Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
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<
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">DEſiderari tantum videtur huius euidentia, quod ſcilicet planum
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inter oppoſita tangentia plana eiſdem a quidiſtanter ductum
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tranſeat perlatera cylindrici, quod aſſumpra eiuſdem figura nunc
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0047-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0047-01
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fiet manifeſtum; </
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<
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tur ergo in ambitu vtriuſuis
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oppoſitarum baſium cylin-
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drici, PN, ſumptum pun-
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ctum, vt, O, in ambitu fi-
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guræ, ZON. </
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<
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">Dico pla-
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num, quod tranſit per, O,
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æquidiſtans planis tangen-
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tibus, AG, VL, tranſire
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per latera cylindrici, PN.
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</
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<
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">Ducatur ergo à puncto, O,
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latus cylindrici, PO, & </
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<
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">ab
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eodem pundo, O, in baſi,
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ZON, recta, ON, paral-
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lela ipſi, XL, igitur pla-
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num, quod tranſit per, P
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O, ON, æquidiſtat plano,
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<
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">15. Vnde-
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cimi Ele.</
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VL, nam, PO, ipſi, VX,
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lateri cylindrici, &</
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<
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">, ON,
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ipſi, XL, ęquidiſtat, quod
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ergo ducitur per, O, eidem plano tangenti æquidiſtans tranſit per
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ipſas, PO, ON, ſi. </
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<
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">n. </
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<
s
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">non, erunt duo plana eidem plano, VL,
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æquidiſtantia, & </
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<
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">ideò inter ſe æquidiſtantia, quibus communis erit
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punctus, O, igitur in eo concurrent, quod eſt abſurdum, non ergo
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illa ſunt duo plana, ſed vnum tantum, illud nempè, quod ducitur
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per punctum, O, ipſi plano, VL, æquidiſtans, tranſitque per, P
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O, ON, neceſſariò: </
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<
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">Siverò à punctis, I, M, N, erigantur latera
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cylindrici, CI, ME, NK, erunt cuncta in plano per, PO, ON,
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tranſeunte, ergo planum, quod ducitur per punctum, O, æquidi-
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ſtans plano, VL, cylindricum tangenti tranſit per latera, PO, CI,
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EM, KN, quod oſtendendum erat.</
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<
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ductis, eiuſdem oppoſitę baſes in figuras ſimiles, ęqua-
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les, & </
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<
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