Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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H, vt etiam parallelogrammum, DH, eſtin eadem baſi, & </
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dinecum ſemiportione, AFH; </
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ctum, O, & </
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<
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">per ipſum ducatur ipſi, FT, parallela, OE, ſecans cur-
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uam, AG, in, N, CG, in, I, curuam, AF, in, M, &</
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<
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E. </
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& eius
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Scholio.</
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MO, erit vt rectangulum, VHA, adre-
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ctangulum, VOA, .</
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ad quadratum, NO, ergo quadratum, F
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H, vel quadratum, EO, ad quadratum,
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MO, erit vt quadratum, IO, ad quadra-
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tum, ON, ergo, EO, ad, OM, erit vt,
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IO, ad, ON, eſt autem, EO, ducta vt-
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cunque parallela, FT, & </
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<
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gramma, DH, CH, in ijſdem baſibus, & </
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altitudinibus cum ſemiportionibus, AFH,
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AGH, ergo omnes lineæ parallelogram-
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26.lib.2.</
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mi, DH, ad omnes lineas ſemiportionis, FAH, erunt vt omnes li-
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neæ parallelogrammi, CH, ad omnes lineas ſemiportionis, AG
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H, ergo parallelogrammum, DH, ad ſemiportionem, AFH, erit
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vt parallelogrammum, CH, ad ſemiportionem, AGH, ergo, per-
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mutando, DH, ad, CH, parallelogrammum erit, vt ſemiportio,
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AFH, ad ſemiportionem, AGH, ergo vt, DH, ad, CH, .</
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baſis, FH, ad baſim, HG, vel vt, FT, ad, GS, ita erit ſemipor-
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tio, AFH, adſemiportionem, AGH, vel ſic eorum quadrupla .</
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GVS, quod, &</
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">_H_INC etiam habetur, quoniam quadratum, EO, ad quadratum,
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OM, eſt vt quadratum, IO, ad quadratum, ON, idcircò, quòd
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eodem pacto, iuxta Th. </
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drata, DH, ad omnia quadrata, CH, eſſe, vt omnia quadrata ſemi-
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portionis, AFH, ad omnia quadrata ſemiportionis, AGH, vel vt
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omnia quadrata circuli, vel ellipſis, AFVT, ad omnia quadrata cir-
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culi, vel ellipſis, AGVS, ſunt autem omnia quadrata parallelogram-
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mi, DH, ad omnia quadrata parallelogrammi, CH, vt quadratum,
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FH, ad quadratum, GH, habetur ergo inquam, quod omnia quadrata
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circuli, vel ellipſis, AFVT, ad omnia quadrata circuli, vel elli-
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pſis, AGVS, ſunt vt quadratum, FH, ad quadratum, HG, vel vt qua-
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dratum, FT, ad quadratum, GS, ſcilicet ſunt vt quadrata ſecundorum
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axium, vel diametrorum.</
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