Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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micirculo, vel ſemiellipſi, FQB, diuiduntur per curuam, FQB, in
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lib. 2.</
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rectangula fub quadrilineo, FQBDZ, & </
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lipſi, FQB, & </
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">in omnia quadrata ſemicirculi, vel ſemiellipſis, FQ
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B, videndum ergo nunceſt, quamrationem habeant omnia quadra-
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ta, FD, ad omnia quadrata ſemicirculi, vel ſemiellipſis, FQB,
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quod fic patet; </
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">omnia quadrata, FD, ad omnia quadrata, FC,
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poteſt ex
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12. lib. 2.</
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ſunt vt quadratum, DB, ad quadratum, BC, .</
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<
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<
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">ad rectangulum ſub,
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DB, BI, nam tres, DB, BC, BI, ſunt continuè proportionales,
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omnia item quadrata, FC, omnium quadratorum ſemicirculi, vel
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">Coroll. 1.
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huius.
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5. Lib. 2.</
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ſemiellipſis, FQB, ſunt ſexquialtera .</
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<
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<
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">ſunt vt rectangulum, DBI,
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ad rectangulum, DBR, quia, BR, eſt, {2/3}, BI, ergo ex æquali om
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nia quadrata, FD, ad omnia quadrata ſemicirculi, vel ſemiellipfis,
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FQB, ſunt vt quadratum, DB, ad rectangulum ſub, DB, BR,
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omnia autem quadrata, FD, ad rectangula ſub, FD, & </
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lo, vel ſemiellipſi, FQB, erant vt idem quadratum, DB, ad rectan-
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gulum ſub, DB, BE, ergo omnia quadrata, FD, ad rectangula ſub
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ſemicirculo, vel ſemiell pſi, FQB, & </
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">ſub quadrilineo, FQBDZ,
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erunt vt idem quadratum, DB, ad rectangulum ſub, DB, &</
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">, RE,
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ad eadem verò bis ſumpta, vt idem quadratum, DB, ad rectangu-
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lum ſub, DB, &</
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">, RV, quia verò omnia quadrata, FD, ad omnia
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quadrata ſemicirculi, vel ſemiellipſis, FQB, ſunt vt quadratum, D
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B, ad rectangulum ſub, DB, BR, ergo colligendo omnia quadra-
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ta, FD, ad omnia quadrata ſemicirculi, vel ſemiellipſis, FQB, vna
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cum rectangulis ſub ſemicirculo, vel ſemiellipſi, FQB, & </
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lineo, FQBDZ, bis ſumptis, erunt vt quadratum, DB, ad rectan-
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gula ſub, DB, BR, DB, RV, .</
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<
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<
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">quia verò ſiab omnibus quadratis, FD, ſubtraxeris omnia quadrata
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ſemicirculi, vel ſemiellipſis, FQB, vna cum rectangulis bis ſub eo-
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dem ſemicirculo, vel ſemiellipſi, FQB, & </
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<
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lib, 2.</
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DZ, remanent omnia quadrata quadrilinei, FQBDZ, ideò, per
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conuerſionem rationis, omnia quadrata parallelogrammi, FD, ad
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omnia quadrata quadrilinei, FQBDZ, erunt vt quadratum, BD,
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ad rectangulum ſub, BD, DV, .</
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<
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proximè verificatur, non .</
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<
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culum, vel ſemiellipſim, FQB, eſt pręcisè, vt 14. </
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proximè, ideò, &</
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E, quod ſic facilè patet, cum .</
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<
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<
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ad rectangula ſub parallelogrammo, FD, & </
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lipſi, FQB, eſſe vt quadratum, DB, ad rectangulum ſub, DB, B
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E, inſuper oſtenſum ſit omnia quadrata, FD, ad omnia </
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