Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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F M, ad omnia quadrata eiuſdem parallelogrammi; </
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R V, ſunt vt, FM, ad, RV, ergo ex æquali omnia quadrata por-
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tionis, RFV, regula, FM, ad omnia quadrata, Δ V, regula, R
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V, erunt vt, {2/3}, ω M, ad, RV, vel vt, {1/3}, ω M, ad, RM, .</
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pta, RM, communi altitudine, vt rectangulum ſub, {1/3}, ω M, & </
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ſub, RM, ad quadratum, RM, vel ad rectangulum, FMH;
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<
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">omnia vero quadrata, Δ V, regula, RV, ad omnia quadrata por-
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tionis, RFV, regula eadem, runt vt, HM, ad compoſitam ex,
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{1/2}, HM, &</
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<
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ctangulum, FMH, ad rectangulum ſub, FM, & </
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{1/2}, HM, &</
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">, {1/6}, MF, erant autem omnia quadrata portionis, RFV,
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regula, FM, ad omnia quadrata, Δ V, regula, RV, vt rectangulum
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ſub, {1/3}, M ω, & </
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<
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omnia quadrata portionis, RFV, regula, FM, ad omnia quadrata
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eiuſdem, regula, RV, erunt vt rectangulum ſub, {1/3}, M ω, & </
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M, ad rectangulum ſub, FM, & </
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M F, .</
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lum ſub, FM, & </
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.</
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tera, IH, porrò ſexquialtera, IH, cum, {1/2}, FM, efficit duas, FM,
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I H, quibus ſi iunxeris, MI, detractam de ſexquialtera ipſius, MI,
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fiet tota, FH, cum, MN, æqualis dimidio, FM, & </
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<
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M H: </
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<
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">Omnia ergo quadrata portionis, RFV, regula, FM, ad om-
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nia quadrata eiuſdem portionis, regula, RV, erunt vt rectangulum
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ſub, M ω, & </
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<
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<
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ta ex, FH, MN, .</
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<
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<
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Elem.</
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F M, & </
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<
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<
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F MH, æquatur quadrato, RM, erunt omnia illa quadrata, vt re-
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ctangulum ſub, ω M, & </
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<
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tum, MF, & </
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<
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</
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<
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<
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dratum, MV, duo quadrata, FM, & </
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<
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N, .</
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<
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<
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tis ipſius, FM, componetur rectangulum, FMH, quod eſt æqua-
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le quadrato, RM. </
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<
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<
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gula, FM, ad omnia quadrata eiuſdem portionis, regula, RV, vt
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rectangulum ſub, ω M, & </
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<
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vno quadrato, FM, quod oſtendere oportebat.</
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