Ioannis Kepleris Strena seu de niue sexangula

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Images reproducecl by courtesy of the Royol Librory, Copenhogen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royol Librory, Copenhogen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

lOANNIS KE

PLERIS.CMAIEST.

MATHEMATICI

STRENA
Seti

De J^^Que Sexanmla.

Cum Priuilegio S. C«£ Maicll:. ad annos x v.

FRANCOpyRTI AD ^MOENFM^
apttd Codefi^idum Tampach»

Anno M. DC.XI.

Early European Books, Copyright © 2009 ProQuest LLC.

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m

AD ILLVSTRE

S.C. MAIEST. CONSILIA-

RIVM IMPERIALEM AVLICVM, D.

lOANNEM MATTHv£VM WACKHaRiVivl

aWaekhenfelsjEqnitem Auratutr,&c. Litc- ato'.uni
& PhilorophorumMecoeuarem Dc-
minum meum bencfi-
cum.

V M non Jim nefcmy qmm Tu ames \^!,non
' ^'^^^n V^^^^^ P^^^^ vilitatem , fed pro: :tr Lyciui

^iicquidtd.-sf quod aliqui. NihiH co^itmme tihi ^lluhefrat ; /V
^ p xru^-. & paruH (r vtli[Jimurn,^ mtPiime clurxhileyhoc c^l ,iH?'e
nthd eftoportet. -ut cum in rerum mitura muJti (if't, r^' tamcn
intere^ ddc^tis, Cogt^xkii fort.^fjt' de ur^o rx ^^tj^t is tpv urr vc-
rum idNjhUcH. N[thilvero a mehaherantea. Ea nwttaq/tdpcr Ele-
mentajjoc cH pcr eayqtht funt in vnaqun^ re m ntwa

Primttm Je Ttrra ,hoceJi de^rchtmedi<s mn tl^ftu-isnefom-
nicSyqut Tcrraminarenasrefoluit ,qui pulufculorum ^iena m lltx
poffidetin vnograno papaucrt Untim entmfiubtrax^ ro 2{^;merc-
rtimillt yA^fyrtadum^, rationesplane confudno. ^ emodhutuj'
modt co pufculommfgtira necocults vtdaur,nec 'i. h ^ ^.frchimcde

d ^ pro-

4 DE NIVE

frocl fur. 7{ullum tgttur in ijs ingcniunty nulU rel non vifa cupid&^
Efi (jr rfs dnrnyiiisyfHluis , vtquxtrabibtis vetufiate /tila^isycarie
confuJij i//Ji^ ens dQminatur. TS^mium igitur dedcro, hoc /i dedcro.

Ignr^ porro fcintilUyCtli paru^(^evantd^, nunquamtamen ftnt
minores aroiulis pyritarum, qux confliciu dcteruntury aut flrigmcn'
tuprunarum : qu^iam interpulufcahsrcicci FiguralcsrtaquePy-
ramid^s , qua^s nunquam vidi , Platoni relinquOy vt ex ijs arbitrat($
fuo concinnet ignenuVentendumad Elementa intermedta^

Ventum crfimesdarefofew.fedhi vcnduntur ; nequehoctan-
tumin vtribtis Ifmdicisyfed ^tn cbarth , qutn ^in verbis yidque
fdfimpcrorbcm terrarum.Res itaque prectofa fumHs^c^qudimagnQ
mihi conjlat. 2{eque h^c aPta ingenio, quia rudis dr informis.

K^d Aqu^tgitur dcvoluimur. Hitrcnteminvrnaguttam fk-
crofincii vates pro re cohtemptijfma reptitant. Et Gcrmani nojlri
nilminus habent illa vinigntuda , qtuPosicyathtim exhatifum fu -
J>er vnguemexcutittiry ibiquehxrensmele fua Jiat. Sihancobtnlcro
gtittam, mint^^fne dederoy qtiamii/c Perfa y vola mant^^s Choafpem
Rcgi fuo ajfundens ; honcjitti^ etiam. muntis y vini gutta ex vngue
Cermaniy qtiamderofumramcntum deungtic infrendentis . ^ vel
tant i/hiM ncgantis Itali :. Denig.^ figuraguttxgtobofi tam (pcculatio^
ncinpollicetur gcomctricam : Jcd vcreor, ne & hoc ttbijit nimium^,
qui tantopcre dclcciaris Kthtld,

£ltitdf adantynalia fiattranfitio? Vereor vtnociuas Athenas^,,
T^pcr enim apud te vidi volamina rerum Jingularitim rara-
rttm , eit^^s quiex vcteri Parmcnidisjchoh motttm tolltt , quta mottts:
fartcm vnam (fctlicct pr.^ttritam ) pcrfctam non habct. J^o in
opcre cum infmt monjirapleraqtic , haud rcor dejuttiraaniniat cula^
prodigioficxilitate. ^jrtnciuamnthiloptistiticoniccluris. Habes
animaduerfoncs Scaltgeri in Cardanifibtilttatcs la vcnie s tbi ani-
malminimtim Excrcttatione c x c i v. ntim.y, CunicKlum fub-
cutaneum. EH vcro hoc nimitirn . l^rn ct4m tncedat idantmal-
itilumyanima non caret. IgiturAnimam tilicur oJfcram,cuicttam
inanimemguttair: d.irerejum. Nfforteex feaograffitricU befit^
cadaucre noua aliquadc^rehcndt pojp Jpcras : dequo vidcrit Dhf
fcnii^sanatomicti^. j^ii^

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SEXANGVLA. y

Talia dum meditans anxiey pontem trmfeo , confufus (tiper ind-
Militatemcay quiceram tefncjirenacomparuifftm \ mf quodeadcm
ferpetuo chorda oberrans identidem Nihil affero ^ ncc inuenirem,
qutdnam effet Nihilo proximum , quod ingentj pateretur acumen\
commodum accidit, vt vaporihu^s vifigoris in niuem cocuntibu^y
flocculifarfimin vefiemmeamdeciderent .omnesfx.tnguli , villo-
fsradtfs.EiameHerculeremquauisgutta minorem ^fguratam ta*
mern , eia frenam exoptatifimam nthil amanti , ^ dtgnam quam
dct\{.J^athematicusy7^hil h^bens.Nihtl acctpiens yquia^ de coelo'
defendir i^fellurum gerit jimilitudinem,

Redeaturadpatronumfdtmi durat frenula^ necorporishalitute-
jpido foluatur in nihilum..

K^tcjueenfatalenomen. O rem VVachhcrio gratifimam Nihil
dmanti. l^am f a Germanoqu^ra^Nixo^uidft.refondcbit Nihtly
fquidcm LatinepoJ^t,.

K^ccipe igittir hanc Nihili accefionem freno vtiltUy ctffipis, a-
nimam contine^ ne denuo nihilaccipias.

Diccndum cnim esiSocrati de fkltu ptdicis : hocefi , ^are Niues-
^rimocafu ypriufqtiam implieenturin jnatores foccos^p^rpctuo ca-
dantyfcxangtiL^:, villofsy vt penntilafnis radifs,

ImofacTffthtncpopulariscontempttu injcittxj^. leno Arifopha^
ves, ^i^id enim mtht opus Socrate , ipf^is fabul.t m^^teria ? Jpfin
Megittm Pfltcn rejpicio^qtiiintcr Dd iaudcs comme''norat,quod dct
ntuem fctit lanam > qua voce ntffaitorexprfitviliofsiiiosniuula
me^radios. Verifmtle enim esi, ctim federet fjftis , attt fiarct inni-
xti5 pedo adcufodiam gregis , vidtjf , &notaJJe ftii^^las hajceni
^aieSytn iana^s ouium defuentes.ibtq^ adhxrentes..

Scdadrem veniamti^ ioco mijfo, Ctirn ^crpetuum hoc ftt, qnoties stdlulx
ningere incipityVt prima iila Ntuis elcmentafiguram prs! fefrant niualcs..
Aferiftfxanguiiy Catiftm certam ejfenecrjjccsi^ j^jm ft azfufty
ctir non d^qtie quinqua};gHla cadtmt , attt fcptangula , curjemperftx^
Angtdafqtitdem nonduracofifa glotfurata muititudtne,vario^
impuifityfdf^arfi o* dtftrMa ?

^^a dc rc, citm ejft mihifrmo cum qttodam nuper yprimttm

A B inta^

# D E N T V E V

tnternosconuemt cnufminoi^^ matcrta ojUitrendamyJedm agente.
AIat(ria enirH niulsdi vaporyisdum orttur cxterra , calore q ttodarn
Jiio (iihtnClu6y nonaliu^^qtMm (oratnum ^cjuaJ/JIuidfi^eH: nm igt-'
turdtflihcipu mfingulares hniifmodtJlellulM^

^u^rasy Tndi hoc fiam ? Curn f tallsetiam fit vapor^ id oculis
cerni nonpofit , quia vapor pclltaidm Refondeo: Vapor ex fitex
rjoluttoni hurnoris f htenancij quod argujtifr ex eius leuttate(^
afenfu. In refolution: utrofgHr^ non hahent loctim Id entm hahet
figuram txfe quodfiipfottrir.inatur , cum termini fguram confi-
tuant^vapor , rejoititionefa^ia ex generthm humtdorumest y
ftitt Jjocef yjeipjo non terminatur , nullam igjturfiguram retinet^
djnec condcnfturtn niuem vtlguttam.

Cum igitur coyfaret yCatf.rn indtt£ figurA fexnngu>!ttef[epenes
dgentem;,duhitatum porro ftiityquodnam id ejjttagens, quomoda
Ageret, num vtjsr^ra inftayan vt cfficiens extrtnjecu:numex necef
(ita,ttmaten£cfficcret ffr^ttram /exangulam , an exjuanattira yputx
jc ut corigcmtPt^ ft velarchetypt^s pulchrttudir^i^ qum est inJcxangHlo,
njcljuti^ nottri ad quem tjta fcrma conducat?

Vtpateaiha^um i^Uiffiicnum difcrimen ^ vtamur exemplis noU-
Ulus Jcdgeometrice dfcriptis, adqudjiiorjirh ncfrarr^ pltiri^

«to.:.

mu rn ft ctctexcurfks ifc

Sitx Geomctris quizrasyquoordine fruBt fntJpumafneoliyre^
fondi huhty ordine(ixangulo, Simplex efrefjofo cx iiauntfmpliii
framir.iifu portart{m,Uterurr;^^yqtiib. cff rr/ dturalueolt. Ci; r/; w-
fantn alucos (ir/guLcsfx aUf fnguUs Utvrth, Je rnttrmedic ji :gtili
comtmtcantts, At z htfundos nluecrumfueri^ contemplatus (ngulcs
.trtnisplants inobttjumdfindt re vidchls anguUm, Fttndu hnnc^
{cartna potitts nucupes ^ ctimfaits alueoh iiterth. coptdant (cx alfjan-
gulttres altiores trtlatcrtypljnctj fmtUs tmo cartn^anguloy trcshti-^
miltoresquadrtlaterttnttrtc^t. Pfatereaiofdtrandu^g.mtnttefi
Alueolorum erdtntm yportis atitrfs -7? cotmrta ypoflt( h initr (e con-
tigttis ^ftpatis , angulis cartnarum (ingtfUrumordinis vnitis y in-
ter angulcs tres trtun/ cartnarum ordtni^ aLtertu^ tnfrtls, ea arte, vt
£uefis qmlthet non tantum Jtx laterthtis commurncet cum Jtnu aU

ueis

nm

iiei

m
cm

]24
Cll

I

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Images reproduced by courtesy of the Royal Library, Copenhagen.

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SEXANGVLA. t
"veis in eedem ordme circtimJiAntthm yfed etixm trinis infundo pla-
nis cum trtbiu altfS alueis ex ordtne auerfo, Ita fit vt apes fingu!^ no-
uem haheant njtcinas , a cjualibtt vno communi pariete dtfltHcl^,
flanacarinarumtrtna,omniainterfefimHixf4nt,atufgiirjic[Hxm
CeometrA Rhombum appelUnt. ^uibtis egoRhombis admonittis, Co
ceptin Geometrta inquirere, num quod Corpt44 fimde regidarthtM ^fS
t^uinfif^ & ^rchtmedeis quatuordecim , ex rhombls merk conPitiu
pojfit linuentg^duo j qnorttm altertim cognatum ftt Cut^o i^Oclae'
dro reliquum dodecacdro ^ Lcohaedro , ( nam cubtisipfc tertijv:-
cem fufltnety cognattis dtiobus tetraedris inutcem coaptatis ) prtmttm
duodecim rhombis claudittir, alterum trigtnta^ Sed primo h<£c est
communk proprtetas ctim ctibo yquodvt angidi oclo ctihorum oclo-
vortim ctrca idem pun^u coaptatt locum omnem explent;, nu/lo reh -
Bo vacuOyftc Rhombtci prtmi y obtufi fcutrtUtcri angult quatcrni
idemprdijlcnt ^ qtiadrtUteri angidifini (imiliter, Itaquejlruipo-^
test loctisfoltdH^ ex mcris htfcerhombts y fic vt femperqtiatuor triU-
teri vt cir fex qttadriUteri anguli ad vnum vnumptincium con-
currant. Et vt fumma quadamfat : quando loca^ folid.ts per ctibos
^quales ordine recio implctur : tunc vnum cubum conTi;/gunt nlif
Iz.angtiUsftngulisy & pr^terea fixquaternisy tta(}^ rontingcntittm
funt o5lo trigintii, o// qtiandv tmplctur toctisfoltdt^s per rhombi-
ca^qualia :tunc vnum rhomhtcum contingunt alta 6 angulisfingu-
lisquadril terisy^prdttereaduodecimy angulisquaterntSy ttag^. con-
tingentium quomcdoctin^^fiunto^odecim.

H^c igitur tllt figtira geometrtcaest y rcgtiUris quAmproximcy
impletrix loci fioltdt , vt fcxangulum quadrangulum trtangHlum
confiummatores Uciplani : hxc inquam esty qua Apes (ffingunt tnfiiis
alueartbus.Nifi hoctantum dcmptOyquod alueoitcarentte£l'k carinA
fimiltbtis.

St enim etiam h^c adchrent y dr qtidihit apis intra abas duode-
cimfieu cclodectm abderetur, non pateret tpfitexittis , coclufin. circum-
circa Ita^^ cum tecfis non indtguerint , mhtlobfi. ttt qno mintis Ut e-
tafienapro modulocorpufcult/tuproducercntvltra vwduhimRhom-
borum in carinis, efficcrentqtic ea illortim attrinfiectis diffimilia.

Porro

8 D E N r V E

Qvx fit fi- p^/^r^ (i duU iirdndms altauodnitalum Grdnxtnmaperhty vtde^
iiia:i ^Mtiubit actr/os pLtrojg^tneandem JigHram cxprejjos y nijtquantumtm^
'ci. fcdit feries radicunjytcr ^iio^s altmentum iUisfutim (uppediiatur.

^aritur tam tn bts duohtis exemplis, qtiis jit autherfgur^
Rhombtca in alueolo apHrntn^granismalipunici, CAMeriaincaU'
Ja non cfi^ KluJlncim enim inucniunt ^^pes huiujinadifol oU rhom^
hica,inpr£parato, qna colligant apes atg^ coaptcnt , ad effigicHdits
fuasdomunctdas, Nequcvertfimtleesi y infilis malis Funicis fponte
excrefcere acinos inangtdos^cuminomntba^alijs Jiuclihtis rotundi
eu.tdant yqua non impediunturyhumorefHggefokntescorticescX'^
J>lente (y ; eferciente, vt turgefcant, qua datur,protuherent,

Est igittir in acino qutdem punict mali figura, ca^fx in anima,
flant^,qu^pomiprocuratincrementum^ . Sednonesihac ad^quatA
Jigur.t catja , rico^ emm hoc pne/Iat fru^itii ex formaHproprietate fed
adtuuAtur nea fttate m.itertali. T^m cum acini trfftr imtia dum
parnifunt , rotundi Jint , quandiu fpaciumtpfsintra corticem fiifji-
^ cir , tMder;'^ indurejcente cortice, crcfccntiht46 vcro continuc actnis,
Inl 1"^^' torum conjitpatto (jr ^-omprefio , vt ^piforti tntra fuos oblongos
jriii:ar;tu- caij/ics^ Scd pif non hubcnt quorfiimccdmt \ oblongtfcnimfiLtqnis
txordine Junt infirtauomp * tmuntur igitur ii duobus tantum Idte-
ribti.r.K^^iininjero rottmdttn A^Ialts Punicis Abcriti^sjp^ctuma prin-
c:piona6ihfactleJfefngulttntfaterndS6rdtne aduajoprottibtran»
tes i.fin^iant , rotunduate fiia adiutt^ humorerr/g^ indt unde irgen-
tur, declinantcs tnjpactar^acua. \^odfi quis altquam vimgLohti •
lortim rotundorum , ihterjjfi'£qt^alium ex materia moHiconjian^
titim, concludat inrotundo ua(e t/Iudg^ ctrculis areis tnciptat coar^
ciare vnd^qtic aplagis omntbn^s: Ghi^uli Dlurtmi exprtmentkr in
fchema Rhombtcum : pr/sjerttm fi prtpt^ illos globulosfuccuftoni va^
fts dtligenti , locum ahgufitorem iibero rotatu c^pKrc permtfiris.
T^am dtrtciaglobulorurn dtjhoftttone . quA turbarinon poJSit , co?n^
prcjfione fatia ctibos ettar/ c/Jictes^

jn vniuerfium cntmduobt^smodisinter fieordtnantur glrbuUa-
qualesin vaJealiquoc^Hifit,pro duobtu modi^ ordtnattonu corum
analiquaplamtie.

■£{am

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Images reproduced by courtesy of the Royal Library, Copenhagen.

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SEXANGVLA. 9

"T^m fnrrifitcs tneodem plano horiT^ntdt gkhuhsA/judescoe'
geris in angujiufn y njt fe nmtuo contwgant\aut trianguUri forma
coeunty iut quadrangulari jbi fex unumtircumfianty hicquatuor:
^trinque eadem esiratiocontailif^piromnes glohulos ,demptise>c^
tremis, ^jnnquangnli forma ncqnit retincri aqualttas yfexangu*
lum refoLuttur in triangula: *vt tta di£li duo ordtnesfolifint^

Mam fi adflrufturam folidorum quam potefferiarBifJimam pro-
grediaris. o^drnesg^ ordinthtu fiiperponas , in plano pripi6 coaptatos,
" aut ij erunt quadrati a aut trigonici:

fiquadrati aut fngtiltglohiordinU
[upcriork (ingulis fupcrfiahunt ordi-
ni4 :/ferioris aut contra fingtdtordi-
ni4 fHpaiorU fedebunt inter quatcr-^
no5 ordtnls infcrtoris. Triori modo
tangitur qutlihet glo!pus a quatuor
circumfantiht/^ in eodem plano , ah
uno fup ^afcy ^ah vno infra fci^fic in vniucrfum a fex altfs , eritg^
ordoctibicti^, (jrcomprcfionefi^afentcttht^fednonerit ar6itfjima
coaptatio, Poilcriort rnod.o pra:ttrquam quod qutlibetgtobtfs a qtia-
tuor circtimfiantthtf6 in eodem pluno tangittir. ettam a quattm tnfra
fcy ^aquatuorfipra fe (^fcin vniuerfttm a dyodecim tangettir^
fentg^ comprefftonc exglohofs Rhornhica. Ordohtc magis affimiU-
hittir oBaedro& Pyramtdi. Coaptatiofiet ar£iiffio^a:njtnuilo prx-
terea ordine pltiresglohub in tdcm vas compingi queant. Kurfum fi
ordincstnplano flrufii fnerint trigonici\tuncinco'ptatione foltda
Aut fingult glohi ordtntsfupcriorisyfuperfiaritftngulis tnfriorisycoa-
ptattonerurfum laxa , aut ftngult Jtip .rioris yfdent tntertcrnos infe-
riori^.Priorimodot^ngtturquilibctglohtid afcx circumflantibHsin
eodem planOyah vno fupra y cjrab vno infrafe^^fic tn vntucrfum ab
cctoalijs. Ordo afmtlahttur Prijmati y & coprcjjione fafiaficnt pro
glohults column^ fenurn kterurn qttadragulorum, duarttmg^ haftum
Jexangularum.PoJiertori modofict tde,quodprtus pojierton modo in

B qua-

lO

Q A

n

^ E

qtuuriLnrfS, hjh ti^vn b /r^^^/vf/^ ^/-/V/w f/lohoru EifHj^frpoy^t ^
hu/,. 0 ai^ucejlo du copnln fc/iu gtohmtm ^y^ali.x dt'%'UD.&
*| /I //^* :jiih?^t 'nm - L:^po;i: f n'pcr cihgnfli-
\ orem Liiijrt ^ '-jt fi.it figurx Pyy ui^/idls.
Etfi igit::^ per hmc impofiliontm fi?;guU
f.pcr:oresfi:d',r:mt i?:tcr trincs i:- feriorcs:
txmcn i.xm z^erffguyay vt nou ^ipex fd
integrum Utus pyramiJis ft loco fupe^
riori y quoties vnumglobulum dcgluheris
efimmis y infrx flahunt quatuor ordine
quadrat0. Et rnrfumHangetur vum glo"
bm vt priiM y a duodccim a/i/s , a fex nem-
pecircumflantihiis in eadem pUno trihtt^
\ fp^^ &trihm infia. Ita tn foltda co^pta-
i ttonc arBtfimanonpotesi effeordo trtan^
\ guUris fne quadranguUrt > nec vicfim^
\ Patetigitur^ actnos Punicimalty materiali
nece(?:tate concurrente cum rattomhus in cremeti acinortim , exprimi
Caufa figi. infi^uram Rhohiri corporis cu^n non infcftis frontihtts Pertinxciter
maii Puiii- ^^^^rtturrotundiexaditerioactnfyfcdcedant expufytnff tciaintcr
ci. tcrnos vcl oiuaternos oppoftos intcrteB a.

In a^ucartht^s vero Apum ratto cst alia. Non n conglobanturapes
co:-^fufcy vt acini in mtlofd arhitrariamfrtiunt aciem, omms cipt^
tiht^s prominentcs invnam vel aduerfam pUgam \ omnes aluorum
Vnde c^o- extrcmis intiicern obnftentes.^odf ex coglobattone hufujmodtex-
munca-is^ ifcretf^urahxc.o^artcrct a/ucos aptbt/^ Oiperindtn ex conftiientix
fua hguia.^ exliidattlcntorts.vtcochUtscotorttsflcnt ftpcr crcfere domu uU,
Cauf^^gu ^t certumcst y npes ipjas ffos fthtfi.jgcnaiueos, totamg^afinda-'
ic 111 al weo. rnrntis' coyitifrrjattonem extrucre.

£>^ire tpf Apis Natura hitnc infiinciu^^i hahct ex proprietatt
fuay Vt ha€Votfftmumfiguradtdtp\n\ htcffli Archetyptisa crea^ort
impreffk cst intlnl hfc materta ncoj^tic cerjL , niOj^tie corpttjculi ^pisy,
nthdincrernenta poffnnt.

H oc antmaducrjo (^umtur iam porro &de fine, no^^uemApis ipfi

nis

S E X A N G V L A. - n

tovfeBitnr drfcur/i^ fuofedojTtem Befi^ ipfe, ApicnU crc^ttorpropr^fi
ttm h.tbuit, cttmilliha^sarchitechir^Juddlegesprafcripff

^tg, htc i:tm demiim rurfnm ingrcd^turfrm icflinatioyjey confi-
deratto ccrportim matert^j-.. Triacnimdehocfinedicipojfi/.t. Pri^
wiifn vulgareeH apudVhyfcos y quiadfolam quidernfcxanguUrem
f.ru^luram rcfpiciunty vt ttla cum htattbu^ extrtnjat^.^ fefc ; ipr^fen-
Uzt, Cum cnirn iocum planum impleant exclufo va^.uo , tarstu:n hyfi*
gtn.il, trtugtiltim. qtiadragtdtim.fhcagidtirniex tfsfxFiguliicapactJJi' j^,^.^,,^^^
fna eftfigura. Capacitatem autern fibi parant apes ad m:Ua condenia. fig,, ca-

?otcj}j,ampltart hac ratio etiarn adflidt conf dtratone, htmc
Tnodtimfqnodctim folidum fpacium non dtuidrJurJinchiattf , nif tn
^uboso^Rhxribica lihombtca funt cubiscapaciora. Sednon fuffirAt
i?£cratio:na7n ficapacitatemqttdLrunt , ctirnonqudfbetfibirotun"
^ttm fingtt nidum , qtdd opu4 esi minutias lori confciari , quafi ntd-
iurn tn toto aiuearirefiet Jpacittm ? Probabtltoreffet h^caltera caufa,
quauls nec illa Jiiffiicicns, ob rattcncs diclasy quod moUta Aptcfdartim
torpiifcula commodi'^s locantttrin ?itdofgHrdplurium ^obtuforum
mgtiioru,qtiAg,^cognatioreftf)h£yicd:,qutincftboyq^^^
procttrretes habet angdosfundiipUmtya corporeterett abJjorretem. j

Igttur tertiayn caufam necejfe cst addere ,cp minuitur ipfisliborft p ^ ut. fignr^
/€mperdu^comtinem/}ruaraparictcm,&qtiodinrc&m
ttonum matorfirmitndoy adcratemtntcgramjttjitnenaamyquar^jji ^^^^^Yis.
JingtiU domunctiU tcrctcs ideo^ ccmprejfu facilcsfui^nt : Deritqtic
fgttra rotfindx hia?tt cum maxime comunila Junt: Itanfigt4^sfper
hiatm infnttaret, ^btu 07nntbus prouidetur, qtiod confortia t cciti
Vrr)is hnbent.vt Virgditt-s canit.

Hastgitttrrationcsmaterialenercjf^fa^erefpicietesitapittof^^^^
^t hocLoco nonexijiime philofoph^.ndude perfeclione & ptdchritti-
dtne vcinobtlttate figunzRhombic^ ^nr^ifatagedumy^vtcjfntiaani-
muU qux efi inApe, ex conteplationc figf^r^y qttafabricattirpcltciat tir:
quale quidnohis ftt :fpt tnceptH ^:f 'v,Ji vftisfgnrdt ^juUus apprruijjet ^

Idijn dt malo runicoint^ll ge 'siii.. ApparetneceJ^ttas m^terialis,
qUitactr^osptrdMatadRhobuttmfi^ctedcritfbjncre
nuy rHdcejfntiaAmr/mtnhacayborecogit^^^
ttff:f/,im^fjictat. B 2 Con-

. " D E N I V E

par i inVa- CorjtrajiqtUYAtur.curomKcs.^deoxrborcs^jruticcSy (autcerte
liisfloriurt pkr^tcj^flQrcrn expliccr^tforma quintiju.tngHUriynumero fcfoltorm($
qumArto , quem florcm inpom^s (^pyrlsfeqtutur fruclm dijpoftto,
w codem velcogr/ato numcro , qninarto vel denarto ; quini tnttis lo -
culicominendisfeminibtiSydmiifiUmenta : quodejr obtinctin cucu-
merihus cr idgent^s alrjs: htanquam (ocum hibet fpccuUtto ptichri-
tiidinls atit proprietatisfgHr^ , qu£ antmam harumpltntarum chx,-
ra£lcrtfuit,Et dctcgam obitercogitationesmeas /^iperhacre;
fe^Xria DuofuntcorporaregtiUrta . dodccacdron & fcofacdron, quortim
q J n a d o ^^^^^^ qttino^uangultsjiguratur exprcfse, hoc triangtiUs qutdem ^fdin
vtcntia cr citiinquangtdiformxmcoaptutis.Vtriufj^horiirncorporum, tpfuisj^
Jortio^nc " ^<^^o^tnquang!fli fru&urapcrjict nonpotcHftneproporttone tlla,
aiuina. qua?n hodternt Geometr^ Diuinam appelUnt^ Esi autem fic compa-
raJayVt duo minores proporttonk contrnu^ tcrrnini ttmffi confitu^
ant terttumyfempcr^^ addttiduo proxtmi,conjhtuantimmedtate fe^
quentem ,cadem femper durante proportioney tn infimtum vfjtie^
In numeris exemplum perfecium dare cf impoffb/le, ^o tongitu
tamenprogredimur abvmtatCyhoc fit excmplum perfcclttfsSint mi^
nimii.efr^^qtiosimaginaberisin^quaUs Addc.fientz, cui adde maiO"
rem ificntj cuiaddez.fient cuiadde^fient S, cuiadde / ficnt ij^
cutaddelfcnt2i. SemperenimvtsadSjicSadis.fere, (^vtSacL
iyfc\^adz,fere,

K^d huiuis proportionis fipfam propagantisfimilitudinemyputd^
tfficiam ejfcfacuitatcm femtnariam ita^ inflore pr^fertur femina-
ri^facultatis yvnTiov vexillum ^inquangulum. U\€itto CAterA
quA ad huiPi^rci conjirmationcm tucundjf^ima contcmpUtione pof^
fentadduci. Sedproprti^illkdebetur loctis. ^jinch.tcexempUtan-
tum caufa prdimifimtis\ vt in rimandafgura 2{itiis fexangulafi^
mtisinflrnciiores exercitatiores^..
Anfrigus enimpropofuiffimi46 inquirere originemfgur^huiusinnU

caufa hgu- ^^^^^^^^^^f^(^>^fri^feca4(^intrinfecas:interexterna4primt

vero vapor coit tn-figuramJielU Vidtbaturtgitur frtgiis tlli figuram
fr^JlareJieliA. TuncttHm eHadcoJiderattoncaltam , an frtgu^ ftNa^

tnrtL

S E X A N G V L A. tj
iuraqtud.imvt Medicoru Ca(or? Videbatur.n.effcmeripruLxtiOy
cuine^^ r?ieSyfexagulifabricatrix,Kec ernntno opcratio nj.ilU propria.

Scdnciyufcexmm quctfitones y m xneatjrigori condcnfitio :potuit
condenfttto ficrt , vt vidctur , in formam globortm rccinis. Imofl
csnfideretur jrigus late fufum, vapor tlit fuperjicietentis occur-^
rtnSy magls esi confentaneurn, vt condenfitto fi.it informam ornnino
flanam yfuperfictcifimtlem • eam qtiorumctincj^ terminortim
fitotaviportscxttmafiiperfctesex ji^tgore denftatem, ex dcnfttate
pondtcsy exponderecafim > ex cafu comminutionem in frttfula fct^
bra^eoi nanctfceretur : vttt^^ non omnes bracldZy quin imo paiicifii •
m^y ac ncfcioan vlU euadmt fexanguU y pr/z(trtt7nradfjs adto con-
ctnne jlrtatis,

K^dmonebant ifa jiriA rei i/litu qu£ contingjt in Hypocaujlis ^^^f^^f^
vapidisybrumalirtgoreptrtufasfeneftr/ts ohjidente. Lucianttircir' pruioofu
caillosangufltasfitgtdtMacra*Vftpor j^oties enim fefimutuo con- cofift nt'. $
ttnguntycalorfupcrtorapetit yjrtgtistnfertora. EHentmincalidodi ^^jj^ ^*^^*^*
Utatia materi^yin frigido denfttas ^pondtt^y pellitjf^ calidafHrfum.
Vapore igitttr conferttm exire nitente y fit ftiga vacui , vt (jr fiigidt^
aerconfertim irrttmpaty vnde Ctmbipatentis fenejira velrtmttU
jirigidtpmiefficiuntHr. K^d eos limbos quicquid appellit vaporis^
continttogeiatur.jiiccedtt^ in iUam matertarn ftigf^ ^que magnum^
vt quicquid porro vaporis ad hanc appclltt pruinam , ipfum
gelettir yappofitione continua, intercedente tamen , fefique intror-
fuminftnuante recits lineisaere frigiaQ iquaalternatione ingrefius^
& egrejfii^SytlU pruinojk vaporis confifienttx ,firids fortiuntHr cr
cutos radios,

T^tft/ad hoc infiar de figurationt niuttU nofira dicipoteU. Nam
quinam hicingreffUsyqui exittiSyqti^angttfii£ qua lu6ia in patentififi-
fnisaeris campis? Conceffcro tnter cadendum ex alto per vapidum
aerem fieri altquam ad v llos appofitionem acontigentihfis vapori^
btts. At qtiare fex locisy qttodnamfinarij princtptum ? quis capite/lu
antequamcaderetinfex effigiamt cernuafiigtda ? ^^dtcaufafiatu^
ens in t/ia fuperficte tam iam condcnfmdx jex pun^a, adqu^ feni
^ircumrad^conne^mtur?

B j Ctm

H D E N I V E

Cuw haque cauft extcrn.x.fii^^^is , b<ec efficire nequeat : micrna,m
alfqur,m ejjemccffe esi , vrvporiJqHe^velcomttem^veUlioquocumque
mcdopropriam?

o// hdcperpendentem fuhfjt admiratioy curradtjnonpotiusin
omnem ambitum Jfh^ricum dtfponnntur? Cur ftinierntiscalortsi
huitis ret author , tn pkfj.t tantummodo fupcrfcie cperatur iqtii vn-
dtquaque ^qtialitcr/ehahet ,non veroin/ola plana fuperfcie v..pO'
rlsinui?

VuminhlshiBor meditationihtis ^dumratio posiulat radios in
omne?n amhiturn dtfrtkutos , tncidtt qtiodalias fape cttm admira--
tionejjcciauiyfe/lulas huitfmodtnonprimo fattmcaft^s momento
/ierni/uperplamiemfed particulis nonnu//i<sfdlimes teneriydeni^
temporismorafuhfdercinpianictem. Ex t//aratiocinraioneve/uti
Nihiliopi- patrcy & ex/jac experientiaveluttmatre , nataesimtht optnioijia:
/ie/ltdas if^s inter cadendum trinis con/iare vt//ofs dtamttrh , de-
cufjatim ad vnum puncium coaptatis , fex extremitattbus in or-
hem ^qualiter difrihutis , itavt trtbmtantttm vt//ofs rad^sinci-
dantyrcliqtiistrtnis, { qui JuntincideituoppofttiiniJJdem reciisdia-
metri6, ) infuh/imi/ient ^ donec flexlsijSy qutbus fe//uia fuftneba-
tur y reltqui hacienm jfuhltmes , tn eandem piamcte?n cumpriortbtis,
intermedjs locis defluant.

Hutpts opintonis vimprofcquarpertottimyposiea demum an
vcraftt examinabo: nefortajfs tmPorttma vamtatl^ dctecJio mc
frobtheatyquod infituiyverha dere Ntfjiltfacere.

ilocigtturincau/kpofttimefioyqtuutiriquecaufaft/^
diorurn , eam vndt^ue AqualUtr ffam cjfc tn omnes piaqas : vt f/fii^
gf^esicaujafenumradtorumfitgtisigiturjh^^^^^
€ti/a6circtimfareaqualuer,autAquaHktiscerte tnterua//'ts vndique:
Sin ca/^r interr;usy& hunt in omnesfhxrd p/agas ex vno, &eodem
ccntro opcra.ri.

r^ct:<iUAreronc^mnq,,e'ucljcj,tmhJldcmnmi>J^^
ftmtnrextodemientri/?

Mt

S E X A N G V L A. rf

lEt fiqujtras i Geom^trls, qtLt m7n tn fiyura trcsjyiimtri fcje
orthogonditcr feti informiuru/U dupitclsy iner^der^m^ntro pcent :
isrcjjwidehit , in oBaedro, connexis anguUs oPpojitcs. Oct.cdron
enim hahtt lcx.tr>^Hlos. ,^^re rgiiur f,, vt nixintercddcn inm,
priHfquam compUneiur , tnbti^s vdlofs diamctris fe invicem ortho"
gondttcr ficantthtt^ innitetnr ipfumiz (m^Xijc^ Ofhedrt- Vt fi ra-
dtorum extrem.i Z'icina reciis dtiodtnis connciJa^ Jntegrurn octde-^
dri corpt^^ rtprxfiijtafis ?

cauj<z tgiturj qnod in bos tres z'il!ofos radios pottHsft
condcnf.tttoqttam tnglohttm integrurn ?

Pojfum qtadem dtcerc ?nodu?nvnum quoif i fitnt /nntertLili nc-
cejjitate Jcdis afjitmit dtqutd y quod rurjum pltis hahet admiratio-
nisj quamhoc ipfum qtiddtdm erat demonflrandum, Dicatvtameny
fforte ex comparatione multortim faljorum eliciattir vcritas.
hfto 'vt vapor ,quando prtmum frigtistrrums fi^itijcit ycoagaletur
tn ffhoeruLts ccrtct quantttatis. Hoc esi confintaneum, jS(jm vt in
aquayGutta mintmunaturaleesi deflndo\prot)tereay qtiodaquafua
pondere non dtjfutt amplttt^ .qtiando cst t?fia giatctquantttatcm:
Jhetitm factleconccdtpoteft , inejf tnvaports materta tinacttatcm
Aitqumh f pojft refficre frtgort , in certa altqua quantitate , putiL
guttxvaptda.

Secundo efo vth^ Jph<x.rAvxpiddt fe tnutcem rontingtnt in cert(t
dtffoftioi2C : p:ita quadrangulart in plano^cuhi^a thf^Lid.^ yqttade
' O ylC^'^ Jftpra Sic entm ta?2g€tur SphsLrula qttjaltbet .4 hatt/sfx,
^1y'''Y'K ^^^^^^^^^^^^ quatuor hic inplano deptngi pojfint qtun-
p:7dw pta c!r fxta intelbgeda estfuperpom crf ^ppom. H/s it/t
a/di^ poftti cr tijfum. ti^figore ve> o pcr jjacta trrueteifph.iL-
rttl^ a contailu vno adoppojttum erunt munit,t contra.
frigm • itaque verfis centra qtitdem fph^rularum fet ccndcnft-
ttOyftc tAme//y vt etixm verftfs dtanh tros contaciuum ^ qmbus fctii'
cet locts tutA Junta frtgore.

Vcrtirn non immertto , vtpr^dtxi, qUArat diquhs^ qua, vifc dif
fonantttr Jfh^rula tn dtrecium ?

Si

_ D E N I V E

fojittovarta, J J

"^"f^^icadfci^^^^
dtJpoJttioeHfibttpfivndt^Jmtlts, & pun^a contaituum dtfiribu-
4trttur^quabter ine^terts»equa>]UarH. Et/temmvtrupradtfh,nt,
gl^btJtngultadiiodentsaltfstangunttir,,tf^^^^^
trtangula &qttadrangt,iajmt : hicomnhvndta^ (juadranmla Illic
dtametrtqmdam duo oppofitorttm contaffttumfefejeeanforthozo-
mltter,reltquaquatuornonttem : htcomnestresdtametrtffeficara
^ifi^ter&orthogonaltterJIIicconnexise^tremtsdt
CHboaoedronMc Oclaedrontntrafph^ruiamquamlibet.

J^f^Mttaq^^tdemhincpatetdtfpofittonisdtre

dtjponat. NumfactthocJ^tgt^s?Atquomodo?

tZfM r '^frPf^^^fi^^f^^recltUnio, verfiJterL:
AttntranJuerJitmvndehAcdtreeito?

^'J^figft^r^^vtCAlortntcrni^svaporishancmtarumdtfhnnt;.

'vthicqutdem,tnprocItuieH. '■'^'^'t^tconjtjo,

Sed&argumer^afunt, -vtpotius tredamu'fi„auU< .tttt^, r
cpee.xterntcontaefus/e,pfisdt/lom Etentm f (S, ,
rrretttrabordtne&corl/acJultttuopT^^^^^
~'^^''^lesejje,fi^^^^^^^^^

dtjcrtmen maonitudtnu It>r^ i ^"^''^^'^ cemttur

turMettnJ%nT^'^^^^^^^^

"^ihtl

Early European Books, Copyright© 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

S E X A N G V L A. 17
Tljhilitcxtj^^profecimuSyniftpateAt modHSyC^uo Cdlorinternmgut- ^^J^'^'^ '^Jr
tam viipidam mrribitsdiametrls^formaocfaedrica ucl certefxan ^aumAzn
gul^ firmety vt adeas fat miteri^per cond€}fitio7U7n colkciio^ efi:', o

Poffit alfqulsexiJ}imar€y 'vo!itarevi//o/a ifa ramer4a fo/itari:?, d^^^rna^c
interg, cadenc, um dccuffatim concurrere fcrtuito. Verum idfalfum cufi lion z
esi, Non enim perpetuo trina ^noninpunBis medijs ^nonadvnum triunidia-
fun^inm concurrerent.Addequodvi//tomncsacentrofuJie//ity feu '"'^'^^'^^
decuJfattonisgcminAauerfi extrorfumporriguntur pcne vt fo/io/a in
ramis ahiegnis : quodargumento esi , in centro nidu/ciri vim forma -
. tricem, indecj^ in omnes p/aga<s squa/iter fefe didere,

Sedfortajfs Ij^c catifa di trtum. diamctrcrum, qucd tctidcm ffnf
diamctri piagarum in anima/iJom? Hahcnt enim fuperas yinferas^
anterioreSyfoJierioresJextera^yCwiJiraspartes ? Siquis hocdixcrit,
rneAis opimoni appropinquahit y fed pr^tcr opinionem inparadox^
pertrahetur conccjfione fua, Primum enim confderet qu^naturaft
huiuscaioris qux fimi/ttudinem a^nm.i/is arc/nte^ettir in Jie//u/a
. niuk, Deinde videatycui hono ? J^id enim a?iima/icommun€ cum
Ntne ? K/Jx advitam.qua caret yp/agis ijiis optis non hahet. Tertio O ccafiorex
ferpendaty ipfas amm.dis partes, non tam adfgtirasgeometricasy ^^f^^l^^^^^
tcuhumque yprimam fo/tdarum fgurartim ,velut ad^rchetypum. hus.
fuum accomm.odatas iqtiam neccjfitate qu.^ imi adfinem obtinen^
. dum direcias, Prima entm fuperi cr inferi dijitnciio esi a /ocoy qtu cJi
terr^ fitperfctcs:pcdestgiturdcorfiim vergttnt vt contra pondns cor-
poris nitantur , Caput fitrf m esi vt neruos imhre opportuno cotintte
humeciety vt^ octdi ^aurcy a p/anitieremotifimip/tirimaeit^s cir-
itmferentiamin cenlprBtt- hahemt, ohjiactdis rcmotis , denig^ vt ci-
bttspondereypotHshumorefuo prxcipitatts^sin fuui^/octim dejcendaty
veg^ cotinua ttt in plantis vno /oco fixis) attraclicne opt/^s h fheret. Al-
teraanttcA poJiicA dijiin^io tribitta esi a^iimantthn^s ad motn^
exercendos , qui inrecia/ineafupcrterrdfuperfciemtendita locoad
locum. liag^ du^hxdtametri neccffarioorthogonaliter fe mtituofc-
-tantyfgnantquefuperfciem^ At ctimanima/ianmpojfntejfjiiper-
JicieSyJedneccffariocorporaaccipiant:tertiam diametrtm dextridr
.fmijiri cx ratiom cQr^u/enti^^ nccejfefuit mcdere,qua ft animul

C quaji

D E N I V E

qmjt geminum: vt fjjlt etUmin incejjjt -, mouentis moti difcri-
men alternis. 7^n t'ntur,qti£ cuhica fnnt, bominis gerimt fimilitu-
dtnempropter ndqn.imjg^irxpnlchritudinem :fed homo atbi acqui-
Jiuitjimilitudtnemfjuaficoncinnatam. cx vxrijs vjthtts ceu Elemen-
tis.

ad t r Jas ^*^*^ omnibtts examiuatis , qus occttrrebantyjic ego fentio , cm-
cnufas iigw-fi^^f^'^'^^ niucfcx i?iTiiU,n9n alta efe, qua qttx esifgttrarttm in
'JJ^^'J^f^^'> pi^>^ftiordtnatarum,numerorumj^conJhntiumMccuminhi^

Ji^ifnerationeftmma, non quidcm quadtfurft ratiocinattonisin-
tteniatur,fed quxprimititstn creatorisfuerit confiho , &ab eo prin-
cipio htfcuf^^ per mtrabilem facultatu ammaltum Natura confrue-
tur, ne in Ntue qtiidem hanc ordtnatarn figuratemere exifere credo.
^ EsiigiturfacultasformatrtxincorporeTelliirisyCuittsvehiculum
esi Vapor, vt httmana .v:ima,Jptritui : adeo vtnulUs vjjiam extfat
vapor, quin^ 'vt caloreqtiodatdefJeaHsesi quodejf dtcttttr,pnta vx-
for,eodem^^ ealoreeonferuatur , vt ide;fe pergat :ficrattoneetiaift<
firm.itrice,quamal/Jcalorcm Opijicem dictint,contineatur.

Sed duartim obiecltonumfoliit!one,quodreltqttu>n est de opinione
mea, declarabo. Etenim obijcerepojfis : Inplantisfnemjicbfcquen-
tem,qtticsi, Co-njittutiocerttcorpons Naturalis, arguere , R.ttioncm
formatricem tn aliqtia materia pr^ceffjji: Vbi enim medtaadcer-
tumfinem ordtnata , ibt ordo , ibt nuiitts caftt,s , ibt mera mcn s . mer^
Ratio : In Nuiis vera formatione finem nttlltim fJcSiari po(J}.,
neqite ficrt per figuram fexangulim , vt ISfix perduret , autcorpy^
^:iuraledefimtumc€rtxa'durabtlisformxfiat.Rei!pondeo,Rttio.
nc:^formatyucenontantuzgerct>rophrfi/enfaetpro^te'-ornt:H,
necfolutcndcread corpora nattiraitaejjictenda fedetfolereluderc_j
influxts , quod mtdtis fojfiitum excmpiis patet. ^orum eoo
vnmerjorum ratio-nema [tidicro{_dii.-ndtctmu.s T^turJm ludere)
adhancfertam intentionem transfero : quodputo , Calorem , qttt ija-
6tenus tutab.:tur (Jlfateriam ; vbta circttmftantijrigore^ vinci-
tur: vt /jacientis ordtn^ agebat ( ratton^ qutppeyorm.itrtc^
tmbuttis) ordinepugnabat fjic iamfuo ^uodam 'ordme^ & fu^^

S E X A N G V L A.

crdw.itrm veb'^ >'cr ^C^ciPm dijiributfs r.r^yiis , qu-nn ta^t re- na cum ai
tirjut m iteru\ unjjccurji h ihcre,Tt{c!fwHe Oljmptxdereferunt ht- fej>ulci d
ftoriiz ) ror:ir:homjtr n:c wucrecimde c^idfit. ^fA^rzi^t
Alffisaltcifiis ohiiciaty yUntisfiiigu!isffngtd.tse(Ji\fictdtdtesnni' hic apud
mal^Sy cnmf.or(i,n eti.tm fithfjt.wt corporfim pliritarfim (f/igifU:^^^^^^^^
propterc.^g,nfl<[i]l njirtcvfffignlisetiavi frjgnla^ aptanjfgnras la ^^\f^^^'^,
nivis vcrQqudtbctfdlubpcctdtirernflng^remimam.^pe^ tvHTyj,^^
xtdum auftrcrieafiidtm ff\urasntv 'i6 eodem modo ex Antrnxoperey ^.^.'^^^rt^s,-
'Vt tnpUntfs dedHccndas. acco n mo -

Rijporfdco.rem vtrinn fmilioremeffey qnam.qnih^cohticit, cre- dat Phnius
derepofjft. Bemtt^.plantlffngfdis ftngnUs effe fictdtates:at c£ ornnes ^^?'
fohotcs ftmt vmtis '^eif^f.fdem faenltatis vmtierfali^ , qu^ in terra in- f^ cuid^i^n
eH : qn.ttj^fhabetadpUntas',vtftcnltasaqtMadpffesfactf/tashft- Ve^^ali qua
rnani corporis adpedtculos.caniniadpfilfrcSyOvilltad alfndgenti^pe- na^^v^iani
dicuhrttm. Non enim omnes pUntizex fcmine ^ pler^g^ i^uvTCfAcir^ deFodit.
primw/n crt^yCtft fefe porro feminent. Facultas enim terrd^qff^fipfi
vna cfi 0" eadcmydfutdtt fefin corpora ef; ctirn corporibtiSytng, eatn-
ofehcft (jr pro cuitisy^ ?nateriic condttfone tntcrna externtsve alwdat'
^ aknd archtteclaturJtain vtporeqtiog^^ quem totum totapoffede^
rat Animaynthilmirtimffrigoredtuiftonem totitt^ continut moltcn-
tCyoh centraBfoncmparttum y circapartesipfa, vtcircafingnUtota
formando occttpctttr.

O vere morttiam vitam fne philofophia, Hmc enim in Niue for-
matricem facultatem ft fctuijfct ilU Aefopicd fahelU adnltera yper-
fuadcre marito potuijfetfe ex ntue conceptjfe yjpurio^fuo non tamfa-
ctle ftiifftt orbata ycallidttate martti,

Dtxtdeauthorefgur^: rejiat vt inqfdramtis defgftra ipfeyfftte
ilU exfflat ex decttjjxtione trium diametrorum y qtiod hafientj^s csi
inter fnppofta: fttie indeab origtne ftt fexangtdayde quo pofiea.
Nunc pergendum in tramite cofpto . Canfa igittir cftrhxc fa-
cultas Ociaedrt dijcfitionem angulorum potins trnitctttr y Imc cf
fepoffft,Primu vniuerftimaentisanimorum Geometricis ^rtgnlari- ^ni=^us 1-
btis puc Cofmopoectii^tsfgurt^cognatHeJt^quod multts aoctimettsprO'' j^^fj^

C 2 hari

D E N I V &

baripotefi, Ctim emm K^mmt fmt qn.^y^. exervplarf.t Z)r/ Crca»
torisy certe inDci Creatoris /ne.. e co/jlfj^tit ] eo ^ostternafiTurxrnm
harum veritas. K^mplius cum cert/f mum //> , jpfs ettarn amrnos-
fenit ijjima fui ejfn/ia recipere quantitxtes yjuit materia Phyficaj an
cum ca y non dijpnto : coKftntancum i ri,/ig'ff at^ts potws reeipcre
quant/tates , quam rrtdes :jlf!guratas, juarefljtras regulares ,foli'
das y qnia animifuut non Jupeyjicterufn fed corporum foUdorum.^
Reditiir ad ^^i^^*'»te7ninterregfilarcsfoi:dasprima: Cubu<ypri^y^cgcmta,parens
op^nioncin cMtrarum. Ei:fs verbfceminaqH.fqtLzdtnesiC^t.^^cdronJjahenS'
^ ^"i tot angkloSy quot cubus pUr iy eoyumqne centra qntbti^s fngulis-:
fngnltrejpondentex Ociaedro ^ngidt.

Portiunculaitaque materu vap:ddi dcferenda .ffguram dehet
reciperey qnodiam fecimus confentaneui i .p, imumcubnmarripret,.,
eiufqucfociufn Oclaedron ^^orfumfupraettam m^iterialts di-de-
bat ?ieceftaSygloborum atqualtum in vnum aceruumconfufrnm..
Confundebantur enim(^ adnmbrabantnr tn punciU centaciunm'
rudi?nenta cubi Ociaedrique. K^t cur Ociaedrt figura n potit^^s
quamCubt ? f^n qtiia Cubtis eii fgura dilatattonts y Ociaedrdn
coiiefiionis? lam vcro &materia cr vis calorifc icoiLgnntur impe--
ttta hofiliter a figore..Fnde vero certumfit , tila?n elje dtiatattonis
fgnram , krnc c^iieliionis ? l^lempe qttta cclo anguit , qntbus tiia
forlsdtd-ttir y ijdem inhac intu^ centrum circumftftunt eodemnn^
mero, Etenirn f cnbo adimas angulos fuos ocionos refecios lateri-
bttsaqualtbus, introrfimqnecomponas pianeconfitues Oiiaedron.
£t Cnbus inpiuresy fc : in ocio angulos dtjfundttur, Ociaedron in
pauciorespputafex^

^ i^^untgemmari, jS{aturalia in^damantibusinHeniri 05ia-
tdrayperj^ccitfima^ltmatifim.zform^^ Idftesi ymuitumnoscon.
frmat . IS^m facnltas animalis , qn^ in terra indidtt K^damantt
fcrmam OHaedri ,expenitiffmofnu fi£7^aturadepromptam,ea^
dem cttm vapore progrcjft de terrafguram eandem indidit & Niui
€X vaporcilio conftflentt.

^^nquam.qtioddecuffationemtriumdiametrorHm attinet^
in^a non magis imii O^acdri quam cubiforma, lilic anguii,

hic^

SEXANG VLA. ii
hiicentrapLinorum connectunt ur huiufmoditrihus dhmetrls\ ilitc
angiilt diametrorurn ndccntrum ,hic nngulmqm corpti^s fimt expri-
naturJrHjlr.x igitHr dctotimfigurjt elcclionerxtxgtmHs , vbtejlv*
trtufg^ rudimentumfltem.

^up vero a hri[ /j r ftultu^ ego, qui dum pcne TJ^jU donrire affe^o^
peneetiam T^hiUgo: qutaexhoc pene Nihtlo pene Mundum tpfm,
tnquoomma.Cjformatiiicum^ ah antmula minutiftmi animalculi
fupra refugcriwyiam tcr maximt Animalis glohi tclluris^animam tr^
2(juis Atomo cxhihco?

Ita^ pedcm referam, crfedtilo daho operam, vt quod donaui^quod-
quedtxtyidnihilfit Fiet autemidfquam cito T^utdamealiquefctt,
tam cito ratifinculasifa^.egocontrariisratitmculisprofigaucro^ at-
qucanmhtlauero.

Dtim entm tjla fcriho , rurfm ninxit, conferttu^, qtiam nuper.
CctempUtt^s fum fedulo corpufctUaNtuis^cadeh^antigtttiromniara-^^^^^
diofa yjed dfiorttmgenertim : quxdam minuta vdde ^ radils circum- gu r a N iuis
circa tnfttis , incerto ntmeroy dr fimplicthtis ^f ne villi<s yfnefriis , e- ^^^^^^^
rant(jjuhtilifimi\ incentro veroco/ltgati adgrandiftJcuLtmglohfi-
lumintg, horttm erat maxima pars Intcrjpargchanttir autem J:cftndi
generis rariores fexangfiU JielltiU earuq-.nuHt aliter niJipUna.nequd
njolttahat/neg^ cadehat, Vtllis etiam in eandem pUnieiem cumy canU
fuocompofitis. Vcrgebat autem inferipi^s decrftmradioltisfipttmtis,
quafi radix aliqttaytn quam cadcntes inctimhchant ^ eafj^ fufimehan*'
tur fiihlimes aiiquxndtu: quodmefiipranonfugit yfedjinifireexce-'
ptum ejl.ac fi terni diametri mn ejfent tn eodem pUno, Itaquenon
rninris quod ha^cnus dtxiyquam quo dedixi, a NthiU quamproximc^
ahefi.

PrimumgenHsgrumofiumyptito ejfe exvaporeiampenedefcrtox
calorcy ^tamiamingtittas aqtica^ condenfimdo^ Itacj^c^rotunds
Junty ^figura?n pulchram nonfortiunttir^defirta iam ab architecio^

radioja funt vndi£ y iis principijsyqu^ fupra ad conternplationem
fruinojk confifientia infneJlrU fiint adhibita^

Jnficttndo verogencrcy quodcfificlULrum , Ucum millumhahet
^mfempUtio ctibi yd Ocia^dri^neg^ vllffsguttarum contaciu^ cum

C y fUns^

right©2009 ProQuest LLC.

jsy of the Roycl Library, Copenhagen.

DE NIVE

fUmmtidmt.no vtfipra fum opinatm , decujp.t.i trims dhrfctrk.

E.fiign u r ror?uatrix anmia hu quon. locur,i fium tuetur, manct-
qt^ei-rfcniifided^e^lionetanienfxH^^trHi^fioefrcdintcg Pri-
mum curpLan.'t?An.^uia non rcae fupra adeniipLMOs ftrm<itricihm
corpsrum. Nam in ommhtu flonbm tn.'ft qui??c;uMiguIum pldnmn :
non doJectedruyn foiidum. T,-inc caHfipUn ^ fgura verc h.ic effet:
quodfrigits caliduyn v-iporeminaliqu tpUmtieta:7git nccit.ttdttim
vaporemjta^ualiter cinumf.it cii:nfeiluUgigntmt:ir, vtcumoru-
mi cxdunt. ^

Cur figura Cur .•HtcmfxanguL^? ^n quia ex regul.nibus hac prinia cf ve-
potiirirtium repUna, &qud:in nullum corpus fcum ccll^galur? mm Trwc-
lexarjguia. „^ Tctragonm fentagomucorpora cfficiunt. Anquiafexangulum
ferntt pUmtiem , excfufo -vacuo ? cxT/ idem facit triavau-
lum quadrangulum ? An quiapro.^ma h^c arcuUexifscjti^pU-
mtiemfcrnunt ,exckf vacuo. An hoc dfrin.wis tnter faculf^
temferiliafigurantcm,^alteramf/Um qu^fc^cundafi<rurat,vttl.
la tri.wguU felfixangtiUfaciaf^h^cquwqifarigtda ?A»dtma, ipU.
fmusformatrtcuN.ttura in intimofmu fii^ejfntix particet>Zftfe.
xanzuli? i

Exqutng^ adduais caufs primafecunda , tertia hoc fibi vftr.
pintfaciiltatemformatrtccm,erenataconflttimcapere, &proop
portunitatecampi actcm infruere: vtquiapugna caltdt vaporis &

Pg^^<ffieristnpUntttecxftt,nonpercorpulentiam,ipnauon//c'u.
ramdtgatqu^plamtterum efpottus,quam corporum. It^n &ma.

*erulunec^pattsrationemhaberett„fectinda&tertf.t.7{,mpri.

grucnttamhutusfgur^adhancpugntm. Jnp/anopu.^na,ncce^arto
tgttttrfgurapiana, ntnonnecefkrtofgurata/is, qLtdnu//umcor.
pusfctirKtpfacoeat,fdtde,fium ta/tsquta vt corportht^s pljyfcls
Jf^l^^^rcfondent qti.fo/td.^^

tlata7Ill

Atinfecttnda&tertia hoc dtcendum efTct , nccf/nt^t.,f -,

\\\

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S E X A N G VL A. i?
€UumyC^ vt commodtHsfcripofHt colkciio vaporkin niim confijle-
tiAm.

In circiilo cnim commod-ffime ficret , dt oiu 'a circdli v tcH.z ,^uia
rclm^^inintyideo ctrctilifmnlioreLtgtturfgura.Vtriim htuccmfr i.xm
fa praftitt oppoftta tndLqnditas flclltiUrum , qtt.^.rttm alii^U£ mtnut tf
fm/pint, radtis cttamexilijjiynis & fimplicthy.< ftncTdlis. ^iod
efl argumento.nomAgnam ai''itiam vxporis plantciemftmHl cotretn
nitie fcdfcorfimplxniticiiitSy minimdSyxliaspof altas.e.tsj^ inxqtia-
lcs 7S(o}2 habet ergo locitm confderatio txdiifonis vacui^qux regnat
tanttimindititftoneintegrs fiperfaeitnfxangnta czc^ualia, Itafct
vt fectinda CTtertia catfi enumero dclcatur , ntft quatenu^adpri-
ma?n rcdt^ipofu nt, vt formatrusfi tiUa^fxang^iliim eltgat , ntiUa
materix, ffacioru?nn,neccfftate coacldfedfolam decentia hac tntiita-
tayquodalta^sfcxangiiltim flyuatpUmciem excltfo vactiofitjfexiis
figtirisyqti£tJempofffnt] circiiltfi^.^/ilima ^ ^^^^^

^arta quidcm cauffc nttd.t conffcreneqttit, Namalhalilia icnanum
trinisfniscf^effgianttirfoliisy(jfeyilta nonfunt:eodcm modomul- numcrum
tiCalycesflorumferefylncf rium, Ntffortehocdtfcriminisfty quod [^"t^adunS
fiucitisfiibflore qtiinquangulo en fcttur carnBffs vt in pomis pyris-
queyautpulpacctA< yVtinrofty cucumerihtis feminthu^intracarnem Con^dera-
velptilpa?naldttis ^tfubflore fexangulo ntUnafcttur y nfiftmen^^^ Botam-
inficcoloculoycfg^veluttn florefiuciti^, Aut ef hocforte dtfirtmeny
quodnulhisflosfixangulns in arhorihti<s crfrutictbti^s yfedtnherhis
(jr fere bulhaceis. Velcoyft lerct ali t-s ipfos ficcosan al-qnod in tfs dtf
crimcn fcundum figurasf orum,

Resmihinondum compcrtaef , itaquefuffciat leuiteradmonuiffe
alios de hac qtttrta caufa . Fi urx fof-

Proquintacatifi faciunt opera huiiis formatricls factdtatis alia^ fiij^j^
vtCryfi.dltyomnesfxanguUyCtimAdamantes Ociaedrictfntrartf ftallifexan.
fimt.Sed Formatrix te/ltris facultas no vnam amplecfttur figuram, 8^^*
gnaratotitis Geometridty ineaexercita. Vtdi entm Dref2^ in ^de
Jiegia ctii fiubulo nomen y exornatum Abactcm ^re argentofoy exqua
quafi efforefiehat dodecacdron aticlUn^paru^magmtudtne y dimi-
dtapart^ €>:^ans.Extat^ m defiription^ th^marum Bollenfitim U

cofxcdri

'ConfiJcra-

DE NIVE

da MctaU ^^f^^^^'^ p^^^ ^^^^^^^0^ wierfcJfilU^ Itaqueverifimileejihancfacul'
lariis&Al- tatemformatric(?n prodiuerfo humore y diuerfam feri. In vttrtolo
ctimiftis. crehra cffgura cuhica Rhc7nht€a In TiUro fua ejifigura. Dicant igi-
tur Chymici.an in 2{iue fit aliquidfalis, & quod nam falisgenHs,
^uam illud alias induat figuram. Ego namque , pufatis Chymi^ fg^
rihuspCum videam^^uantum rejiet dtcendumyVt caufa rei ha-
heattirimalo ahste , Vir folerti(?tme,quid
fentias,audire,quam dtjjerendo
amplttts fatigari.
^ihilfequitur

T I N I s.

Early European Books, Copyright© 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147

Early European Books, Copyright © 2009 ProQuest LLC.

Images reproduced by courtesy of the Royal Library, Copenhagen.

KB 55,147