Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIB ER IV.
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quadrata, AM, ad rectangula ſub, AE, EH, ſunt vt quadratum,
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DM, ad rectangulum, DEM, rectangula verò ſub, AE, EH, ad
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rectangula ſub ſemiparabola, BDE, & </
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ſemiparabolam, BDE, (quia, EH, eſt parallelogrammum) idelt
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ſexquialtera .</
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<
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<
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">vt rectangulum ſub, DEM,
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(ſumpta, EM, communi altitudine) ad rectangulum ſub {2/3}, DE, & </
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ſub, EM, ergo, ex æquali, omnia quadrata, AM, ad rectangula
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ſub ſemiparabola, BDE, & </
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<
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">ſub, BM, erunt vt quadratum, DM,
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">Coroll. 1.
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26. l. 2.</
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ad rectangulum ſub {2/3}. </
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<
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<
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<
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">ad eadem verò bis ſumpta
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erunt, vt idem quadratum, DM, ad rectangulum bis ſub {2/3}. </
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<
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quadrata, AM, ad omnia quadrata, BM, & </
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<
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miparabolæ, BDE, cum rectangulis bis ſub, HE, & </
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la, BDE, ideſt ad omnia quadrata figuræ, HBDM, erunt vt qua-
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dratum, DM, ad quadratum, ME, & </
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<
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cum rectangulo ſub ſexquitertia, DE, & </
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nobis erant demonſtranda.</
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omnia quadrata, AF, ad omnia quadrata figuræ, CBDF, eſſe
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vt 24. </
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">prius demonſtrando omnia quadrata, AF, ad omnia qua-
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drata figuræ, CBDF, eſſe vt quadratum, DF, ad quadratum, FE, {1/2}. </
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drati, ED, & </
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pè 24. </
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nem etiam hoc pacto teneamus.</
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quadrata, BM, ad omnia quadrata figurę, BFMH, eſſe
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vt quadratum, EM, ad quadratum, MF, cum rectangulo ſub
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{2/3}. </
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retenta.</
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uidun-
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tur in omnia quadrata, CM, in omnia quadrata trilinei, BCF, & </
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<
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23. l. 2.</
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in rectangula bis ſub trilineo, BCF, & </
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<
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fingula comparemus omnia quadrata, BM; </
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