Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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angula, eodem pacto oſtendemus parallelogramma, QF, BH, eſſe
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æquiangula, vnde concludetur etiam parallelogramma, AN, QF,
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eſſeinter ſe æquiangula, quod oſtendere opus erat.</
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">_S_I autem intelligamus oppoſitarum baſium cylindrici, AF, ita pra-
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ducta plana, vt ſecentur à plano per latera, AD, PN, QM, RF,
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ducto in rectis, AR, DF, quarum portiones extra cylindricum manen-
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tes ſint, PQ, NM, manifeſtum eſt etiam parallelogrammum, PM,
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quod extra cylindricum conſtituitur, & </
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<
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">quod integratur ex parallelo-
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grammis, AN, PM, QF, .</
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<
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">i. </
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">SI planum æquidiſtans plano perlatera cylindrici ducto
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tangat cylindricum, contactus fiet in recta linea, velre-
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ctis lineis, quæ erunt latera eiuſdem cylindrici: </
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<
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xml:space
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">Vel ſi tan-
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gat in plano, aut planis, plana contactus erunt parallelo-
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gramma, æquiangula perlatera ducto.</
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<
s
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">Sit cylindricus, AC, per cuius latera ducatur planum in eo pro-
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ducens parallelogrammum, AC, ſit autem ductum aliud plannm
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0042-01
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huic æquidiſtans, quod tangat cy-
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lindricum, AC. </
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tactum fieri in recta linea, vel rectis
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lineis, quę erunt latera cylindrici, A
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C, vel ſi tangat in plano, aut planis,
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plana contactus eſſe parallelogram-
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ma, æquiangula ipſi, AC. </
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igitur non tangat ipſum in plano,
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quia ergo tangit cylindricum, ali-
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quid ſuperficiei cylindrici commune
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eſt ipſi, & </
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ctus, O, exiſtens, & </
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te, & </
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">in ſuperficie cylindracea, & </
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per, O, ſit ductum latus cylindrici,
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quod ſit, EM. </
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<
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">Dico totum, EM,
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reperiri in plano tangente cylindri-
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cumin, O, ęquidiſtante ipſi, AC. </
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rallela, XR, quia ergo, XR, ęquidiſtatipſi, BC, & </
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