Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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xml:space
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">INeadem antecedentis figura oſtendemus omnia quadra-
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ta portionis, BSF, ad rectangula ſub eadem portione,
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BSF, & </
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<
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xml:space
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">ſub figura, SEF, regula communi, BF, eſſe vt, B
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F, ad, FE.</
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<
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<
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xml:space
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F, ad, FE; </
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<
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xml:space
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">ſimiliter ducta vtcunque, CD, parallela regulę, BF,
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oſtendemus quadratum, CD, ad rectangulum, ſub, CD, DZ,
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eſſe vt, CD, ad, DZ, eſt autem vt, BF, ad, FE, ita, CD, ad,
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DZ, ergo quadratum, BF, ad rectangulum, BFE, erit vt qua-
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dratum, CD, ad rectangulum, CDZ, ſic oſtendemus quamlibet
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ductam intra portionem, BSF, parallelam regulę, BF, ad eiuſdem
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xml:space
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4. 1. 2.</
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portionem incluſam figura, SFE, eſſe vt quadratum, BF, ad re-
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ctangulum ſub, BF, FE, ergo quadratum, BF, ad rectangulum
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ſub, BF, FE, erit vt omnia quadrata portionis, BSF, ad rectan-
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gula ſub portione, BSF, & </
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<
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xml:space
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">ſub figura, SEF, vt autem quadratum,
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BF, ad rectangulum ſub, BF, FE, ita, BF, ad, FE, ergo omnia
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quadrata portionis, BSF, ad rectangula ſub portione, BSF, & </
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gura, ESF, erunt vt, BF, ad, FE, quod oſtendere opus erat.</
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xml:space
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<
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">SI intra curuam parabolæ duæ vtcunque ducantur rectæ
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lineę in eandem @terminatæ, quarum vna rectè, altera
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obliquè axim ſecet, ſint autem conſtitutarum ab eiſdem pa-
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rabolarum diametri inter ſe æquales: </
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rabolæ per eam, quæ rectè axim ſecat, conſtitutæ, regula
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eadem, erunt æqualia rectangulis ſub parabola per obli-
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quam ad axem conſtituta, regula eadem, & </
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ſtantiarum eiuſdem parabolæ per obliquam ad axem con-
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ſtitutæ.</
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