Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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poſitam ex ea, quam habet, BV, ad, ON, vel, BD, ad, OM, cum
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ſunt æquiangula, & </
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">ex ea, quem habet quadratum, CD, ad qua-
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dratum, GM, quod oſtendendum erat.</
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">_H_Inc patet, ſi vice quadratorum ſumamus alias figuras planas ſimi-
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les, quod eodem pacto oſtendemus omnes figuras ſimiles, AD, F
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M, habere inter ſerationem compoſitam ex ratione quadratorum, CD,
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GM, & </
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<
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">altitudinum, BV, ON, vel laterum, BD, OM, æqualiter
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baſibus inclinatorum, cum parallelogramma ſunt æquiangula.</
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">P Arallelogrammorum, quorum baſium quadrata altitu-
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dinibus iuxta eaſdem baſes ſumptis reciprocantur, vel
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lateribus æqualiter dictis baſibus inclinatis; </
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<
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">omnia quadra-
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ta, regulis eiſdem baſibus, ſunt æqualia: </
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">Et quorum paral-
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lelogrammorum, regulis baſibus, omnia quadrata ſunt æ-
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qualia, baſium quadrata altitudinibus, vellateribus æqua-
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liter dictis baſibus inclinatis, reciprocantur.</
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">Sint parallelogramma, HX, AD, quorum baſium, VX, BD,
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quadrata altitudinibus iuxta ipſas baſes ſumptis, vel lateribus, RX,
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CD, ſi hæc baſibus, VX, BD, æqualiter ſint inclinata, recipro-
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centur. </
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rallelogrammorum, HX, AD, eſſe
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inter ſe æqualia. </
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ced.</
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drara, HX, ad omnia quadrata, A
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D, habent rationem compoſitam ex
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ea, quam habet quadratum, VX, ad
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quadratum, BD, .</
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<
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habet, CO, ad, RZ, vel, CD, ad,
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RX, cum ſunt æquiangula, & </
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<
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">ex ea, quam habet, RZ, ad, CO,
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vel, RX, ad, CD, quæ duæ rationes componunt rationem, CO,
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ad, CO, vel, CD, ad, CD, quæ eſt ratio æqualitatis, & </
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<
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nia quadrata, HX, erunt æqualia omnibus quadratis, AD.</
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D, regulis eiſdem, VX, BD. </
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tum, BD, eſſe vt, CO, ad, RZ, vel, CD, ad, RX, cum ſunt </
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