Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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echoid-s1985
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LIBERI.
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ZX. </
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<
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echoid-s1986
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">Dico hanc tangere dicta ſolida, ſi enim non tangit ſecet, ve-
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luti, D2N, in puncto, N, igitur punctus. </
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<
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echoid-s1987
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xml:space
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">n. </
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<
s
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echoid-s1988
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xml:space
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">erit extra planum figu-
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ræper axem, nam ipſa, D2N, eſt parallela ipſi, ZX, quæ eſt ad
<
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rectos angulos figuræ per axem tranſeunti, & </
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<
s
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echoid-s1989
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xml:space
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">ideò etiam, D2N,
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xml:space
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">8. Vndec.
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Elem.</
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eſt illi ad rectos angulos, occurrit autem illi in puncto, 2, ergo non
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occurret illi in alio puncto, ergo, N, eſt extra planum figuræ per a-
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xem, ducatur per, N, planum æquidiſtans plano, PXRZ, circuli,
<
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">34. huius.</
note
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quod producat circulum, BNFC, & </
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<
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echoid-s1990
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">ſit, BF, communisſectio ip-
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ſius circuli, & </
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<
s
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echoid-s1991
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">figuræ per axem, quæ erit ipſius circuli diameter, &</
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echoid-s1992
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">,
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">Corol. 34
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huius.</
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N, non erit aliquis punctorum, BF, ergo ſi ab, N, duxerimus ipſi,
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ZX, parallelam, vt, NC, cum etiam, BF, ſit parallela ipſi, PR,
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continebunt angulos æquales, ſed, ZX, ſecat perpendiculariter, P
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<
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">10. Vnd.
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R, ergo, NC, ſecabit perpendiculariter, BF, ducta non ab extre-
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mitate diametri, ergo intra circulum, BCFN, erit, & </
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<
s
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echoid-s1993
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xml:space
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">bifariam ſe-
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cabitur ab ipſa, BF, ergo non tranſibit per circuitum figuræ per a-
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xem ductæ, & </
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<
s
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echoid-s1994
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xml:space
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preserve
">per ipſum tranſit, D2N, ergo, NC, N2D, ſunt
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duæ rectæ lineæ eidem, ZX, parallelę, ergo etiam inter ſe erunt pa-
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rallelæ, quod eſt abſurdum, cum tranſeant per idem punctum, N,
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ergo ducta per punctum ambitus figuræ per axem parallela ipſi, ZX,
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tanget dicta ſolida: </
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<
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echoid-s1995
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">Sit nobis nunc punctus, N, pro puncto vtcung;
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</
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<
s
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echoid-s1996
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">in ſuperficie ambiente ſumpto extra circuitum figuræ per axem, à
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quo ducta ipſi, ZX, parallela, occurrat producta ſuperficiei ambienti
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in puncto, C, oſtendemus ergo eodem modo ſupra adhibito (poſt-
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quam duxerimus per, N, planum circulo, PXRZ, æquidiſtans,
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quod in ſolido producat circulum, BNFC,) ipſam, NC, intra cir-
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culum, BNFC, cadere, & </
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<
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echoid-s1997
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">bifariam diuidi à recta, BF, ſiue à figu@a
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per axem ducta (nam eſt, NC, perpendicularis ipſi, BF,) quod o-
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ſtendere opus erat.</
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<
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echoid-s1998
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<
head
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<
s
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echoid-s1999
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">SI ſolidum rotundum, vel conus ſcalenus, ſecentur plano
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per axem, & </
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<
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echoid-s2000
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">deinde alio plano ſecentur, cuius, & </
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<
s
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echoid-s2001
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">vnius
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planorum rectè axem ſecantium communis ſectio ſit recta li-
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nea perpendicularis communi ſectioni eiuſdem, & </
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<
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echoid-s2002
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">plani per
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axem; </
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<
s
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echoid-s2003
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">figura à ſecundo ſecante plano in ſolido producta erit
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circa axem, in cono ſcaleno autem erit circa axem, vel dia-
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metrum, & </
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<
s
xml:id
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echoid-s2004
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xml:space
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preserve
">axis, vel diameter erit communis ſectio per dicta
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ſecantia plana productarum figurarum.</
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<
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echoid-s2005
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