Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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E, ideſt rectangulum bis ſub, MF, & </
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lum bis ſub, MF, & </
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<
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">eiuſdem quadrati, vnde
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omnia quadrata, BM, ad reſiduum, demptis omnibus quadratis figuræ,
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BFMH, erunt vt quadratum, EM, ad rectangulum ſub, MF, & </
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quitertia, FE, cum {5/6}. </
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<
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<
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quadrata figuræ, BDMH, demptis omnibus quadra-
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tis, BM, ad omnia quadrata, BM, demptis omnibus qua-
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dratis figuræ, BFMH, eſſe vt, EM, cum {1/2}. </
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ad, MF, cum {1/3}. </
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">Omnia enim quadrata, AM, ad omnia quadrata figuræ, DBH
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M, oſtendimus eſſe,
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vt quadratum, D
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M, ad quadratum,
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ME, rectangulum
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ſub, ME, & </
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tertia, ED, cum {1/2}.
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</
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dem verò ad omnia
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quadrata, BM, ſunt
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vt quadratum, DM, ad quadratum, ME, ergo omnia quadrata, A
<
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M, ad omnia quadrata figuræ, HBDM, demptis omnibus qua-
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Matis, BM, erunt vt quadratum, DM, ad rectangulum ſub, ME,
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& </
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ad illa erunt, vt rectangulum ſub ſexquitertia, ED, cum {1/2}. </
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ti, ED, ad quadratum, DM: </
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nia quadrata. </
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<
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& </
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<
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omnibus quadratis figuræ, BHMF, ſunt vt quadratum, EM,
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autec.</
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ad rectangulum ſub, MF, & </
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<
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FE, ergo, ex æquali, omnia quadrata figuræ, BDMH,
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demptis omnibus quadratis, BM, ad omnia quadrata, BM,
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demptis omnibus quadratis figuræ, BFMH, erunt vt rectangu-
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lum ſub, ME, & </
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<
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<
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ctangulum ſub, MF, & </
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</
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