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

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186166GEOMETRIÆ

COROLLARIVM II.

_H_Abetur ſecundò cylindricos in eadem altitudine exiſtentes eſſe in-
terſe, vt baſes, quod de cæteris, veluti de ſupradictis, FE, GD
E, oſiendetur, quamuis aliter etiam id aliundè infra colligetur.

COROLLARIVM III.

_H_Abetur tertiò, ſi non ſint in ſupradictis duobus Theorematibus ex-
poſita duo parallelogramma, & duæ figuræ, ſed vnum tantum,
& vna figurain eadem baſi, & altitudine cumipſo, cuius baſi poſita pro
regula, & ſumpto vteunque puncto in vno laterum baſi inſi§tentium,
perque ipſum baſi ducta parallela, reperiatur eam, quæ intercipitur pa-
rallelogrammo ad eam, quæ intercibitur figura, vel figuras ſimiles ab
ipſis deſcriptas, tanquam homologis lineis, vel lateribus, eſſe vt vnam
ex maximis abſciſſarum lateris, in quo ſumptum eſt punctum, ad abſciſ-
ſam per ductam baſi & ae; quidiſtantem, vel vt iſtas adiuncta quadam recta,
linea, vel vt iſtarum figuras ſimiles ab ipſis tanquam lineis, vel lateri-
bus homologis deſcriptas, ita vt figuræ deſcriptæ & a4; ſingulis earum, quæ
dicuntur omnes lineæ parallelogrammi, & dictæ figuræ, ſint ſimiles, vt
pariter, quæ deſcribuntur & a4; ſingulis earum, quæ dicuntur maximæ ab-
ſciſſarum, vel abſciſſæ dicti lateris, quod adbuc dictæ magnitudines col-
lectæ erunt proportionales: Vt ex. gr. ſi in Theorematis antecedentis fi-
gura habeamus tantum parallelogrammum, BF, & in eiuſdem baſi, E
F, & eadem altitudine, figuram, BEF, & ſumpto in vno laterum, B
E, DF, vtcunque puncto, O, & per, O, ducta, OQ, parallela ipſi, E
F, reperiamus, QO, ad, OP, eſſe vt, EB, ad, BO, vel figuras ſimiles
deſcriptas ab, OQ, OP, tanquam lineis, vel lateribus homologis, vt
ex. gr. quadratum, QO, ad quadratum, OP, eſſe vt, EB, ad, BO, vel
vt, EB, adiuncta quadam linea ad, BO, adiuncta eadem, vel vt abiſtis
deſcriptas ſimiles figuras, dico collectas magnitudines, quæ comparan-
tur eſſe proportionales: Nam ſi ipſi, BE, intelligatur applicatum pa-
rallelogrammum, AE, cuius baſis ſit, CE, in directum ipſi, EF, con-
ſtituta, & , CE, & ae; qualis ipſi, EB, tunc omnes lineæ, AE, regula, C
11_Corol. 2._
_19. huius._ E, ſunt & ae; quales maximis abſciſſarum, BE, vt probatum eſt, & omnes
abſciſſæ & ae; quales omnibus lineis trianguli BCE, ſi ſit iuncta, BC, (quæ
ſecet, MO, in, X,) vnde vice earum, quæ dicuntur maximæ abſciſſa-
rum, vel abſciſſæ ipſius, BE, rectè ſumemus omnes lineas, AE, & tri-
anguli, BCE, & itareperiemus quadratum, QO, ad quadratum, OP,
ex. gr. eſſe vt, MO, ad, OX, vel vt quadratum, M, O, ad

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