Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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ſub, MX, &</
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<
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ſub, MYT, & </
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nia quadrata, MYT, cum rectangulis ſub, MYT, & </
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<
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lineo, MTXC, erunt vt, MX, ad, MYT, .</
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<
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.</
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<
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<
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verò ad hæc quater ſumpta erunt, vt quadratum, XY, adrectangu-
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lum ſub, XY, & </
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<
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miportionis, MYT, quater ſumpta æqualia omnibus quadratis por-
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tionis, MST, & </
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quater ſumpta æqualia rectangulis ſub eodem quadrilineo, & </
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portione, SMT, bis ſumptis, nam portio, SMT, bis continet ſe-
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miportionem, MYT, ergo conuertendo, omnia quadrata portio.
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</
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<
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C, ad omnia quadrata, MX, erunt vt rectangulum ſub quadrupla,
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YZ, & </
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X, ad omnia quadrata, HV, cum rectangulis bis ſub parallelogram-
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mis, HV, VC, ſunt
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vt vnum ad vnum.
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cum rectangulis bis
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ſub, RV, VX, ergo
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exęquali omnia qua-
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drata portionis, SM
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T, cum rectangulis
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bis ſub eadem, & </
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quadrilineo, MTX, adomnia quadrata, HV, cum rectangulis bis
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ſub parallelogrammis, HV, VC, erunt vt rectangulum ſub, XY, & </
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<
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quadrupla, YZ, ad quadratum, RV, cum rectangulis bis ſub, RV
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X, vel vt eorum dim dia .</
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pone autem rectangulum ſub, RV, VY, cumrectangulo ſub, RV,
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VX, ex quibus fit rectangulum ſub, RV, YX,). </
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ſub, ZY, YX, ad rectangulum ſub, RY, YX, .</
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.</
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grammis, HV, VC, ad omnia quadrata, RF, cum rectangulis bis
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ſub parallelogrammis, RF, FX, funt vt, HR, ad, RD, & </
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dem modo ſuperiori oſtendemus omnia quadrata, RF, cum rectan-
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gulis bis ſub parallelogrammis, RF, FX, ad omnia quadrata
<
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portionis, SET, cum rectangulis bis ſub eadem, & </
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