Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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quadrata, CM, ſunt vt quadratum, EM, ad quadratum, MF, quod
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ſerua. </
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vt quadratum, ME,
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ad quadratum, EF,
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omnia verò quadra-
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ta, BF, ſunt ſexcupla
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omnium quadratorú
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trilinei, BCF, .</
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<
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<
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ad illa, vt quadratum,
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EF, ad eiuſdem {1/6}. </
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">er-
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go, ex æquali, om-
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nia quadrata, BM, ad
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omnia quadrata trili-
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nei, BCF, ſunt vt quadratum, EM, ad {1/6}. </
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<
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xml:space
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">quadrati, EF, quod etiá
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ſerua. </
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">Tandem omnia quadrata, BM, ad rectangula ſub, BF, FH,
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ſunt vt quadratum, EM, ad rectangulum ſub, EF, FM, rectangu-
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26. l. 2.</
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la verò ſub, BF, FH, ad rectangula ſub trilineo, BFC, & </
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M, ſunt vt, BF, ad trilineum, BCF, (nam, CM, eſt parallelogram-
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mum) ideſt ſunt eorum tripla .</
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gulum, EF/M, ad rectangulum ſub {1/3}. </
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<
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quali, omnia quadrata, BM, ad rectangula ſub trilineo, BCF, & </
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ſub, FH, erunt vt quadratum, EM, ad rectangulum ſub {1/3}. </
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ſub, FM, ad eadem verò bis ſumpta, vt quadratum, EM, ad re-
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ctangulum bis ſub {1/3}. </
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M, ergo, colligendo, omnia quadrata, BM, ad omnia quadrata; </
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M, ad omnia quadrata trilinei, BCF, & </
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<
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lineo, BCF, & </
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xml:space
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">ad omnia quadrata figuræ, BFMH,
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erunt vt quadratum, EM, ad quadratum, MF, rectangulum ſub
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{2/3}. </
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erat.</
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eiſdem omnibus quadratis figuræ, BFMH, eſſe vt quadratum,
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EM, ad reſiduum, demptis à quadrato, EM, his omnibus .</
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FM, rectangulo ſub, MF, & </
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<
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reſiduum eſt rectangulum ſub, MF, & </
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drati, EF; </
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nebunt duo rectangula ſub, MF, FE, cum quadratum, FE, vlterius ſi à
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rectangulo bis ſub, MF, FE, dempſeris rectangulum ſub, MF, & </
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