Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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P, in eadem altitudine ſumpta iuxta baſes, TP, OP, & </
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xml:space
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">Ex prima
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par. huius
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Propoſ.</
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vt ipſæ baſes, TP, OP, ideſt vt latera, TP, OP, æqualiter baſi,
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NP, inclinata, hæc autem pariter verificabuntur etiamſi baſis, NP,
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non ſit communis, ſint tamen duæ baſes æquales, quæ oſtendere o-
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pus erat.</
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tione baſium, & </
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<
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xml:space
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">altitudinum iuxta eaſdem baſes ſum-
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ptarum, ſiue laterum æqualiter baſibus inclinatorum, cum
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ſcilicetilla ſunt æquiangula.</
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">Sint parallelogramma vtcunque, AD, FM. </
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</
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<
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">re inter ſe rationem compoſitam ex rationibus baſium, quæ ſint, C
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lib. 1.</
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D, GM, & </
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">altitudinum, quę ſint, BV, ON, ſumptæ iuxta baſes,
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CD, GM, illiſque productis, ſi opus ſit, in punctis, V, N, occur-
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rentes, ſiue ex ratione laterum, BD, OM, ſi ſint æquiangula: </
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ſcindatur à, BV, verſus, V, ipſa,
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XV, æqualis ipſi, ON, & </
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<
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ducatur, XP, parallela, CD, ſe-
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cans, BD, in, R, vt fiat paralle-
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logrammum, PD, in eadem altitu-
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dine cum parallelogrammo, FM,
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& </
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<
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mo, AD. </
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go, AD, ad parallelogrammum,
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FM, ſumpto medio de foris parallelogrammo, PD, habet ratio-
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lib. 1.</
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nem compoſitam ex ratione parallelogrammi, AD, ad parallelo-
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grammum, PD, ideſt ex ratione, quam habet, BV, ad, VX, vel,
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ON, ſiue, BD, ad, DR, quoniam, AD, PD, ſunt æquiangu-
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la, ideſt ex ratione, BD, ad, OM, & </
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<
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par. ant.</
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M, ſint pariter æquiangula, & </
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<
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">inſuper eſt compoſita ex ea, quam
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habet parallelogrammum, PD, ad parallelogrammum, FM, ideſt
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ex ea, quam habet, CD, ad, GM, ergo parallelogrammum, AD,
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">Ex prima
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parte an-
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teced.</
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ad parallelogrammum, FM, habet rationem compoſitam ex ea,
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quam habet, BV, ad, ON, quæ ſunt altitudines, vel etiam ex ea,
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quam habet, BD, ad, OM, ſi, AD, FM, ſint æquiangula; </
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ea, quam habet, CD, ad, GM, quod oſtendere opus erat.</
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