Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER II.
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quilatera figuræ, BCE, eſſe, vt omnes circuli, BF, ad omnia po-
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lygona vniſimilia figuræ, BEF.</
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<
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">Eodem modo fiet demonſtratio, ſi vice iſtarum aliæ aſſumantur
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figuræ planæ, quarum poſſunt etiam, quæ ſunt duarum figurarum
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eſſe ſimiles, vt ſi comparentur omnia quadrata parallelogrammo-
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rum, AE, ED, & </
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<
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">quilatera figurarum, BCE,
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BEF, vel ſi comparentur omnia quadrata, AE, & </
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<
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xml:space
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& </
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<
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<
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eſſe omnium quatuor figurarum omnes figuras eſſe ſimiles, vt ſi com-
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parentur omnia quadrata eorundem, vel omnes circuli, &</
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<
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autem hic demonſtrationem currere quotieſconque ea, quæ compa-
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rantur ſunt eiuſdem generis .</
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">vel lineæ, vel ſuperficies, ſi verò con-
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tingat magnitudines diuerſi generis comparari, vt ſi compararentur
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omnes lineæ, AE, & </
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gurę, BEF, tunc quia &</
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tari, cum lineam ſuperficiei comparare ſit abſurdum, ideò demon-
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ſtratio pro his non currit, quapropter aliud Theorema pro hoc ſut-
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iungemus.</
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gnitudines diuerſi generis, adhuc comparatæ magnitu-
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dines erunt proportionales.</
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omnes lineæ, AE, re-
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gula, CE, ad omnes li-
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neas fi uræ, BCE, & </
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omnia quadrata, BF,
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regula, EF, ad omnia
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quadrata figurę, BEF,
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ita vt ducta vtcunq. </
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<
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CF, paraliela, MQ,
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reperiamus, MO, ad,
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OI, eſſe vt quadratum,
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QO, ad quadratum, O
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P. </
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lineas, AE, ad omnes
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lineas figurę, BCE, eſ-
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ſe vt omnia quadrata, B
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F, ad omnia quadrata figurę, BEF; </
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