Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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EP, PH, vt quadratum, GP, ad rectangulum, GPZ, ergo, exæ.
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<
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">quali, omnia quadrata, DG, ad rectangul a ſub trilineis, DPG, D
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EG, erunt vt quadratum, PG, ad {1/6}. </
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<
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<
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fexcupla: </
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DG, &</
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<
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xml:space
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">trilineo, DGP, ſunt vt, DG, ad, DGP, .</
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<
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compofitam ex {1/2}. </
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<
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<
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">PG, ſunt autem omnia quadrata, D
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G, ſexcupla rectangulorum ſub trilineis, DPG, DEG, .</
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vt, ZP, ad {1/6}, ZP, ergo omnia quadrata, DG, ad omnia quadrata,
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D GP, erunt vt, ZG, ad reſiduum, dempto {1/6}. </
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<
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{1/2}. </
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<
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1. </
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vt, ZP, ad compoſitam ex {1/3}. </
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<
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<
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<
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<
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">Quia verò nunc oſtenſum eſt omnia quadrata, DG, ad omnia
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quadrata, DPG, eſſe vt, ZP, ad compoſitam ex {1/3}. </
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<
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">PG,
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omnia autem quadrata, DG, ad rectangula ſub trilineis, DPG, D
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E G, ſunt vt, ZP, ad {1/6}. </
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<
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rectangula bis ſub, DPG, DEG, erunt vt, ZP, ad compoſitam ex
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{2/3}. </
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">DG, ad reſiduum, demptis
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omnibus quadratis, DPG, & </
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ad omnia quadrata trilinei, DEG, erunt vt, ZP, ad reſiduum, dem-
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ptis {2/3}. </
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<
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<
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<
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">figura, ducta, AX, parallela baſi,
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Z G, quæ tanget parabolam in, A, cui occurrat, GE,
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producta, in puncto, X, oſtendemus omnia quadrata trili-
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nei, DPG, ad omnia quadrata ſemiparabolæ, AQG, ha-
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bere rationem compoſitam ex ea, quam habet compoſita ex
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{1/3}. </
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<
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<
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<
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">ex ratione parallelepipedi ſub,
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D P, & </
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<
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A Q, & </
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<
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G. </
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poſitam ex ea, quam habet parallelepipedi ſub, AQ, & </
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drato, QG, ſexta pars, ad parallelepipedum ſub, DP, & </
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quadrato, PG, & </
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<
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ptis ab eadem, ZP, {2/3}. </
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<
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<
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