Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER II. ſibus æquidiſtante, eo nempè, quod producit figuram, CNX, er-
go, CNX, erit æqualis ipſi, BVG, quod cum alijs adhuc ſerua.

212.1.

Exis: @@
Elem.
Percõſtru
ctionem.
0162-01
Def. Cy-
lindrici
confor-
miter.
Corol. 12.
hb. 1.

213. F. SECTIO VI.

QVia verò, LE, ad, EO, eſt vt, BH, ad, HC, . ſ. vt, VE,
ad, EN, permutando, & diuidendo, LV, ad, VE, erit vt,
ON, ad, NE, . i. vt, 35, ad, 54, ergo, LE, 34, ſunt ſimi-
liter ad eandem partem diuiſæ a figuris, BVG, RSP, ergo ſunt ip-
ſæ figuræ inter ſe ſimiles, quarum latera homologa ipſæ, VG, SP,
lineæ homologę figurarum ſimilium, LFE, 374, quarum inciden-
tes ſuntipſę, LE, 34, vnde eſt, EF, ad, 47, vt, LE, ad, 34, . ſ. vt, VG, ad, SP, ſunt verò figuræ, DEF, 647, quia ſimiles, in
dupla ratione ipſarum, EF, 47, & ipſæ, BVG, RSP, in dupla
ratione ipſarum, VG, SP, ergo vt figura, DEF, ad figuram, 64
7, ita erit figura, BVG, vel, CNX, eidem æqualis ad figuram, R
SP, Quoniam verò ſolida, LEDF, 3647, ſunt ſimilia, vt facilè
oſtendi poreſt, & eorum figuræ incidentes, & oppoſitorum plano-
rum tangentium (quorum ex vna parte duo ſunt ipſa, 647, DEF,)
ſunt figuræ, LEF, 347 quarum lineæ incidentes, LE, 34, ideò
plana ipſis, DEF, 647, æquidiſtantia, quæ ſimiliter ad eandem
partem diu dunt incidentes, LE, 34, diuidunt etiam altitudines di-
ctorum ſolidorum reſpectu dictorum tangentium ſumptas ſimiliter
ad eandem partem (hocdico quotieſcunque, non contingat, LE,
34, eſſe perbendiculares ipſis, DEF, 647, tunc enim ſiunt eædem
incidentes altitudines dictorum ſolidorum) cum igitur, vt, LE, ad,
34, . i. ad, EO, ita ſit altitudo ſolidi, LEDF, tum adabſciſſam al-
titudinem per planum tangens in, O, ipſi, DEF, æquidiſtans . i. ad
altitudinem ſolidi, OEDF, tum ad altitudinem ſolidi, 3467, ideò
ſolida, OEDF, 347, erunt in eadem altitudine ſumpta reſpectu
baſium, DEF, 647, & plana ipſis baſibus æquidiſtantia partes æ-
quales ab ipſis, OE, 34, abſcindentia, et am ab eorum altitudini-
bus abſcindent partes æquales, oſtendimus autem figuras, quę ab ip-
ſis, OE, 34, abſcindunt partes æquales, eſſe proportionales, ergo
in ſolidis, OEDF, 3467, in eadem altitudine exiſtentibus ſumpta
reſpectu baſium, DEF, 647, figuræ, quę ab eiſdem altitudinibus
vtcunque abſcindunt partes æquales, ſunt ſemper, vt ipſæ baſes, er-
go vt vna ad vnam, ſic omnes ad omnes, & ſic ſolida ad ſolida . ſ. vt
baſis, DEF, ad baſun, 647, ita erit ſolidum, OEDF, ad ſolidum,
3467, eſt autem, DEF, ad, 647, in ratione dupla eius, quam
habet, EF, ad, 47, . i. in ratione compoſita ex duabus rationibus
ipſius, EF, ad, 47, velipſius, LE, ad, 34, ergo ſolidum, ODE

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