Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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<
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ſi, & </
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<
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">circa eundem axim, vel diametrum conſtituta,
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baſiſque ſumatur pro regula: </
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<
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">Omnia quadrata dicti paral-
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lelogrammi ad omnia quadrata figuræ compoſitæ ex para-
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bola, & </
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<
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">alterutro trilineorum, qui fiunt extra parabolam,
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demptis omnibus quadratis eiuſdem trilinei, erunt vt di-
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ctum parallelogrammum ad dictam parabolam; </
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<
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verò cum omnibus quadratis illius trilinci erunt, vt dictum
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parallelogrammum ad dictam parabolam ſimul cum {@/2} {1/4}. </
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<
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ctiparallelogrammi .</
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<
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">i. </
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<
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<
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<
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">Sit ergo parallelogrammum, AF, in eadem baſi, DF, & </
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eundem axim, vel diametrum, BE, cum parabola, DBF, regula
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ſit, DF. </
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<
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a figuræ,
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CBDF, demptis omnibus quadratis trilinei, BCF, eſſe, vt, AF,
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ad parabolam, DBF, eadem verò ad omnia quadrata fig. </
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0346-01
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F, eſſe vt, AF, ad parabo-
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lam, DBF, cum {@/2} {1/4}. </
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<
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lelogrammi, AF; </
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<
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enim, BE, eſt axis, vel dia-
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meter tum parabolæ, DBF,
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tum parallelogrammi, AF,
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ideò ſi ducatur intra paralle-
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logrammum, AF, vtcunq-
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recta linea parallelaipſi, D
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F, portiones eiuſdem inclu-
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ſæ trilineis, ADB, CFB, erunt inter ſe æquales, & </
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bola, DBF, erit figura, qualem poſtulat Prop. </
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<
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pter omnia quadrata, AF, ad omnia quadrata figuræ, CBDF,
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demptis omnibus quadratis trilinei, BCF, erunt vt, AF, ad para-
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bolam, DBF.</
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<
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ſunt vt quadratum, DF, ad quadratum, FE, .</
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24. </
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<
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<
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">omnia verò quadrata, BF, ſunt ſexcupla omnium qua-
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dratorum trilinei, BCF, .</
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<
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<
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<
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<
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">igitur omnia quadrata, AF,
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ad omnia quadrata trilinei, BCF, erunt vt 24. </
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<
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ad ſui ipſius {@/2} {1/4}. </
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