Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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bis, cum {2/3}. </
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imi
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Con.</
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lę, AC, ipſę, VS, TR, igitur, TR, tanget ſectionem, AMC, & </
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ſunt parallelogramma, TC, VC, VD: </
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<
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<
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">rallelogrammi, VC, ad omnia quadrata hyperbolæ, AMC, ha
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bent ratiíonem compoſtionem ex ea, quam habent omnia quadrata,
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l. 1.
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10. l.2.</
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VC, ad omnia quadrata, TC, .</
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ratione omnium quadratorum, TC,
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ad omnia quadrata hyperbolę, AMC,
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ideſt ex ea, quam habet, NE, ad cõ-
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poſitam ex, OM, & </
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rationes autem .</
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<
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ad, EM, &</
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OM, & </
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<
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">ME, componuntrationem
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rectanguli ſub, NE, EO, ad rectangu-
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lum ſub, EM, & </
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M, & </
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VC, ad omnia quadrata hyperbolę,
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AMC, ſunt vt rectangulum, NEO, ad
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rectangulum ſub, EM, & </
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ſita ex, OM, & </
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<
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le rectangulis ſub, OM, &</
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<
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{1/3}. </
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<
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<
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<
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a verò rectangulum, NEO, ęquatur rectangulo, NEO, cum
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quadrato, OE, quadratum verò, OE, ęquatur quadratis, EM, M
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O, cum rectangulis bis ſub, EMO, ideò ſi ab his dempſeris ſemel
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rectangulum, EMO, remanebit de quadrato, OE, rectangulum,
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EMO, cum quadratis, EM, MO, rurſus ſi dempſeris {1/3}. </
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EM, à quadrato, EM, remanebunt {2/3}. </
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EMO, cum quadrato, MO, rectangulum verò, EMO, cum qua-
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drato, OM, ęquatur rectangulo, EOM, vel, EON, quod collectũ
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ſimul cum {2/3}. </
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rectangulo, EMO, cum {1/3}. </
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detracto rectangulo, EMO, cum {1/3}. </
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O, iuncto rectangulo, EON, .</
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<
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duo rectangula, NOE, cum {2/3}. </
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eſt omnia quadrata, VC, ad omnia quadrata hyperbolę, AMC,
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eiſe vt rectangulum, NEO, ad rectangulum, OME, cum {1/3} qua-
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drati, ME, ideò, per conuerſionem rationis, omnia quadrata, V
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O, ad reliquum, demptis ab ijſdem omnibus, quadratis hyperbo-
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lę, AMC, erunt vt rectangulum, NEO, ad rectangulum bisſub,
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NOE, cum {2/3}. </
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