Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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lum, DES, ad rectangulum ſub, DE, & </
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<
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xml:space
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">, {1/2}, FE,
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vna cum rectangulo ſub, EF, & </
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<
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xml:space
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">compoſita ex, {1/6}, EF, &</
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">vt
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rectangulum, ZEV, quod eſt vnum rectangulorum maximis æqualium,
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ad rectangulum ſub, ZE, & </
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<
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<
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">, {1/2}, BE, vna
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cum rectangulo ſub, EB, & </
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<
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xml:space
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">compoſita ex, {1/6}, EB, &</
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<
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xml:space
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">, {1/2}, BV, regulam
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autem bic pariter ſuppone ipſam, DS, & </
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<
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">abſciſſas, reſiduas & </
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<
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xml:space
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">maxi-
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mas abſciſſarum tum bic, tum in ſupradictis, & </
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<
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">ſequentibus, niſi aliud
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dicatur, ſemper intellige, vel recti, vel ei uſdem obliqui tranſitus, recti
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_huius._</
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nempè, cum parallelogramma ſunt rectangula, obliqui autem, cum
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non ſuerint rectangula, cum diffinitiones de his allatas.</
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<
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">EXpoſitis duabus vtcunq; </
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">figuris planis, & </
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">in earum vna-
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quaque ſumpta vtcumque regula, vt omnia quadrata
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earumdem figurarum ſumpta iuxta dictas regulas, ita erunt
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ſolida quæcumq; </
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nita iuxta eaſdem regulas.</
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">Sint duæ vtcunque ſiguræ planæ, ABC, DEF, in quibus duæ
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vtcunque ſint iumptæ regulæ, BC, EF, rectæ lineæ. </
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<
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vt omnia quadrata figuræ, ABC, regula, BC, ad omnia quadrata
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figuræ, DEF, regula, EF, ita eſſe ſolidum fimilare quodcunque
<
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">Vide B.
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Definit. 8.
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huius.</
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genitum ex figura, ABC, iuxta regulam, BC, ad ſibi ſimilare ge-
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nitum ex figura, DEF, iuxta regulam, EF. </
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<
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">Ducatur in altera di-
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ctarum figurarum, vtin, DEF, vtcumque regulæ, EF, parallela,
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0197-01
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HM, quia ergo quadrata habent inter ſe du-
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plam rationem laterum, à quibus deſcribun-
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">8. & 15.
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huius.</
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tur, ideò quadratum, EF, ad quadratum,
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HM, habebit duplam rationem eius, quam
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habet, EF, ad, HM, ſed etiam aliæ duæ
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quæcumque figuræ planę ſimiles ab eiſdem
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tanquam lineis, vel lateribus homologis ea
<
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rumdem deſcriptę habent duplam rationem
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earumdem, ergo, vt quadratum, EF, ad
<
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quadratum, HM, ita erit alia quælibet figura plana deſcripta ab, E
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F, ad ſimilem ſibi deicriptam ab, HM, ua vt, EF, HM, ſint ea-
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rum homologæ, &</
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<
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">, permutando, quadratum, EF, ad aliam ngu-
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ram deſcriptam ab, EF, erit vt quadratum, HM, ad figuram præ-
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dictę ſimilem ab, HM, deſcriptam. </
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<
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dratum cuiuſcumque in figura, DEF, ductæ ipſi, EF, </
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