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

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197177LIBER II. lum, DES, ad rectangulum ſub, DE, & compoſita ex, SF, & , {1/2}, FE,
vna cum rectangulo ſub, EF, & compoſita ex, {1/6}, EF, & , {1/2}, FS . i. vt
rectangulum, ZEV, quod eſt vnum rectangulorum maximis æqualium,
ad rectangulum ſub, ZE, & ſub compoſita ex, VB, & , {1/2}, BE, vna
cum rectangulo ſub, EB, & compoſita ex, {1/6}, EB, & , {1/2}, BV, regulam
autem bic pariter ſuppone ipſam, DS, & abſciſſas, reſiduas & maxi-
mas abſciſſarum tum bic, tum in ſupradictis, & ſequentibus, niſi aliud
dicatur, ſemper intellige, vel recti, vel ei uſdem obliqui tranſitus, recti
11_Hux. diff .i._
_huius._ nempè, cum parallelogramma ſunt rectangula, obliqui autem, cum
non ſuerint rectangula, cum diffinitiones de his allatas.

THEOREMA XXXIII. PROPOS. XXXIII.

EXpoſitis duabus vtcunq; figuris planis, & in earum vna-
quaque ſumpta vtcumque regula, vt omnia quadrata
earumdem figurarum ſumpta iuxta dictas regulas, ita erunt
ſolida quæcumq; ad inuicem ſimilaria ex eiſ dem figuris ge-
nita iuxta eaſdem regulas.

Sint duæ vtcunque ſiguræ planæ, ABC, DEF, in quibus duæ
vtcunque ſint iumptæ regulæ, BC, EF, rectæ lineæ. Dico igitur,
vt omnia quadrata figuræ, ABC, regula, BC, ad omnia quadrata
figuræ, DEF, regula, EF, ita eſſe ſolidum fimilare quodcunque
22Vide B.
Definit. 8.
huius. genitum ex figura, ABC, iuxta regulam, BC, ad ſibi ſimilare ge-
nitum ex figura, DEF, iuxta regulam, EF. Ducatur in altera di-
ctarum figurarum, vtin, DEF, vtcumque regulæ, EF, parallela,

116[Figure 116] HM, quia ergo quadrata habent inter ſe du-
plam rationem laterum, à quibus deſcribun-
338. & 15.
huius. tur, ideò quadratum, EF, ad quadratum,
HM, habebit duplam rationem eius, quam
habet, EF, ad, HM, ſed etiam aliæ duæ
quæcumque figuræ planę ſimiles ab eiſdem
tanquam lineis, vel lateribus homologis ea
4415. huius. rumdem deſcriptę habent duplam rationem
earumdem, ergo, vt quadratum, EF, ad
quadratum, HM, ita erit alia quælibet figura plana deſcripta ab, E
F, ad ſimilem ſibi deicriptam ab, HM, ua vt, EF, HM, ſint ea-
rum homologæ, & , permutando, quadratum, EF, ad aliam ngu-
ram deſcriptam ab, EF, erit vt quadratum, HM, ad figuram præ-
dictę ſimilem ab, HM, deſcriptam. Sic etiam eſſe oſtendemus qua-
dratum cuiuſcumque in figura, DEF, ductæ ipſi, EF,

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