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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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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 dg 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 dtar' 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 sxdg 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-
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
ia\ KavovLOv tg)v iv kvxXcj sv^eiobv.
TteQLCpe-
Qeicbv
tv^eioiv
£|7]XO(yTc6l/
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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
KAATAIOT nTOAEMAIOT
QBl&V
SV&Bl&V
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60
KAATAIOT rrrOAEMAIOT
TtSQLCpS-
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MA0HMATIKHS STNTAgjEiiS A'.
61
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tjW ^. 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] 
