Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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141121LIBER II.

Sint igitur parallelogramma, AM, MC, in eadem altitudine. Di-
11A. Deſ. 8.
huius. co omnia quadrata parallelogrammi, AM, ad omnia quadrata pa-
rallelogrammi, MC, regula, GH, eſſe vt quadratum, GM, ad
quadratum, MH. Sit intra parallelogramma, AM, MC, ducta
vtcunque, DI, parallela ipſi, GH, cuius portio, DE, maneat in,

81[Figure 81] AM, & , EI, in, BH, quoniam ergo, D
E, eſt æqualis ipſi, GM, figurę autem pla-
næ ſimiles deicriptæ à lateribus, vel lineis
2225. lib. 1. homologis æqualibus ſunt æquales, & ideò
quadratum, DE, erit æquale quadrato, G
M, & quadratum, EI, quadrato, MH,
ergo, vt quadratum, GM, ad quadratum,
MH, ita erit quadratum, DE, ad quadratum, EI, & quia, DI, vt-
cunq; ducta eſt parallela ipſi, GH, ideò, vt vnum ad vnum, ita om-
33Coroll. 4.
huius. nia ad omnia idelt vt quadratum, GM, ad quadratum, MH, ita
erunt omnia quadrata parallelogrammi, AM, ad omnia quadrata
parallelogrammi, MC, regula, GH, quod erat oſtendendum.

COROLLARIVM.

_H_Inc patet, ſi vice quadratorum ſumamus alias quaſcunque figuras
ſimiles, quod eodem pacto oſtendemus omnes figuras ſimiles pa-
44_A. Def. 8._
_huius._ rallelogrammi, AM, ad omnes ſimiles figuras parallelogrammi, MC,
vt ex. gr. omnes circutos parallelogrammi, AM, ad omnes circulos pa-
rallelogrammi, MC, eſſe vt ſimiles ſiguras ab ipſis b ſibus, GM, MH,
d@ſcriptas, nam fi uræ planæ ſimiles quæcunq; vt dictum eſt, deſcriptæ à
lateribus, vel lineis homologis æqualibus ſunt æquales; omnibus pari-
55_25. lib. 1._ ter aſſumptis figuris ſimilibus, regula eadem, GH.

THEOREMA X. PROPOS. X.

PArellelogrammorum in eadem baſiexiſtentium omnia
quadrata, regula ipſa baſi, ſunt vt altitudines, vel vt la-
tera, quę æqualiter baſi ſunt inclinata, ſi illa ſint ęquiangula.

Sint parallelogramma, AD, BD, in eadem b ſi, CD, exiſten-
tia, quorum ſint altitudines iuxta baſim, CD, ſumptæ, AO, CN.
Dico omnia quadrata parallelogrammi, AD, adomnia quadrata
parallelogrammi, BD, regula, CD, eſſe vt, AO, ad, CN, vel
etiam vt, AC, ad, CB, ſi parallelogramma, BD, DA, fuerint æ-
quiangula, producantur autem, CA, CB, indefinitè ad partes

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