Cavalieri, Buonaventura
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Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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Dico, RO, eſſe parallelam lateri cylindrici, FG. </
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mi Elem.
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p. 16. Vn-
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dec. Elem.
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10. Vnde-
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cimi Ele.</
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MN, quoniam ergo, CE, MN, coniungunt extrema laterum cy
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0041-01
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lindrici, CM, EN, quæ ſunt æqualia, & </
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parallela, erunt & </
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">ipſæ æquales, & </
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læ, ſunt etiam parallelę ipſæ, CR, MO, er-
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goangulus, ECR, erit æqualis angulo, N
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MO, eodem pacto oſtendemus angulum, C
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ER, eſſe æqualem angulo, MNO, vnde
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<
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Elem.</
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etiam, CR, MO, erunt æquales, & </
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<
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rallelæ, ergo eas iungentes, quæ ſunt, RO,
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CM, erunt ęquales, & </
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<
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">parallelę, eſt autem,
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CM, latus cylindrici, FG, ergo, RO, com-
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munis ſectio duorum planorum dictum cy-
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lindricum ſecantium, erit eiuſdem lateribus
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parallela. </
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">Idem oſtendemus, ſi ſectio contingat fieri intra cylindri
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cum, ſiautem fiat in ſuperficie, patet non poſſe fieri, niſi in latere
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cylindrici, nam plana ſecantia ducuntur per latera, quodfibet autem
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latus eſt cęteris eiuſdem cylindrici lateribus æquidiſtans, & </
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cumq; </
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perlatera cylindrici ductorum ſe inuicem ſecantium, eſt parallela la-
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teribus cylindrici. </
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oſtendendum.</
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ductis conceptæ in cylindrico figuræ erunt parallelo-
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gramma æquiangula.</
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parallelis per latera ductis, ſit autem vnius
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in cylindrico, AF, concepta figuræ paral-
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lelogrammum, BH, alterius autem paral-
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lelogramma, AN, QF. </
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ęquiangula, quod enim ſint parallelogram-
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huius.</
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ma, patet, quia plana ſecantia ducuntur per
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latera, quod verò fint æquiangula patet e-
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tiam, nam in parallelogrammo, AN, la-
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tus, AD, æquidiſtat lateri, BO, &</
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ipſi, BC, nam ſunt communes fectiones pla-
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ni, ABCR, & </
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AN, BH, & </
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cimi Ele.</
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tur angulo, CBO, ergo parallelogramma, AN, BH, erunt </
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