^^yid^r] tav i7CL6xotf]6£cciv dLacpOQav 6vv£7C£Xo- 
yC6ato ti]v 7cX£C6tr]v ^dXL6ta y£y£vr]^£vr]v iTcl tovtcjv 
tcbv ixX£C^£CJv dcd tb ti]v ^£v 7CQot£Qav xatd tb ^i- 
25 yL6tov d7c66tr]^a trjg 6£Xf]vr]g ov6r]g y^yovivaL^ ti]v 



1. avzfiv] corr. ex xoiavxTqv C^. 2. xfiv'] om. A^ 3. strft] 
L D, £* D*. 4. h8i\ L D, £* D2. KdXinTiovl^ BC et -in- 
in ras. A\ KdXXinnov D. 5. GvvxQfiTai D, sed corr. 6. 

Twv] ins. D^ f|] -i in ras. 2 litt. D^ 11. atg yf] -g ys 

ins. D*. w£To] M- e corr. D. t?)?] supra scr. D. 13. 

iytyvsto D, ' 15. Ante naz' del. sv D. 20. ovSs] supra 

scr. C^ 23. tovTcav] -tcov supra scr. D^. 



MAGHMATIKHS STNTASESJS $'. 527 

dh dsvrsQccv xata xh iXdxLGrov dvdyKr} ydg rrjv rov 
avrov d' ^SQOvg s7ti0x6rr]6LV TtaQrjxokovd^rjxsvaL xard 
li€v ri}v TtQorsQav sxXstipLv d%o sXd^6ovoq dLa^rd^scog 
rov dvapL^dt,ovrog 6vvds6^ov^ xard ds r^^v dsvrsQav 
dno ^SL^ovog^ g)v rrjv dLaq)OQdv djtsdsi^a^sv [p. 520 5 
tab. 1 lin. 10 et tab. 2 lin. 10] fiLdg ^OLQag xal ns^Ttrrj- 
^OQLOv 6vvayo^svr]v ^ ag xal svrsvd^sv ra ro6ovrm 
jtlsovd^SLv rrjv rov nXdrovg TtSQLodov fisd"' oXag dito- 
xara6rd6SLg. ro ^sv ovv o6ov sit avrfj rfi %kdvri 
ratg s^ d^(porsQ(ov rcbv d^aQrL&v 6vvayo^svaLg dvalv 10 
syyL6ra ^iOLQaLg s0g)dXrj dv ri jtsQLodLxrj rov jtldrovg 
d7toxard6ra6Lg^ sl srv^ov d^g)6rsQaL TtQog rb fAarrov 
rij TtQog rb itXstov cpsQOvaaL rrjv SLacpoQdv^ sjtsl d' ri 
ILSV iXXsLTtsLV STtOLSL rijv d7toxard6ra6Lv, rj ds TtXsovd- 
t^SLV^ xard rLifa 6vvrv%Lav ^ -jjv i6(x)g xal 6 "IitTtaQiog 15 
AvravaTtXrjQOv^svrjv Ttcog xaravsvorjxsL^ fi6vG) ra rfjg 
VTtSQOxrjg r&v d^aQtL&v rQLrco ^sqsl {iLag ^OLQag sg)dvrj 
jtXsLCov ov6a rj STtLXrjij^Lg rfjg djtoxara6rd6SG>g. 

l'. 'HlLaxcbv sxXsLtl^scov dLdxQL6Lg. 

'H [isv o{)v r&v 6sXrjVLaKcov sxXsLjf^scjv S7tL6xs^Lg 20 
fi6vG)g dv dLa ravra yCvoLro vyLcjg^ xad'' ovg sxrsd^SL- 
[isd^a rQ^Jtovg^ rav s7tLXoyL6^G)v dxQL^ov^svcov s^rjg 
ds rijv rcbv rjXLax&v sxXsCipsov dLdxQL6LV xara6xsls6- ^ 



1. iXdxiGtovl corr. ex lXa%^x D. 10. 6vvayo[i£vccc A*. 11. 

(loig D. 13. Post nXstov ras. 1 litt. D. 14. sTtoLSi] om. D. 

anoyidGtaGLV C. 15. l'aos C. 18. inCXTjiiilJLS D, sed corr. 

cc7tov.attda8cos D, dnov.atatdas(os D^, ut saepius. 19. t'] 

om. A^CD, mg. A*B. 20. Post syiXsiipscov del. inLav.stpis C. 

21. ysvoLto BC. 23. ■nataytsXXsatigav D, corr. D^ 



528 KAATAIOT nXOAEMAIOT 

rsQccv o\)0av dua xag TtaQaXldi^eig xrig 6sX7Jvrig itoLrj^o- 
^sd-a rbv rQOTtov rovrov 

0xeipd^evoi yaQ rbv hv ^Ake^avdQeCa rr}g dxQifiovg 
0vv6dov iQovov^ TtQO 7t66(Dv rj iierd 7t66ag coQag s^- 

5 e7te0ev iarjfieQivag rrjg fiearj^^Qiag^ eiteira^ edv ereQOv 
ri rb VTtoxei^evov xXt^a rijg eTti^rjrov^evrjg olxTJaecog^ 
rovre6riv idv fi?) vTtb rbv avrbv fj ^e^rjfi^Qivbv tgj 
did rrjg ^Ale^avdQeCag^ 7tQ06%^a(pel6vreg rb xard ^fixog 
didcpoQOv ev rotg dvalv ^e6ri^fiQivoig r&v i6rj^eQiVG)v 

10 aQ&v xal fiad^^vreg^ JtQb 7t66(ov ri ^ierd 7t66ag i6rj^e- 
Qivdg aQag xa\ TtaQ^ exeCvoig e^S7ts6sv 6 rfjg dxQi^ovg 
6vv6dov ^^oi^og, diaxQivoviisv 7tQG)rov xal rbv rrjg 
(paivo^evrjg 6vv6dov xq6vov iv ra i7tit,rjrov^evc} xXC- 
|LtaTt rbv avrbv eyyi6ra e66^evov np ^e6a) rr^g exXeC- 

15 il^ecog d7tb rrjg 7teQl rdg %aQalld^eig exred^ei^svrjg rjfitv 
iv rotg s^7tQ06d^sv i(p6dov. Xa^6vrsg ydQ ex rs rov 
rav ya)ViG)v xav6vog xal rov rcbv TtaQaXXd^scjv oixeCcjg 
rp re xXCyban xal rf] rcbv dtQcbv d7to6rd6ei rov ^e6- 
rj^^Qivov xal en rm 6vvodixa ^SQSi rov ^cjdiaxov xal 

20 7tQbg rovroig ra rfjg 6eX7Jvrjg d7to6rri^ari rfjv ytvo^e- 
vrjv 7tQG)rov avrfjg 7taQdXXa^iv cog i^tl rov did roi 
xard xoQvq)fjv 6rj^eCov xal rov xsvrQov rfjg 6s2,7]vrjc 
yQa(po^svov ^syC6rov xvxXov xal dTtb ravrrjg dq)sX6vtsg 
Ttdvrors rfjv xatd tov avtov 6tC%ov TtaQaxsi^svrjv 

25 rjXiaxiiv TtaQaXXa^iv d7tb tfjg Xoi7tfjg diaxQivovfisv^ Sg 



A 



2. Ante tov del. ^ Dl 9. BmC^, dv6 D. 12. tov] 

x&v C. 13. 'nXCficcri] corr. ex KXC^aza D. 15. n^^XXd^sig D. 

16. diccXa^ovtsg BD^, SiaXXa^ovtEg D. 18. djq&v'] ra- e 

corr. A^ 19. hC] corr. ex rt D^ 22. y.svtQOv] >t-f D. 23. 

ano] ins. Dl rav D, ^ add. D^. 25. naQdXa^LV D, corr. Dl 
ojg] corr. ex go D^. 



MA0HMATIKHS STNTASESiS <5\ 529 

vitodsdeLxrcct^ dia rf}g evQL0xo^8vr}g Ttegl rriv ro^rjv 
rov ^(pdtaKov xal rov dca roi) xara xoQvcprjv ^rj^siov 
ygaifo^evov ^eyt^rov kvkXov ycovtag rr^v ^vvayo^evrjv 
Sg TCQog ^6vr]v rijv xara ^rjxog TCaQodov TtaQalXa^iv 
Tcal ravrrj TtQO^d-evreg itdvrore rb eTtipdXlov rotg TteQu- 5 
£%o^evoLg V7t avrrjg xQovotg L6rj^eQLVotg rijg eitLitaQ- 
uXXd^ecog dLd(poQOv^ rovre6rLV rr]g ev r^ avr& Tcavovi 
xaraXa^Pavo^evrjg vjteQoxrjg r&v itaQaxei^evcav 8vo 
jtaQakXd^ecjv rfi re TtQarrj tov Kard KOQVcpriv Orj^eLOV 
dLa6rd6eL xal rfj [lera rfjg TtQO^d^rjxrjg rcbv i^rj^eQLvav 10 
XQOVcov rd rfi xard /Ltijxog ^ovrj TtdUv ejtL^dXlovra 
TtaQakXd^eL ^erd rov ro6ovrov ^eQOvg avrcbv^ edv 
ccL^d^rjrbv fj^ o6ov xal avrd ^eQog e6rlv rfjg TtQcorrjg 
TtaQaXXd^ecjg^ xal rotg ovrco 6vvax^et6L rfjg oXr]g xard 
^f]Xog TtaQaXXd^ecog ^OQLOLg TtQo^d^rj^o^ev itdXLV rb dco- 15 
dexarov avrcov^ dvd"^ ov 6 rjXLog eTtLKLvetraL^ xal rd 
6vvax^£vra dvaXv6o^ev elg coQag C6rj^eQLvdg ex. roi) 
{ieQL6^ov rmv TteQl rf^v 6vvodov rfjg 6eXrjvr]g dvco^d- 
Xcov coQLaCcov dQo^cov^ xdv ^ev eig rd e7t6^eva r&v 
^codLcov rj xard ^fjxog naQdXXa^Lg fi yLVO^evrj' dedeL%a- 20 
ft£v yaQ ev rotg efiTtQo^d-ev^ itcbg rjfitv rj rotavrrj d^d- 
XQL6Lg Xa^pdvrjraL' rd ^ev etg rdg GtQag rdg i6r]^eQL- 
vdg dvaXeXv^eva ^6QLa dcpeX6vreg ditb rcbv xard rbv 



5. ravxT]] corr. ex xccvt D^. snipdXlov'] corr. ex ct^dXlov D*. 

6. civtiig] corr. ex avtotq in scrib. C; avr"^ D, ^ add. D^. inL- 
iiaQccXd^scog D, corr. D^. 7, tovtsot D, comp. B, tovtioz^ D^. 

13. ^] corr, ex v D^ iativ'} comp. B, -v eras. D. 14. 
xat] supra scr. D^. ovtmg CD. avvax^sLGi] avv (a supra 

add. D^) ^EQ ictl i Ttgcot x^^tav D. 18. avvoSov] corr. ex 

cvvoX' D^. dvco^dXXcov D, sed corr. 20. ^adicov] corr. ex 

^(p^La-K&v A^ et A^ yiyvoyLivT] D. 22. td] corr. ex 

tdg A^ 

Ptolemaeus, ed. Heiberg. 34 



530 KAATAIOT nTOAEMAIOT 

dxQiPfj trjg ^vvodov %q6vov TtQodiaxexQiiiiivav trig 
6£X7]vrjg [i0LQG)v xcjQig ixd^tov tov te ^TJxovg zal roi) 
nXdtovg xal trig dvco^aliag e%o^ev tdg ev t« XQovcy 
tijg (paivo^evrjg 0vv6dov dxQL^etg 7taQ6dovg tfjg 6eXri- 
5 VYig^ avtdg 8e tdg cjQag ea^^ed^a evQrj7i6teg^ oaacg 7tQ6- 
teQOV rj fpaivo^evrj 6vvodog yevrj^etai, trjg dxQcpovg. 
edv de elg td jtQorjyov^eva t&v t^codCcov rj xatd ^fjxog^ 
TtaQdXla^ig y evQrj^evr]^ td ^ev ^6QLa TtQoad-yjao^ev 
dvditaXiv talg %atd tbv dxQi^fi tfjg 0vv6dov xQ^^^ov 

10 TtQodLaxexQL^evaLg 7taQ6doig exdatov tov te ^t^xovg 
Ttdhv xal tov itkdtovg xal tfjg dvco^alCag^ tdg de coQag 
e^o^ev^ 06aLg v6teQov rj (paLvo^evrj 6vvodog eOtaL tfjg 
dxQL^ovg. TtdlLV ovv xatd tijv tfjg (paivo^bvrig 6vv- 
6dov tcbv Carj^eQLVcov Sqcov ditb tov fie^rj^^QLvov did- 

15 0ta0Lv e7tL0xe^d^evoL dta t&v avtcbv e(p6dc3v^ 7t66ov 
TtQCJtov rj 6eX7]vrj 7taQaXld66eL 7tQbg tbv dC avtfjg acwl 
tov xatd xoQV(prjv 0rj^eCov yQa^p^^evov ^eyL6tov xv- 
xXov^ xal d(peX6vteg dTtb tcbv e{)QL6xo^evG}v trjv t» 
«vrd5 dQL&^a 7taQaxeL^evrjv tov rjXCov TtaQaXXa^LV dTtb 

20 tcov koL7tcav c36avt(og ex tfjg t6te 7feQl tijv t&v xvxlcov 
tO[ifiv evQL6xo^evrjg ycjvCag dLaxQLVov^ev tijv xatd 
TtXdtog tbg eTtl tov TtQbg 6Q%-dg ta ^(pdtax^ xvxXov 
yLVOfievriv 7taQdXXa^Lv xal td 6vvax^evta ^6QLa ^fra- 
7tOL7]6avteg elg td xatd tbv Xol,bv xvxXov e7tLpdXXovta 

25 t^riiiata^ tovte6tLV dcjdexdxig avtd 7tOL7]6avtegy tdg 
yLvo^evag ^ioCQag^ edv ^ev rj xatd TtXdtog 7taQdXXa^ig 



1. Ante alt. xfig del. r D^ 5. BVQL6v.ovxtg BC. 06aig\ 
als D. ^ 11. %at(alt.)] om. D. 13. rijv] supra scr. Dl 

T^g] r D. 15. 7i6d D. 16. TtUQaJddaeL A^; naQaXXd^SL D, 
corr. 1)2. 24. za] x6 D. 25. xovxiGxiv] comp. B, -v eras. D. 
dcodev,'' D, corr. D^. 26. yiyvofiivas D. 



MA0HMATIKH2 STNTASEiiS S'. 531 

cos ^Qog rag ccQKtovg fi tov dLoc ^£6(dv aTtotsXov^svrj^ 
TteQi ^hv tbv ava^L^dt,ovta 6vvd£6^ov tfig 6s^7]vi]g 
ov6Yjg 7tQ06%"ri6oiJbEv ty xata tbv %q6vov tfjg g)ai,voii£vr]g 
6vv6dov TtQodiEVKQtVTj^Evr] TtXattxy TtaQ^dcOy TtEQl ds 
tbv xataPifid^ovta dcpsXov^Ev b^oCcog' iav dh rj xatd 6 
TtXdtog TtaQakXaitg d)g TtQbg ^E^rj^^Qtav d%otElritaL 
tov ^(pdcaxov^ xatd t6 ivavttov TtEQu ^ev tbv dva- 
^^i^dt.ovxa 6vvdE6^ov ov6rjg tfjg 6Elrivrig dcpEXov^Ev 
tdg ix trjg jtaQaX^d^Ecog ^ocQag dnb tCbv TtQodiaxEXQL- 
^Evcov iv t(p XQ6vcp tfjg cpaLvofiEvrjg 6vv6dov tov Ttkd- lo 
tovg ^oiQcbv^ TtEQL ds tbv xata^L^diovta jtQO^d-rj^ofiEv 
b^OLcog. xal ovt cog e^o^ev tbv iv rc5 %Q6vGi tfjg (patvo- 
^Evrjg 6vv6dov tov cpaLvo^Evov jtXdtovg dQLd-^^v, bv 
EL6EVEyx6vtEg Elg td T(5v rjXLaxcov ixkELil^Ecov xav6vLa^ 

idv 6VV£^7tL7tty tOtg tcbV TtQCOtCOV dvo ^eIlSlCOV dQLd'- 15 

fiolg^ exXel^lv £6E6^aL Toi) iiXLOV q)rJ6o^£V^ fig ^e6ov 
EyyL^ta %q6vov tbv ti^v (pai^vofiivrjv 6vvodov tisql- 
EXovta. ix^EiiEvoL ovv tf]v 7to66trjta tcbv jtaQaxEL^i- 
vcov tm tov (paLVo^ivov Ttldtovg dQL&^^p daxtvlcov ts 
xal fioQLCov tav tE tfjg i^7tt(b6£cog xal tcbv tfjg dva- 20 
xad-dQ^Ecog %co()fcg i^ ixat iQov tcbv xavovCcov e16ol6o^ev 
xal tbv dTtb tov djtoyELOv xatd tr^v (paLVO^ivrjv 6vv- 
odov tfjg dvco^aUag dQLd^^bv tfjg 6EXr]vi^g ELg tb tf\g 
dLOQd^co6Ecog xav6vL0v^ xal td TtaQaxEt^Eva avta i^rj- 
xo6td 66a idv fj^ td rocJaiJTo: Xa^6vt£g xfig Exd6tov 25 
tG}v aTtoyEyQa^^ivcov v7tEQ0xf}g 7tQo6d-r}6o^Ev atEl tolg 



2. tov'] xhv avTov B, 6. TCQog] supra scr. D^ ccTto- 

telfjtccL] D^, ccTCotsXsnai A^BCD. 7. tov] tbv avtov BD, 

9. TtQodicczEyiQi.^Evav] tiqo- in ras. A^. 10. sv] 8 A^ 15. 

Svo] -0 supra scr. D^ 16. fig] supra scr, D^, 23. t' dioq- 

^ooGScov D, 26. vTtSQOxfjg] -o- in ras. A^ 

34* 



532 KAATAIOT IITOAEMAIOT 

i/C rov TtQCotov TiavovCov KcctSLlrj^^evoLg Tial tovg ^sv 
yevoy.evovg ix rijg toiavtrjg dLOQd-cj^eiag daxtvlovg 
€%o^£v^ itp^ o6a dcodsxata Ttdkiv tf^g dia^stQov tfjg 
riXiaKilg rj i7tL6K6tr]6Lg s6taL Ttata tbv ^s6ov syyLGta 
5 XQovov tfjg izXsLilJStog. toig d' sxatSQag tf^g TtaQddov 
^OQLOLg JtQO^d-svtsg TtdkLV t6 l^' avtcbv^ dvd'' d)v 6 
7]XLog iTtLXLVsttaL^ Kal td ysvo^sva jtQog ro tfjg 6slfivrig 
dvGi^aXov KLvrj^a JtOL7]6avtsg S^ag L6rj^sQLvdg to6- 
ovtov s%o^sv tbv XQ^vov SKatSQag trjg ts i^7tt(h6scog 

10 Kal tfjg dva7tXr]Qd)6scog^ G}g ^rjds^Lccg ybsvtOL JtSQL roifg 
XQOvovg tovtovg i7tL6v^paLV0'66r}g did tdg TtaQaXXd^SLg 
dLacpoQccg. 

ijtsl ds yCvstaC tLg dvL^otrjg aL^d^rjtfi TtSQl avtovg^ 
Tcbv 7taQalXd^sc3V ^svroL tfjg 6sX7]vrjg xaQLV Kal ov%i 

15 tfig dvcj^aXCag tG)v (pcbtcjv^ Kad"' rjv Kal ^sC^ovg djto- 

tsXovVtaL XGJQLg SKdtSQOL tdV TtQOSKtS^SL^lSVOV 7tdv- 

tots Kal cyg i7tl tb TtoXv dvL60L dXXfjXoLg^ ovds tavtrjv 
dvs7tC6tatov id6o^sv^ sl kol pQaxsta ov6a tvyxdvsi. 
^taQaKoXov&st ^sv ovv tovto tb 6v^7ttcj^a did ro 

20 yCvs6^aC XLvag iv tfj cpaLvo^svr] tfjg 6sX7]vr]g ^taQoda 
7tdvtots tcbv 7taQaXXd^so3V svsksv c367tSQ 7CQoriyr]tLKdg 
tLvag (pavta6Cag^ sl ^rjdsv idCog slg td S7t6^sva d^a- 
Xa^^dvoLto KLVovybSvr]. idv ts ydQ 7tQb tov ^s6r]^^QL- 
vov 7taQodsvov6a cpaCvrjtaL^ Kat oXCyov dvacpSQo^svr] 

25 Kal ^Xa66ov aisl tov ^taQsXrjXvd-btog 7taQaXXd66ov6a 



1. v.aviov A^, corr. A*. 'natSLXTifi^^vrig C, sed corr. 4. 
STCGKotriGLg D, sed corr. tov'] to D, to* D^ 6. l§'] t'|3' 
AiBC, SoodiyiccTov D. ccvd-' av] corr. ex avd''^ D^. 13. 

ylyvixai D. 20. yBVSGd-ai BC, yCyvtGd-aL D. 21. ca67tEQ] 

-£Q e corr. D. 25. eXaaoov atsQ iXd66ova D. naQsXriXv- 

&6tcog C, sed corr, 7iaQaXd66ov6a D. 



MA0HMATIKHS STNTASESiS <5\ 533 

TtQog tccg avatolag ^qddiov (paivExaL rijv slg xa eico- 
^sva ^Etdpa6iv Ttotov^svrj^ sdv ts ^std tbv ^s^tj^Pqc- 
vov TtaQodsvT]^ KatacpSQO^svT] TcdXiv ;car' bXCyov xal 
TtXsov aisl tov jtaQsXrjXvd-otog 7taQaXXd66ov6a TtQog tdg 
dv6^dg o^OLcag ^QadvtsQav triv sig td sno^sva ^std- 5 
pa6Lv (pav7]6staL jtOLOviisvrj, tovtov ^sv ovv svsxsv 
oC jtQOSLQrj^svoc XQovoL Ttdvtots ^sC^ovsg s6ovtaL tcbv 
aTtlcbg ovtcog Xa^^avo^svcov^ ^sC^ovog d' aisl dLacpOQccg 
sv talg V7tsQ0%atg tcbv TtaQaXM^scjv yLvo^svrjg STtl 
tGfv syyvtSQG) tov ^s6r]^PQLvov TtaQodcov dvdyKrj xal 10 
tovg TtQog ttp ^s6rj^PQLV(p ^dlkov t&v sxXsCil^sov xqo- 
vovg pQadvtSQOv aTtotsXst^d-aL^ xal dLa tavtrjv tr]v 
aitCav^ orav ^lv sig avtr^v trjv ^s6rj^^QCav 6 ^s6og 
XQovog trjg SKlsCipscog SKJtCTttrj^ tots ^ovov l'6ov syyL6ta 
yCvs6&aL tbv tfjg s^jttd}6scog xqovov r« trjg dvaTtXrj- 15 
QG}6scDg^ L'6rjg S(p\ sxdtSQa 6v^PaLvov6r}g syyL6ta tots 
xal tfjg SK t&v TtaQalld^scov itQorjyrjtLxfjg (pavta6Cag^ 
orav ds TtQO tfjg ^s6rj^PQCag^ tots tbv tfjg dvanXriQch- 
6scog iyyvtSQOv ovra rov ^s^rj^^QLvov ^sC^ova yCvs- 
^d^aL^ otav ds ^std ri)v ^s6r]^PQCav^ tots tbv tfjg 20 
s^7ttd)6scog syyvtsQov ovta tov ^s6rj^pQLVov ^sC^ova 
yCvs6d-aL. 

Xva ovv xal tr]v tOLavtr]v tCov %q6vcov dLOQ^co^LV 
TtoLdy^sd^a^ 6Ksi^6^s&a^ aad'' ov vTtsdsC^a^sv tQ^itov^ 



1. ^QccdELOv D, corr. Dl (jpaiVrjrat D, sed corr. 4. 

nXitov icEL D. nuQccXdccovGu D. 7. [iel^ov D. 8. ocsl D, 
corr. D^ 9, yLyvofiivrjg D. 10. eyyvrsQcoL BCD. tcuq- 

odcov'] corr. ex Ttaoodovcov D. 13, t?]V] om. A\ add. A*. 

15. yCyvhc^aL D. x6v'\ x6v xe D. toj] corr. ex xo C^. 

17. t-A x&v'] supra scr. Dl naQuXXdh^mg D, corr. D^; deinde 

del. £x xcbv TtuQuXXd^scov D. 20. oxav'] o D, o D^. 24. 

TQ^Trov] in ras. 1 — 2 litt. D^. 



534 KAATAIOT nTOAEMAIOT 

tov t£ TCQO tavtfjg trjg diOQd^a^scDg 6vvay6^evov %q6- 
vov ixatSQag tmv sktcsl^evcov TCaQ^dcov ocal tijv xata 
tbv iiE^ov %q6vov tr^g ixXsLipscog aito tou xaxa koqv- 
q)i]V d7c60ta6LV. 
5 satci} ds k^yov svsxsv 6 [isv XQ6vog ixdtsQog fiictg 
coQag i6Y]iiSQLvfig ^ y] ds tov Tcatd KOQV(pr]V d7t66ta6ig 
^OLQCJV of.. ^KSJp^^sd^a dr] sv Td3 TtaQaXlaxtiKa Tca- 
vovL td TtaQaKSL^sva t<p tcbv os dQLd^^m trjg %aQ- 
alld^scjg i^r]Ko6td mg Tcatd tb ^syLCtov d7t66tr]^a 

10 ?.6yov svsKSV ov6r]g trjg asXrjvrjg^ TtQbg o d7t60tr]^a td 
iv ta y' 6sXLdLG) TtaQaxsL^sva Xa^pdvstaL' svql6ko^sv 
ds iTtL^dklovta tatg os ^OLQaLg i^r]xo6td v^. %al iTtsl 
ixdtSQog XQ6vog trjg ts i^Tttco^scog xal rrjg dva7tXr]Qco- 
asog v7t6xsLtaL ^iaog dsoQov^svog ^Lccg ^sv wQag 

15 L6r]iiSQLvf]g^ %q6vg}v ds ls^ tovtovg d(psX6vtsg ^sv d7tb 
tG)v os trjg d7to0td6SG)g aoLQ&v sxjql^xo^sv tatg Xol- 
Ttatg J ^OLQaLg td TtaQaxsC^sva TtaQalkd^sog i^r]xo6td 
iv ta avt^ 6skLdL(p fit,^ cog tr]v xatd tr]v ^s6r]v TtQbg 
Td5 ^s6r]^PQLVca TtdQodov ix tf]g ^taQakkd^sag 7tQO7]yr]0LV 

20 s^r]xo0t&v £ 6vvf]%%^aL. 7tQ06d-ivtsg d' avtovg tatg o£ 
xal tatg 6vvayo^ivaLg 9 ^otQaLg svql6xo^sv fV tm 
avt& CskLdCcp 7taQaxsC^sva td tf]g okr]g 7taQakkd^scjg 
i^r]xo6td vy i\ Sg xal ivd^dds tr]v 7tQor]yr]6LV tr]g 
7tQbg Td5 OQC^ovtL 7taQ6dov 6vvf]%^aL tcbv avtcbv i^r]- 

25 X06tG)V d L'- 't^V SVQSd^ivtCJV OVV dLa(p6QG)V td TC3 

^rjxsL i^tL^dkkovta kaii^dvovtsg xal ixdtSQOv 7tdkLv 



3. rov] corr. ex rd D^ 7. v,avovC(o D, corr. Dl 8. r7)e] 
om. D. 11. 2,ccfi§civBTaL' BvQia-iiOfisv] -t b- in ras. D. 13. 

8y.dT£Q0s 6 xQOvos Halma. 14. Q^BcoqovyLBvoL D. {liv'] seq. 

ras. 2 litt. D. 21. 9] in ras. D. (lOLQOLg A^ 22. oXrjg] 
avtiig D. 23. vy [_'] T L' A\ TtQOT^yrjOLv] -r\- in ras. A^ 

24. naQobov] corr. ex TiaQa8ovg D^. 



MA0HMATIKH2 STNTASESiS <;'. 535 

dvaXvovtsg sk tov trjg 6skrivrjg avo^dkov xovTJ^atog 
slg ^SQog agag l^rj^SQLvfjg ^ cjg vitodsdsLKtai^ to 6vv- 
ccyofisvov acp' sxatSQOv 7tQo6d^r]6o^sv oixsLcog sxatSQG) 
tcbv ^sacjg xal ankcbg sUrj^^svcov xQdvcav tr]g ts 
s^7ttcb6scog xal 'tfjg dvajtkrjQCJdscog^ tb ^sv ^st^ov tS 5 
oiatd trjv syyvtSQav tov ^sCyi^^qlvov TtdQodov^ tb dh 
^la66ov tG) xata trjv syyvtsQav tov oQL^ovtog. df}lov 
S\ otL xal rj tcbv jtQOxsL^svcjv xq6vcov VTtSQOir] ^oqlcov 
fisv ysyovs y L\ ^' ^^ syyL0ta ^Lccg a>Qag iarj^sQLvrlg^ 
sv o6c3 td toaavta s^r]xo6td ^s6(Dg rj 6sXr]vr] XLvrjd^rj- 10 
^staL. xataXsLTtstaL ds sx 7tQO%SLQOV xal tb tdg L6r]^s- 
QLvdg wQag^ sdv ^sXcoiisv^ xad'' sxd6tr]v dLd0ta6LV 
dvakvsLv sig tdg xatd ^SQog xaLQLxdg xatd tbv sv 
rotg TCQOCvvtstay^svoLg VTtodsdsLy^svov r]^tv tQoitov. 

la . TIsqX t&v sv tatg sxXsLJps6L 7tQo6vsv6scov, 15 

'Ecps^fjg d' ovtog tov xal tdg ytvo^svag tcov S7tL- 
6xotr]6SG)v 7tQ06vsv6SLg i7tL6xo7tstv 6vvL6tataL [isv r] 
tOLavtr] xatdXrjjpLg sx ts trjg avtcbv twi/ STtL^xof^^scov 
TtQbg tbv dLa ^s6cov tcbv ^ojdLcav xvxlov 7tQo6vsv6sc3g 
%a\ i% tY]g avtov tov did ^s6cov 7tQbg tbv bQL^ovta. 20 
rovtcov d' sxdtSQOV sv sxd6t(p tcbv sxXsL7ttLXcbv %q6vcov 
7tlsL6tr]v dv xal d7tSQLXr]7ttov 7taQd6%0L TtSQL tdg ^sta- 

4. ELXrKifjisvcov] -co- in ras. A^ 6. zov (is^-qfi^Qivovl to- 

et ^S6r]- in ras. A^ ds] om. D, d' supra scr. Dl 9. yi- 
yovsv D. atQug] iioLQccg D. 10. 17] postea ins. D. 11. 

Supra TO del. a D. 13. rdg] td C. 14. 7iQ066vvtstayfii~ 

voig D, sed corr. cc7ioSsdsLy(isvov D, 15. lu'] ccl B, om. 
A^CD. 16. tov] supra scr. D^ 17. s7ti6yiozsLv C, sed 

corr. 18. v.cctdXrjiiif^Lg D, (i eras. avtiov tav] D, tmv ccv- 
xG>v A\ t&v ccvtwv BC. 19. TtQog tov] supra scr. D^ y.vy.Xov] 
TLvX^ D. 21. sv] supra scr. D^ 22. naQaGxoL] corr. ex 

'jtaQxoL D*, et similiter saepius. 



536 KAATAIOT nTOAEMAIOT 

0vd6sig BvakXayiqv^ si' rig xag 8l oXov tov xqovov 
ysvrj^o^svag JCQ06vsv6ELg JtSQLSQyd^sad-aL ^sXol^ /lh^ 
Ttdvv TL rfjg stcI ro6ovzov JtQOQQ7]6scog dvayxaLag rj 
XQV^i^^^i^S V7CaQX0v6r}g. rijg ^sv yaQ rov ^cydLaxov TtQog 
5 rbv oQL^ovra ^x^^sog ^scjQov^svrjg sx rrjg rcbv dva- 
rskXovrcov iq dvvovrcav avrov 6rj^SLCov xard rov oql- 
^ovrog STCoxrjg dvdyxrj ocard rbv rfjg ixksLtjJSCjg xQovov 
dLacpoQCDV 6vvsxcbg yLvo^svcov rciv dvarsXlovrcjv xal 
dvvovrcjv ^SQcov tov ^adLaKov xal rdg vjc avrcbv 

10 dTCorskoviisvag rov bQL^ovrog ro^dg 6vvsx&g dLacpoQOvg 
yLvs^d^ac^ G}6avrcag ds xal rrjg cCQog avrbv rbv dLa 
^s6c3v rcbv S7CL6zor7]6Eov 7CQ06vsv6sc3g d-scoQOv^svrjg 
STcl rov Sl d^cporsQcov rcbv zsvrQcov rov rs rfjg 6skri- 
vr]g xal rov rrjg 6KLdg rj rov rjXLOv yQacpoiisvov ^s- 

15 yL^rov kvkXov TcdXcv dvdyKrj d^d rr^v sv r<p XQ^'^^ '^V^ 
SKksLiJjsog rov KSvrQov rrjg 6sXr]vrjg TCaQodov xal rbv 
dc' d^(porsQC3v r&v KsvrQCJv yQaq)6^svov kvkXov rr^v 
d-s6iv dXXrjv dsl JCQbg rbv t^codcaKbv ka^^dvsLV xal rdg 
VTcb rrjg ro^rjg avTGJV jcsQLSxo^svag ycovcag 6vvsxcbg 

20 dvL6ovg 7C0LSLV. avrdQKovg ovv s6o^svr]g rfjg roLavrrjg 
i7Ci6Ksi)sc3g, idv iTcX fi6vcov r&v i7CL6r]^a6Lav rLvd i^ov- 
6cbv i7CL6Kor7]6Ecov Xa^^dvrjraL Kal Kard rb blo6xs- 
Qs6rsQov r&v 7CQbg rbv OQL^ovra ^scoqov^svcov 7Ceql- 
(psQELcbv^ dvvarbv ^sv s6raL Kal avrbd-sv rotg ys rb 

25 yLvo^svov 7cdd^og V7C oiIjlv 2,a^pdvov6L rsK^aLQE^d-ac 



\ 



1. i^aXXayijv D. 2. yevrioo^ivag] corr. ex iviaofisvag D*. 

6. rov] T corr. ex r D^. 8. SiacpoQcov] corr. ex dLacpoQcoG D*. 

yiyvo^ivcov D. 11. yLVEGd^ai^ A\ ysviod^aL BC, yiyvs- 

6%aL D. 14. r\\ ins. D*. 16. x6v'\ corr. ex x&v C^ 18. 

asC\ a- in ras. D^ 19. vnol corr. ex ano D. 20. r^g] 

g xf\g D. 21. fiovcov x&v\ in ras. D. 25. yLv6^svov\ -l- 

in ras. D. Xafi§dvov6 D. xs-niiaLQSO&aL] -aC- in ras. D^. 



MA0HMATIKH2 2TNTASE£iS ?'. 537 

dca xfig xkt^ d^^oteQag rag 7iXC6£i,g dva&6G)Q7]6£cog tdg 
ijiLTcaLQOvg rcov 7tQ06v£v6£G}v Lxavfjg iv tolg tOLOvtOLg 
V7taQ%ov0rig Tcal tTjg Kad"' blo0x£Q£Lav^ d)g £(paiL£v^ dia- 
Xriilj£G}g^ o^cog df, Lva ^ri naQ^XriXvd-ot^g g)^£v tbv 
toTCov^ 7t£LQa66^£%^a xal TtQbg tijv tOLavtrjv £(po8ov ix- 5 
&£6^aL tLvdg tQOTtovg cog £vl ^dheta %Qo%£LQOvg. 

t&V ^£V OVV i7Cl6X0t7]6£G)V 7taQ£LX7](pa^£V Tcal riiiL£Lg 

Sg i7tL6rj^a6Lag d^Lag triv t£ tov 7tQ(btov ixX£L7tovtog^ 
ijtLg iv tfj dQ%fi tov olov %q6vov tfjg ixl£Ltl)£(X)g yCv^taL^ 
xal tijv tov i6%dtov ixk^C^tovtog^ 7]t Lg iv tf] dQ%fi la 
tov tfjg ^ovrjg %q6vov yCv^tat^ %al trjv tov 7tl£C0tov 
ixX^C^tovtog , 7]tLg iv ta ^£6(p %q6vg) tf^g i7tX£C^£G)g 
dv£v tfjg ^ovfjg yCv£xaL^ xal tfjv tov 7tQC0T0v dva7tXrj- 
Qov^ivov^ TjtLg iv rc5 tiX^o tov oXov tfjg ^ovrjg %q6vov 
yCv£taL^ %al tfjv tov i6%dtov dva^tXrjQOv^ivov^ r]tLg iv 15 
t(p t£l£L tov oXov tfig ixX^C^l^^cog %q6vov yCv^taL. xal 
xcbv 7tQo6v£v6£G)v dh TtdlLV G)g £vloyG)X£Qag x£ xal 
ili(paxLKG)X£Qag 7taQ£Llri(pa^£v xdg d(poQL^o^ivag V7t6 x£ 
xov ^£6r]^pQLVov xal xCbv xov dLa ^£6g)v dvaxoXcov x£ 

Xal dv6£G)V L6rj^£QLVG)V X£ Xal d-^QLV&V Xal %£L^£QLVG)V 20 

xrjg XG)v dv£^G)v dQ%fjg dLa(p6QG)g ^lv dv ^toXXotg tcoX- 
XdxLg V7taxov6d^r]6o^ivrjg^ dvva^ivrjg d' ovv^ £i! xtg 
^ovXoLXo^ xal dTtb xcov ixx^L^ivcov xov oQC^ovxog yco- 
VLcbv iii(pavCt,£6Q'aL. xcbv ^ev ovv yLvo^ivcov V7tb xov 



3. SiaXrjfitpscog D, fi eras. 8. tog] om. D. 9. yiyvhxai D. 
11. yCyvexa.i D. 12. Ti)g iv.Xdiptoig^ om. BD. 13. avev\ 

om. D. 14. xov — 16. oXov'] mg. D^ 14. oXov^ A\ 

oXov xov BCD^ 16. tov oXov^ etiam in textu D. xfi? fx- 
XELipstog'] tfjg Ih- in ras. A^. ylyvEtai D. 18. TtaQSiXri- 

cpaybBv'] -X- in ras. D^ 19. twv'] -&v in ras. A^ 21. av] 

a K^. 23. Post oQL^ovtog del. tojx'' ndvtotE D. 24. ovv\ 

corr. ex iov C^ yiyvonivcov D. 



538 KAATAIOT nXOAEMAIOT 

^sefrj^PQLVov to^&v tov oql^ovzos trjv ^lv ^oQeiov 
ccKovcjfisv aQZtovg^ trjv ds vot lov ^s07]ufiQtav^ tav d' 
dvatohxG)V xal dvttKcav tag ^sv vito vfjg aQxfig tov 
Kqlov xal tGJv XrjXav yLVO^evag tov OQL^ovtog to^ag 
6 Ttdvtots tb i'6ov tstaQtri^6QL0v d7ts%ov6ag tav vtco 
tov ^s6r]^PQLVov yLvo^svcov L6r]^SQLvrjv dvatoXrjv xal 
dv6LV^ tdg d' vito trjg dQxrjg tov KaQXLvov d^sQLvrjv 
dvatokriv xal dv6LV^ tdg d' {)7tb trjg aQxrjg tov Aly^- 
%SQG) ;f£i|^£()tv^v dvatolrjv xal dv6LV^ tav ^sv xatd 

10 tavtag dLa6td6scov xatd TcXt^a dLacpdQCJv ditotsXov- 
fisvcsv^ s^aQxovdrjg ds trjg t&v 7Cqo0vsv6sg)v dTCocpd- 
^scog^ otav iqtOL Katd tLVog i^ ^sta^v tLVCov tcjv TtQo- 
KSL^SVCJV 0QC3V dsLKVvrjtaL, 

svsKSv iisv tOLVVv trjg SKd6tots tov ^adLaxov JtQbg 

15 tbv bQL^ovta 6x^6 scag STtsXoyL^d^sd^a ocatd tbv iv tolg 
7CQG)tOLg trjg 6vvtd^sG)g vTtodsdsLy^svov tQO^cov tdg 
yLvo^svag stcI Tot) dQL^ovtog sv tatg dvatolatg xal 
6v6s6lv V7cb trjg dQxrjg svbg md^tov t&v dodsxatri- 
^OQLG)v d7to6td6SLg S(p' STcdtsQa tcbv dTtb tov L6r}^SQL- 

20 vov yLvo^svcov to^&v Tcad"' sxa^tov tCbv d7tb MsQorjg 
[isxQL BoQv^d-svovg xh^dtcjv^ scp^ g)v Tcal tdg ycjVLag 
s^sd^s^sd-a^ xal dLsyQd^a^isv xatd tb svdscoQrjtov dvzl 
xavovLOv zvxXovg rj 7Csql tb avtb xsvtQov sv tc5 tov 
OQL^ovtog S7CL7Csd(p voov^svovg Kal TCSQLSxovxag td tcbv 5 



1, xriv\ corr. ex t D^ 2. aQv.tovq] -vl- in ras. D^. trrjV] 
corr. ex r' D*. x&v] post ras. 1 — 2 litt. D. 3. Post Svxi- 
-a&v del. xds /x vnb t oql^ovxos D. tdg] corr. ex td D^. 4. 
yiyvofiivag D. tofiag tov OQL^ovtog B. 6. LarjfXEQLVi] D, 

corr. D^ 7. tdg d' vnb tfjg aQifig tov KaQV.LVov bsQLvi]v 

dvatoXr}v v,al 8v6lv] D, om. A^BC. 9. dvatoXi^v] dv- in 

ras. D. 16. dTtodsSsLyfiBvov D. 17. ini] A^D, vtco BCDl 
20. yLyvo^^vcov D. 22. xat] x- in ras. A^ 



MA0HMATIKH2 STNTASEiiS g'. 539 

Tch^dtcov 8ia6triiLaxa xal tag bvo^a6iag' eitSLta •xaqa- 
yQdtfjavtsg svd^stag dvo dca Ttdvtov t&v tcvjcIcjv TtQog 
dQd^dg ycovCag dXXijkaig^ triv ^ev it£Qav xal itXayCav 
wg xoLvrjv tofiiiv tav iTttTtedcjv tov ts hQCtpvtog Tcal 
Toi) i0rj^£QLvov^ trjv d^ itSQav Tcal oQd^rjv (bg xocvriv 5 
to^ijv tcbv STtiTtsdcDv tov ts OQi^ovtog Tcal tov ^s^rjfi- 
Pqlvov^ 7taQS6r}fiSLco6dfisd'a xatd tav TtQog tbv ixtbg 
xvkXov TtsQatcov tfig fisv itXayCag yQafifi7}g C^rjfisQLVTJv 
ts dvatoXijv xal L6rjfiSQLvrjv dv6LV^ trjg ds dQ&rjg ccqk- 
tovg ts xal fis6rjpiPQCav. co6avtcjg ds TtaQayQdil^avtsg lO 
ixatSQcod-sv tf}g l6r]fi£QLvrjg svd^sCag Tcat l'6rjv ai)tr}g 
d7t66ta6LV did Ttdvtcov ndUv tcov kvkIcov JtaQsd^tjxafisv 
xal Tcatd tovtcov iv fisv totg fista^i) iittd dia6trjfia6iv 
tdg svQrjfisvag xad'' £Ka6tov xkifia tcbv tQOitLK&v 6ri- 
(isCc3v ditb rov i6rjfiSQLV0v 8La6td6SLg iitl tov 6qC^ov- 15 
rog cjg tov tstaQtrjfioQCov fiOLQcbv ovtog 9, iv ds totg 
TtQbg tb ivtbg tcbv kvkIcov 7tSQa6L totg fisv :tQbg tfj 
fis6riii^QCa xsLfisQLvijv dvatoXijv koi %SLfiiSQLviiv 8v6lv^ 
totg 8s JtQbg tatg aQKtoig d-sQivijv dvatoXijv Kal d^SQi- 
vi]v dv6iv. svsKsv ds t&v fistalv dcodsKatrjfioQicov 20 
7tQ06svtd^avtsg [ista^v i^d^tov t&v ts66dQcov dia6trj- 
lidtcjv dkXag dvo yQa^ifidg ^taQsd^rJKafisv Kal Kaxd tov- 
tcov tdg tcbv oCksCcjv dcjdsKaxrjfiOQCcov iTtl tov bQC^ovtog 
d7to6td6Sig tov C6r]fiSQivov trjg 6vofia6Cag i^d^tov Katd 
tbv s^co kvkXov i7tiyQa(pofi£vrjg. 7taQ£67]ii£icj6d(i£d-a dl 25 
Kal 7t£Ql tijv fi£6r]fiPQivi}v yQaiifiriv tdg t£ 6vofia6Cag 



5. $'] 8s B. 10. Post xat del. 6 in scrib. D. di] 

om. BC. 11. t6ri^£Qivfig] -6r\- supra scr. D^ Y,at] -t in 
ras. D. 13. dLcc6rrjpLcc6L B, 610(6x1] fia6l\ D. 14. Ante Tobv 

del. 6ri^Ei D. 17. roig] comp. D, ut saepe. 18. (ie6rifi- 
^QLCiv D, sed -V eras, 19. xccLg] totg C. 22. v.cctd] v,ci C. 
23. ol'AEioiv] om. D. 24. v.citcc] tov vcctcc C, corr. C^ 



540 KAATAIOT nTOAEMAIOT 

tav TtaQalXriXcov nal %a cjQiata ^eyed^rj Kal xa rcbv 
7c6X(ov i^aQ^ara triv tcbv poQetotdtcov iTtLyQatprjv aTtb 
tov ^Ei^ovog Tcal jtSQLSxovtog tcvxXov TtOLrj^d^evoi,. 
OTtcjg de xal tdg avtcov tcov i7tL6Kot7]0ecov TtQog 
5 tbv dtd ^eamv (patvo^evag 7tQo6vev0eLg ixxeLiievag 
excofiev^ tovte^xLv tdg yLVO^evag ycovCag i(p exd6trjg 
tcbv eLQrj^evcov i7tL6r]^a0Lcbv ijTtb trjg to^fjg tov te 
^cjdLaxov xal tov di' d^cpoteQcov tcov dedrjXco^evcov 
xevtQcov yQa(po^evov ^eyCatov xvxXov^ xal tavtag iTt- 

10 eloyLdd^ed^a xad^' exd<jtrjv tcov evl daxtvXco trig iTtt- 
0xotr]6ecog dLacpeQove&v TtaQodcov trjg 6eX7]vrjg^ ijtl 
^ovav ^evtoL dLa tb avraQxeg t&v xatd tb iie0ov 
dTtodtrj^a ytvo^evcov xal cjg ^taQaXXriXov 7tQbg al6%-ri6Lv 
ov6cbv t&v iv tatg i7tL0xotri0e6L 7teQL(peQeLcbv tov ts 

15 dLd ^e6cov tcbv ^mdLCJv xvxXov xal tov Xo^ov tfi$ 
0eXrjvr]g. 

'e6tc3 ydQ 7tdXLV v^todeCy^atog evexev r] ^ev dvtl 
tfig TteQLcpeQeCag tov d^d ^e^cov t&v ^adCcov evd^eta rj 
AB.^ icp' ^g tb tov '^XCov xevtQov ri tb tfjg 6xLdg "bTto- 

20 xeCod-cj tb A^ rj de dvtl tov Xo^ov xvxlov tfjg 6eX7]vrjg 
ri FAE^ xal tb ^ev F 6rj^etov^ xad'' ov tb xevtQOv 
tfjg 6eXr]vrjg xatd tbv ^e6ov xqovov yCvetaL tfjg ix- 
XeC-tpeojgy tb de z/, xad-' ov TtdlLV e6taL tb xevtQov 
avtfjg^ orai^ 7tQ(otcjg oXrj ixXeCTtrj ij 7tQ(btcog dQ%ritaL 



1. v,aX td (alt.)] corr. ex xo: D^. 5. (liaov C. 6. tovt- 
eativ] comp. B, -v eras. D. yiyvo^evccg D. 7. sIqtj^svcov] D, 
yivoyiivaiv A^BC. 10. tcoi;] D^, too A^C, tan B, t&^ D. 8av.- 
tvX~ D, 8uv.tvX^ D^, ut saepius. 11. iiaqodcav] naqo- e corr. D^ 

13, yiyvofi^vcov D. 14. sniGyiOf^GEG D. 18. svQ^ei&v C. 

22. tov'] to D. 23. ■naQ'' ou] 'naQ'^ D. 24. TiQmtmg (pr.)] 
TCQOt mut. in TtQmt D, corr. D^. 




MAOHMATIKHS STNTASEiiS ?'. 541 

avaxad'aLQS6d'ai^ rovri^riv orav £6(x)d-sv sq^ccTtrrjrac rov 
rfjg dXLag tcvkXov^ t6 8s E^ %a%-^ ov yCvsrai rb xsv- 

rgov ax)t7}g^ orav TtQchrcDg 
ccQXTjrac SKksiTCSiv ij t6 
s&%arov avaTckriQov&^ai 5 
^TOfc 6 rikiog r) Ttal rj 0s- 
Xrivri^ rovrs6riv oTav s^- 
cod-sv ajtrcovrai dklTJlcjv 
01 KVKkoi' ycal sits^svxd^co- 
6av ai AF Ttal A^ Kal AE. 10 
on iLsv ovv aC ^sv vno BAT xal AFE ycovlai 
rov ^s6ov XQOvov nsQisxov6ai rcov sxXsitl^scov dQd^ai 
siatv TtQog al'6d-rj6iv^ rj d' VTtb BAE 7tSQis%si ri^v 
yivofisvr^v sitC rs rov itQcjrov sxXsCnovrog xal rov 
i^Xdrov dvaTtXrjQoviisvov ^ r] d' 'bnb BA/J rrjv STtC rs 15 
xov s^xdrov sxXsCitovrog xal tov TtQchrov dvaitXriQOv- 
lisvov^ (pavsQov, drjXov d' avrod^sv^ OTt 9cal rj fi^kv AE 
Ttdliv rdg sx r&v xsvrQCOv d^(porsQcov rav xvxXov 
%SQiSxsi^ rj ds A^ rijv xjitSQOxriv avrcbv. 

v7toxsi6d'C3 ovv VTtodsCy^arog svsxsv sxXsitpig^ xad^' 20 
-^i/ iv Tip (is6a) jjp(5vG) t6 ri^i6v rfjg dia^srQOV rrjg 
rjXiaxfig STtiexorrjd^Tj^sraL, xal s6rco t6 A xsvrQov rov 
riXCov^ G)6rs rrjv ^sv AE itdvrors did t6 ^s6ov vjto- 
xsL6d-aL t6 rflg 6sXilvrjg d7t66rrj^a ^vvdys^d^aL ^oqCcjv 
A/3 3c, rrjv ds AF XsC7tov6av aifrfjg ra ri^C6SL rf]g 25 
'^Xiaxfjg dLa^srQOv rcbv aurrai/ Tg ji. iTtsl ovvy oicov 

6. r;'] om. CD. 8, cc7tT0iv\T0ivxai, A^, corr. A*; anxxai D, 
corr. D^ 11. Post oxi eras. x6 D. 13. el6Lv^ comp. B, 

sld mut. in dai D. 14. yiyvoiihriv D. 15. i] 8' — 16. ava- 
nXr]qovyi,Bvov] om. D. 16. BAzi] BA- e corr. A^ 19. tt^V] 
om. A^ 24. To] supra scr. D^ fioQLcov] (iolq D. 25. tc5] 
corr. ex vvv t6 D^. 



542 KAATAIOT nTOAEMAIOT 

i0tlv 7] EA v7tOT£Lvov0a Xp 3c, TOLOvtcov ^vvdysTai 
Tcal 7] AF xaTa to skxsl^svov r^g i7ti6xoT7]6£cjg ^£y£- 
^og Tg ji, xal oicav £6tIv aga ri AE v7toT£ivov6a QXy j 
Toiovtcov xal Yj fi£v AF £6Tat, ^a va^ rj d' iit avtrig 

5 7t£Qi(p£Q£ia tOiOVtaV 1/3 j3, OXCOV l0tlv 6 7t£Ql t6 AFE 

oQd^oycjviov KvxXog t^. w(?r£ xal rj vTtb AEF^ tovt- 
£(JTiv rj vTto BAE [Eucl. I, 29], olcjv fiiv si^iv aC p 
OQd-al T^, TOiovTcjv £0tIv |/3 ^, Oicov d' aC d OQd^al t^, 
TOiovTCDv Xa a. 

10 TtdUv xal rcbv 6£kriviaxcbv £x^£if£C3v £V£X£v £0tco 
t6 A t6 rrjg 0xiag xdvTQOV^ &6t£^ £7t£i t6 ^£0ov b^oicag 
v7t6x£iTai Tfjg 6£X7Jvrjg d^to^Trj^a^ tcbv avTCJv d^l 6vv- 
dy^aO^ai Trjv (i£v AE ^vd^^tav |, Ti^v dl A^ b^oCcog 
xg /I, xal £xX£i7t£Tco r] 6£krivri xaTa rijv t&v Trj daxTv- 

15 Xg3v TtdQodov^ cS6t£ tc3 ri^i6£i Trjg diafi£TQOv TtdXiv 
iXaTTOva £ivai Trjv AF Trjg AA^ xal xaTaX£i7t£6^ai 
T&v avTcov T o. 

i7t£l OVV^ OtCOV i^TLV 7] AE V7tOT£iVOV6a QX^ TOi- 

ovTcov xal 7] ji£v AF yiV£Tai jc o, rj d' iTt avTrjg 

20 7t£Qi(p£Q£ia tOiOVtCOV i^ t/3, olaV i6tlv 6 7t£Ql t6 AFE 

tQiycavov dQd^oycoviOv xvxXog t|, £i7] dv ^iat 7} V7tb\ 
AEF ycovia^ tovt£6tiv rj V7tb BAE^ olcjv ^iv £i6iv 
ai p OQd^al T^, TOiovTCJv id" fc/3, o^icov d' aC d OQd-al r^, 

1. X§'} it^, %- in ras. B^ 3. tg] corr. ex ? D. AE] 

EA D. 6. AEF'] corr. ex ^E ET D^; deinde add. ycovCa D.. 

7. BAE] corr. exABE J)\ BEAB. ^ ^] A^ 8vo BCD.: 

8. toiovxoiv — 9. a] mg, D^. 8. d''\ 8i D^ 9. tolovxcov 
Xa a\ etiam in textu D (aao:). 11. v,ivxQOV ., mGxt] xal wffre 
in ras. B^ a)6xi\ -e add. D^ 12. ccTiocxri^a, xobv] corr. ex 

anoGx^fia Dl avx&v] supra scr. C^ 13. Ante | del. a?A*. 
14. iv.lBi%ixoi\ supra -ft- add. t D^ 15. naQodo} D, corr. D^ 
Tc5] t6 C. 16. Hcct — 17. xa)v\ in ras. D, is! AE\ EA D. 
19. yiyvsxaL D. 



MA0HMATIKHS STNTASE^S S'. 543 

roLOvtcov d" Xg. cj^avtcjg de^ eTCELdii xcct^ otwv i^TiV 
rj AA v7tot6LVOv6a qtc^ toLOvtcov ical rj ^av AF yi- 
vetaL Jie^ ri d' iii avtr\g TCEQLcpeQSLa tOLovtcov ^d p, 
OLCOv i6tlv 6 JteQL tb AFA oQ&oycovLOV xvxlog t|, eLrj 
ccv xal 7] VTto AAT ycovLa^ tovt i&tLV rj 'bjtb BAA^ 5 
OLGiv fiev eL6LV aC ^ OQ%^al r|, toiovtcav ^d ^, otcov 
d' aC d OQd-al t% tOLOvtcav x/3 a. 

tbv avtbv 8yi tQoitov xal iitl tcov aXlcov daxtvXcov 
Xaii^dvovteg tag TtrjXLXOtritag t&v iXa666vcov tr^g ^Q^rig 
ycovCag cog enl xfig fitdg t^rj^dtcov ov6rjg 9, 66cov xal 10 
t6 tov bQL^ovtog xetaQtrmoQLOV vTtdxeLtaL^ itd^a^ev 
xavovLOV iitl 6tLxovg ^ev xfij ^eXCdLa de d, gjv tb ^ev 
7tQG)tov neQLe^eL tovg evQL6xo^evovg avtfjg trjg ^caTci 
Tijv dLa^etQov ijtL^xotrj^ecog daxtvXovg iv ta ^e6(p 
XQ6vcp trjg ixXeCiljecog^ t6 de devteQov tag iv tatg 15 
rjXLaxatg ixXeCfe6L yLvo^evag ycovCag ev te xa tov 
TtQcotov ixXeCTtovtog Xq6vg} xal iv t^ tov i^xdtov 
dvaTtXrjQov^evov^ t6 de tQCtov tdg iv tatg ^eXrjvLaxatg 
ixXeCipe6L yLvo^evag ycovCag xatd te tbv tov TtQ^tov 
ixXeCitovtog XQOvov xal xbv xov i^xdtov dvaTtXrjQov- 20 
liivov^ t6 8e tetaQtov tdg yLvo^evag ycovCag iv taig 
6eXrjVLaxatg TtdXLv ixXeCil^e^LV xatd te tbv tov i^xdtov 
ixXeCjtovtog xq6vov xal xbv xov TtQcoxov dvaTtXrjQov- 
^evov. xaC eL6LV at dLayQacpal xov xe xavovCov xal 
xcbv xvxXcov tOLavtaL' 25 



1. Ss] d' D. 8. yial STii] add. J)\ 9. Xcc[i§dvovTsg] A\ 
Xa§6vtsg BCD. 10. ymviag] corr. ex yoDvT D^ inC] st D, 
mg. iQ toff STil trjg (iL&g D^. oaav] corr. ex oa D^ 11. tov] 
to- in ras. AV 12. ds S] corr. ex j A'. av] corr. ex co D^ 

13, TCQmtov] a B. 15. dsvtsgov] b' B. 16, yiyvo^svag D. 

18. tgCtov] f B. tdg'] supra scr. D^. 20. tov] om. B. 

21. tstaQtov] y B, yiyvoasvag D, 24, ai] at ts BC, 



544 



KAATAIOT nTOAEMAIOT 



i/8'. ^'Exd^s^cg rcbv itQog tag 7tQ0CvBv6aig 
diayQatpav. 



5 


' a' 
SdtitvXoL 


§' 

■TtQmtov iyiXsL- 

Ttovtog ■nal 

iaxdtov ccva- 

nXrjQovfisvov 


y 
(L 

TtQojtov iv,XsC- 

Ttovtog %ai. 
iaxdtov ava- 
nXriQOVfiivov 


8' 

icxdtov 

iiiXsLnovtog 

%at nQoatov 

avanXrjQov- 

(livov 


10 




a 


9 

V? vQ' 


9 

o|3 X 

|f i 






y 
d 

s 


lid' Lg 
(ip X^ 
X? Xs 


v% x^ 

v8 %t 

V l8 




15 




Xa a 
%£ fig 


(i^ Xa 
Xd- p 




20 


L 

La 


LS va 

La g 

<5 v,S 


Xs ii§ 
Xp H^ 
x^ xy 






lP 
Ly 
td 


a (i^ 


>ig xy 

xy X7? 

X Xg 


9 
v§ yi8 


25 


LS 
L<S 




Ls a 
Lp Lri 


(ly X? 
Xs (la 
Tir} Xrj 


30 


Lri 

L%- 

v,a 




Q' Xc, 

<S VE 
. 8 LS 

a X<5 


H|3 a 
LS (ly 

% X? 
y Xs 



1. L^'] om. A^BCD. STi&sCLg — 2. 8LayQa(p&v] D, om. 
AiBC. Tabulam totam om. C. 3. a' — 8'] A\ om. BD. 

4. — 8. om. D. 5. i-nXs Cnovtog (tert.)] -s- supra scr. A^ 11. 
1«] -s e corr. D*. 14. v] seq. ras. D. 15. a] corr. ex (la D. 
16. fig] (i- e corr. D. 17. /x^]_corr. ex (la D^. Xd^] -& 



e corr. D. 18. Xs] corr. ex Xd' Dl 

%S] xe D. 23. x^] xa D. 

o D. 30. Des. fol. l^^'' B. 



21. (i^] in ras. A^ 
25. a] e corr. D. 27. '9'] 



MA0HMATIKH2 STNTASESiS 5'. 545 

Ly'. ^toixQL6Lg 7tQ06V€V6£(xiV, 

"Exovteq ovv TtQodtaxexQiiievovg^ bv vTtedeila^sv 
TQdTtov^ tovg xQ6vovg exdetrjg t&v ixxei^evcov e:tL- 
6rj^cc6Lcov xal ano tcjv %Q6v(Xiv drjXov6tL ta xar' avtovg 
dvateXXovta xal dvvovta ^eQrj tov dta ^e6(ov a7t6 te 5 
tfjg xatayQacprjg tag xata tbv bQilovta d^e^etg avtav^ 
otav ^ev xat avtbv tbv Sl^ ^e6cov fj tb xevtQov tfjg 
6eXrjvrjg rjtoL tb (paLv6fievov ag eitl tcov rjXtaxav ex- 
XeC^ecDv rj tb dxQL^eg i}g inl tcov 6eXrjvLaxG)v^ tijv fihv 
xatd tb TtQcbtov ixXetJtov tov rjXCov 7tQ66vev6Lv xal 10 
etL tijv xatd tb e6%atov ixXei%6v te xal dvaTtXrjQov- 
fievov tfjg 6eXrjvrjg e^o^ev ditb trjg avtov tov t6te 
dvvovtog xatd tbv bQL^ovta &e6ecog^ tijv dh xatd tb 
i^xatov dvajtXrjQov^evov tov 'fjXtov ^cal ett tfjv xatd 
t6 TtQCJtov ixXetTtbv te xal dvajtXrjQov^evov tfjg 6eXfj- 15 
vrjg di^ aiftov tov dvateXXovtog' orav de ybfj xatd tbv 
dtd ^e6cov fj tb xevtQov tfjg 6eXfjvrjg^ Xa^6vteg ix tov 
xavovLOv tovg olxeCovg tfj 7to66trjtL t&v daxtvXcov 
TtaQaxet^evovg tcov ycovLcbv dQid^^ovg TtQO^ex^aXov^ev 
xal avtovg d7tb tcbv xolvcov to^&v tov te bQC^ovtog 20 
xal tov dLd ne6cov^ idv ^ev ^OQeL^teQov rj avtov t6 
xevtQov tfjg 6eXfjvrjg^ iTtl ^ev tov 7tQcbtov ixXeCTtovtog 
tov fjXCov xal tov i6%dtov ixXeCTtovtog tfjg 6eXfjvrjg 
hg TtQbg aQZtovg tfjg dvtLxfjg to^ifjg^ i7tl de tov i6%d- 



1. ty'] ri B, om. A^CD. 3. xo %qovG D, ra x^ova D*. 

5. \iic D. 6. ^^0 D, ^iG^ Dl 7. Jj D, om. AiBC. 9. 

dx^taD. 11. i-Alhinov Tf] corr. ex I-aX^itiov D^. 15. rf\<i 
GiXf\vr\<s\ -fig 6sX- et -v- in ras. A^. 16. avaxiXovxoq D, corr. D^ 
17. Tj] corr. ex riv D. 19. nQ06Eyi,^oiXXoviiBv D, corr. D^ 
Ptolemaeus, ed. Heiberg. 35 



546 KAATA. nTOAEM. MAeHMATIKHS STNTAgES^S S'. 

rov avccTcXrjQovnsvov tov yikiov xal rov TtQcorov dva- 
TcXrjQov^evov Tfjg 08X7Jvr}g cog TtQog ccQxtovg tijg dva- 
toXLjtflg, xal TtdXiv iitl ^ev tov TtQcotov ixXeCitovtog 
tijg 0£X7]vrjg cjg JtQog ^60r}^PQtav trig dvatoXiTcrjg to^rjg^ 
5 STtl ds tov s0%dxov dvaTtXrjQov^svov trjg askrjvrjg ag 
TtQog ^s0r]y,pQLav trjg dvtiKrjg' sdv ds voticotSQOv r) 
tov dtd ^60cov tb otsvTQOv tfjg ^skilvrjg^ iitl ^lv tov 
TtQcotov ixXsLTtovtog tov r]XCov xal tov i6%dtov ix- 
^sCjtovtog tfjg 66Xr]vrjg cjg JtQog ^60rj^PQCav tfjg dvtt- 

10 xfjg to^fjg^ iTtl dh tov i6xdtov dvaTtXrjQov^ivov tov 
r}XCov xal tov jtQatov dvaTtXrjQov^ivov tfjg ^eXrjvrjg 
G)g TtQog ^60rj^PQCav tfjg dvatoXiKf]g^ xal Ttdhv inl 
^6v tov JtQcotov ixX^CTtovtog tfjg 06Xr]vi^g cjg TtQog 
ccQXtovg tfig dvatoXixfjg toiifjg, inl dl tov i^^dtov 

15 dvaitXrjQovfiivov tfjg 66kr]VY]g cog TtQog aQXtovg tfjg 
dvttxfig. xal tb 6vvc6td^6vov ix tfjg toiavtrjg dLOQd-co- 

06C3g ^6Q0g tOV bQC^OVtOg £%0^6V^ » 7tOLY]€6taL tf]V 

7tQ66v6v6LV^ G)g 6cpa^6v^ bXo6%6Qi0t6QOV td 86%6^sva 
tti)v (pcotcjv ^SQr] tdg ztQcbtag xal tdg i6%dtag tcov 
20 ixlsC^^cov xal tcbv dva7tXr]Qco66cov i7tL6r]^a0Cag. 



1. Tov r]X(ov — ccvanXr^Qov^EVOv'] supra scr. C*. 2. rrys^alt.)] 
supra scr. D^. 4. Ante rr)? (alt.) del. Ti}s SvTL^fjg D^ 6. 

voTLmTeQOv'] BD^, votlotsqov A^C, votbi6tbqov D. 7. dLa (is- 
ccov'] -Lu (i- in ras. D. 8. >tat — 9. GBX^^vT^g] mg. D^ 16. 
ix] corr. ex t-»' D*. 17. o5] om. D, 6 Dl 18. 6Xo6xeQe6TSQOv~\ 
ult. in ras. A^ In fine: KXavdCov IlToXefiaLov nad'r](iaTL'nfig 
avvTa^scog ? B, KXavdCov IlToXe^Laiov (iad"riaaTLK&v ? C, TsXog 

TOV SHTOV D. 



I 




¥^jM& 



k Ul / _ IM^EiS. _ J 



*»^ A «7«^^ 



PA 

A2 

1898 
v.l 
pars 1 



i^olemaeus, Claudius 

Claudii Pfcolemaei Opera 
quae exstant omnia 



^-i^ 



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