Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER IV.
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autem vt, OC, ad, CQ, ita, ſumpta, QC, communi altitudine,
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rectangulum ſub OC, CQ, ad quadratum, QC, ergo ratio com-
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poſita ex ea, quam habet, OC, ad, CQ, & </
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<
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">quadratum, QC, ad
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quadratum, CO, eſt eadem compoſitæ ex ea, quam habet rectan-
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gulum ſub, OC, CQ, ad quadratum, CQ, & </
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<
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">quadratum, CQ,
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ad quadratum, CO, . </
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<
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">i. </
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<
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">eademei, quam habet rectangulum ſub,
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QC, CO, ad quadratum, CO, . </
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<
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<
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">eadem ei, quam habet, QC, ad,
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CO; </
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">ergo omnia quadrata trianguli, DAF, ad omnia quadrata
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trianguli, MHC, vel omnia quadrata parabolæ, DAF, ad om-
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nia quadrata parabolæ, MHC, regulis iam dictis, erunt vt, QC,
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ad, CO, quod ſerua.</
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">Vlterius omnia quadrata parabolæ, MHC, ad rectangula ſub
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parabola, MHC, & </
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">trilineo, HRC, regula, MC, ſunt vt, M
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C, ad, CR, vel ad, CX, . </
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<
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">vt, OC, ad, CQ, ergo omnia qua-
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drata parabolæ, DAF, regula, DF, ad rectangula ſub parabola,
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MHC, & </
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<
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">trilineo, HRC, regula, MC, habebunt rationem
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compoſitam ex ea, quam habet, QC, ad, CO, & </
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habet, CO, ad, QC, ideſt habebunt eandem rationem, quam
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habet, QC, ad, QC, ideſt eruntillis æqualia, quod oſtende-
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re opus erat.</
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">_H_Inc patet omnia quadrata parabolæ, DAF, regula, DF, ad om-
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nta quadrata parabolæ, MHC, regula, MC, eſſe vt QC, ad,
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CO, vel, XC, ad CM, vel, DF, (quæ eſt æqualis ipſi, XC,) ad, MC,
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dumdiametri, AZ, HO, ſunt æquales, vt in Theoremate oſtenſum eſt.</
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">_P_Atet vlterius, ſi intra cùruam parabolicam duæ vtcunq; </
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neæ obliquè axem ſecantes, & </
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">in ipſam terminantes, ductæ fue-
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rint, regula pro qualibetparabola ſumpta earum baſi, quod rectangula
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ſub dictis parabolis per eaſdem conſtitutis, & </
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">ſub figura diſtantiarum
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earundem parabolarum, inter ſe erunt æqualia, quotieſcunq diametri
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earundem ſint æquales, vtraq; </
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qu dratis parabolæ, cuius baſis ſecet perpendeculariter axem eiuſdem
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qui ſit æqualis diametris dictarum parabolarum, & </
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eiuſdem baſis.</
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