Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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ribus æqualiter baſibus inclinatis, reciprocantur, ſunt
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æqualia, & </
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">quæ ſunt æqualia, baſes habent altitudinibus,
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vel lateribus æqualiter baſibus inclinatis, reciprocas.</
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<
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">Sint parallelogramma, HX, AD, quorum baſes, VX, BD, re-
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ciprocentur eorum altitudinibus, CO, RZ, vel lateribus, CD, R
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X, quotieſcunq; </
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<
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lelogramma eſſe æqualia; </
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<
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">etenim parallelogrammum, HX, ad pa-
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rallelogrammum, AD, habet rationem compoſitam ex ea, quam
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habet, VX, ad, BD, &</
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<
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">, RZ, ad, CO, ſiue, RX, ad, CD, cum
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0139-01
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illa ſunt æquiangula, eſt autem, vt,
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VX, ad, BD, ita, CO, ad, RZ,
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vel, CD, ad, RX, cum illa ſunt
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ced.</
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æquiangula, ergo parallelogram-
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mum, HX, ad parallelogrammum,
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AD, habet rationem compoſitam
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ex ea, quam habet, CO, ad, RZ,
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&</
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<
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">, RZ, ad, CO, ſiue ex ea, quam
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habet, CD, ad, RX, &</
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<
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">, RX, ad, CD, quæ eſt eadem ei, quam
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lib. 1.</
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habet, CD, ad, CD, vt illa eſt eadem ei, quam habet, CO, ad,
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CO, ſuntque proportiones æqualitatis, ergo parallelogrammum,
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HX, erit æquale parallelogrammo, AD.</
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">Sint nunc parallelogrammum, HX, æquale parallelogrammo, A
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D. </
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RX, cum ſunt æquiangula. </
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X, eſt æquale parallelogrammo, AD, erit ad illud, vt, CO, ad,
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CO, vel vt, CD, ad, CD, ideſt (de foris ſumpto, RZ, vel pro
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ſecunda ratione, RX,) inratione compoſita ex ea, quam habet, C
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lib. 1.</
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O, ad, RZ, & </
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habet, CD, ad, RX, &</
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<
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habet etiam rationem compoſitam ex ea, quam habet, VX, ad, B
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D, &</
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<
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ergo duæ rationes, CO, ad, RZ, &</
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<
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RX, &</
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<
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duæ.</
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">, RZ, ad, CO, vel, RX, ad, CD, eſt
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autem communis ratio, quam habet, RZ, ad, CO, vel, RX, ad,
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CD, ergo reliqua ratio .</
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