Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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">SI intra curuam parabolicam duæ vtcunque ductæ fue-
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rint rectæ lineæ in eandem terminantes, quarum vna
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rectè, altera obliquè ſecet axim; </
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<
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">omnia quadrata conſtitu-
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tæ parabolæ per eam, quæ axim rectè ſecat, regula eadem,
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ad rectangula ſub parabola conſtituta per obliquè ſecantem
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axem, regula huius baſi, & </
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">ſub ſigura diſtantiarum eiuſ-
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dem parabolæ, erunt vt quadratum axis primò dictæ para.
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</
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<
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xml:space
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">bolæ ad quadratum diametriſecundò dictæ parabolæ.</
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<
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">Sintigitur intra curuam parabolicam, ADH, duæ ductæ rectæ
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lineæ in eadem terminantes, quarum vna rectè, altera obliquè ſecet
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axim, ſi ergo conſtitutarum ab ijſdem parabolarum diametri ſunt
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æquales, pater veritas Propoſitionis ex antecedenti Theor. </
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<
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xml:space
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">non ſint
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autem conſtitutarum parabolarum diametri æquales, ſint autem
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duæ parabolas conſtituentes, AH, rectè ſecans axem, DO, & </
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G, obliquè ipſum diuidens, exiſtatq;
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</
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<
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læ, CEG, quæ ſit, EM, & </
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<
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cta linea, ER, & </
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<
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G, figura diſtantiarum parabolæ, C
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EG. </
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parabolæ, ADH, regula, AH,
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ad rectangula ſub parabola, CEG,
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& </
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">trilineo, ERG regula, CG,
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eſſe vt quadratum, DO, ad quadratum, EM, abſcindatur ergo
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ab, OD, DN, æqualis ipſi, EM, & </
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<
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parallela, BF. </
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<
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">Omnia ergo quadrata parabolæ, ADH, ad omnia
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quadrata parabolæ, BDF, regula communi, AH, vel, BF, ſunt
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vt qúadratum, OD, ad quadratum, DN, vel ad quadratum, E
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M, ſedomnia quadrata parabolæ, BDF, regula, BF, ſunt æqua-
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lia rectangulis ſub parabola, CEG, & </
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G, ergo omnia quadrata parabolæ, ADH, regula, AH ad re-
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ctangula ſub parabola, CEG, & </
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<
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xml:space
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erunt vt quadratum, OD, ad quadratum, EM, quod erat oſten-
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dendum.</
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