Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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cta demon tratione propoſitum oſtendemus; </
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<
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xml:space
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">vnde patebit pariter quadra-
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ta maxim trum abſciſſarum propoſitæ rectæ lineæ, vt ipſius, EM, adiun-
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cta quædam, vt, EF, ad quadrata omnium abſciſſarum eiuſdem adiuncta
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eadem, eſſe vt quadratum vnius maximarum abſciſſarum adiuncta iam
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dicta .</
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lum ſub hac compoſita, & </
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">ſub adiuncta, vnacum, {1/3}, quadrati differen-
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tiæhuius compoſitæ, & </
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">vt quadratum, MF, ad rectangu-
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lum ſub, MF, FE, vnacum, {1/3}, quadrati, EM, quæ eſt differentia ea-
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rundem, & </
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<
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vno laterum ad omnia quadrata eiuſdem regula altero
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laterum cum prædicto angulum continentium, erunt vt pri-
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ma regula ad ſecundam.</
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eiuſdem, regula, DB, eſſe vt, CD, ad, DB: </
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ta, AD, regula, CD, ad omnia quadrata, AD, regula, DB, ha-
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bent rationem compoſitam ex ea, quam habet quadratum, CD, ad
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quadratum, DB, & </
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quam habet, BD, ad, DC,
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(quia, BD, &</
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<
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tur baſi, CD, ac, CD, ipſi
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baſi, DB, nam ſunt circa eun-
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dem angulum) .</
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habet quadratum, BD, ad re-
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ctangulum ſub, BD, DC, duæ autem rationes, nempè quadrati, C
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D, ad quadratum, BD, & </
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D, DC, componunt rationem quadrati, CD, ad rectangulum ſub,
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lib. 1.</
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BD, DC, quę eſt eadem ei, quam habet, CD, ad, DB, ergo om-
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nia quadrata, AD, regula, CD, ad omnia quadrata eiuſdem, AD,
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regula, DB, erunt vt, CD, prima regula ad, DB, ſecundam, quod
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oſtendere opus erat.</
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regula, CD, ad omnia quadratratrianguli eiuſdem, regula, DB,
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eſſe vt, CD, primam regulam ad, D B, ſecundam, nam omnia </
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