Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Sit cylindricus, AE, ſectus a planis quomodocumque per latera. Dico per eadem diuidi in cylindricos; ſint autem ſecantia plana, quę
in cylindrico, AE, producant parallelogramma, AE, ME. Quia
igitur, AE, eſt parallelogrammum, ſi in ipſo ducantur rectæ lineæ
ipſi, AD, HE, parallelæ, & in, AH, DE, terminatæ, erunt ei-
ſdem, AD, HE, æquales, & ſubinde erunt æquales, & parallelæ
regulælateris cylindrici, AE, vnde erit, AE, ſuperficies cylindra-
cea deſcripta latere, AD, ſiue latere cylindrici, AE, ergo ſolidum,
ARXE, erit cylindricus. Eodem pacto oſtendemus ſolida, AM
HDVE, MZHVIE, eſſe cylindricos, talibus igitur planis cy-
lindricus, AE, ſemper diuiditur in cylindricos, quæ eſt prior pars
huius Theorematis.

67.1.

Ex def. 3.

Secetur nunc duobus planis vtcumque inter ſe parallelis coinci-
dentibus cum omnibus ciuſdem lateribus, quæ in cylindrico, AE,
producant figuras, BNGK, COFL. Dico ſolidum compræhen-
ſum inter has figuras, & ijs incluſam ſuperficiem
cylindraceam, eſſe cylindricum. Sintadhuc pla-
na per latera cylindrici, AE, vtcumque ducta, A
E, ME, quæ ſecent figuras, BNGK, COFL,
in rectis, BG, CF, NG, OF, igitur eiuſdem pla
ni, & ipſarum, BNGK, COFL, communes ſe-
ctiones erunt parallelæ, quę ſint, BG, CF, ſicut
etiam ipſæ, NG, OF, ſunt autem parallelę etiam
ipſæ, BC, NO, GF, ergo, BF, NF, erunt pa-
rallelogramma, & latera eorumdem, BC, GF,
NO, inter ſe æqualia, & æquidiſtantia; ſi igitur
eorum quoduis, vt, GF, ſtatuatur pro regula lateris ylindrici, ſu-
perficies incluſa duabus figuris, BNGK, COFL, erit deſcripta
vno laterum, BC, vel, NO, properante per circuitum figuræ, C
OFL, ſemper ipſi, GF, æquidiſtante, donec redeat vnde diſceſſit,
igitur hæc erit ſuperſicies cylindracea, cuius oppoſitæ baſes ipſæ fi-
guræ, BNGK, COFL, & ſolidum eiſdem incluſum erit cylindri-
cus, quod erat poſterior pars huius Theorematis à nobis demon-
ſtranda.

67.1.

0044-01
Def. 3.

68. THEOREMA VIII. PROPOS. XI.

CViuſuis cylindrici oppoſitæ baſes ſunt fimiles, æquales,
& ſimiliter poſitæ.

Sit cylindricus, PN, cuius oppoſitæ baſes, APK, OZN. Dico
eas eſſe ſimiles, æquales, & ſimiliter poſitas. Ducantur vtcumque

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