Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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<
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">Sint intra curuam parabolicam, BAC, duæ vtcunquæ ductæ in
<
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eandem terminatæ, DF, MC, quarum, DF, rectè, altera, MC,
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obliquè ſecet axem, AP, ſit autem deſcripta linea, HR, vt ſit con-
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ſtituta, HRC, figura diſtantiarum portionis, MFC, & </
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<
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vertice, H, à quo ducitur linea, HR, ducatur, HQ, parallela
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axi, AP, & </
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<
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">ſint diametri, AZ, HO, parabolarum, DAF, M
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HC, inter ſeæquales. </
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<
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F, regula, DF, eſſe æqualia rectangulis ſub parabola, MHC, re-
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gula, MC, & </
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<
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MHC. </
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<
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<
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">à puncto, M,
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ducatur, MX, axi, AP, æquidiſtans, à puncto verò, C, perpendi-
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cularis axi, AP, producta vſq; </
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<
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">in, B, tandem à puncto, H, ipſa, H
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I, perpendicularis ipſi, MC: </
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<
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xml:space
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bolæ, regula, DF, adrectangula ſub parabola, MHC, regula, M
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C, & </
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<
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">ſub trilineo, HRC, habent rationem compoſitam ex ea,
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quam habent omnia quadrata parabolæ, DAF, regula, DF, ad
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12. 1. 1.</
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omnia quadrata parabolæ, MHC, regula, MC, & </
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habent omnia quadrata parabolę, MHC, regula, MC, adrectan-
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gula ſub parabola, MHC, & </
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<
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MC: </
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<
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bolæ, DMF, regula, DF, ad om-
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nia quadrata parabolæ, MHC, re-
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gula, MC, ſunt vt omnia quadrata
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trianguli, DAF, regula, DF, ad
<
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omnia quadrata trianguli, MHC,
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regula, MC, nam omnia quadrata
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parabolarum ſunt ſexquialtera om-
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nium quadratorum triangulorum in
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eiſdem baſibus, & </
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<
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lis baſibus: </
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<
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">Omnia inſuper quadrata trianguli, DAF, regula, DF,
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ad omnia quadrata trianguli, MHC, regula, MC, habent ratio-
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22. 1. 2.</
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nem compoſitam ex ratione altitudinum, & </
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<
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. </
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<
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">i. </
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<
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">ex rationẽ, quam ha-
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bet quadratum, DF, ad quadratum, MC, vel quadratum, ZF,
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ad quadratum, OC, eſt autem, AZ, æqualis ipſi, HO, ex hypo-
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teſi, &</
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<
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">, ZF, ipſi, QC, ergo omnia quadrata trianguli, DAF, ad
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17. huius.</
note
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omnia quadrata trianguli, MHC, regulis iam dictis, habebunt ra-
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tionem compoſitam ex ea, quam habet, OH, ad HI, & </
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<
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quam habet quadratum, QC, ad qu adratum, CO, quia verò trian-
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guli, HIO, OQC, ſunt æquianguli, ideò, OH, ad, HI, erit vt,
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OC, ad, CQ, ergo illa habebunt rationem compoſitam ex ea, quam
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habet, OC, ad, CQ, & </
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<
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