Cavalieri, Buonaventura - Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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9777LIBER I. E, ED, erunt æquales, eodem pacto oſtendemus quaſcumque du-
ctas à puncto, E, ad lineam ambientem, MBND, eſſe æquales
cuilibet ipſarum, BE, EN, ED, EM, ergo figura, MBND, erit
circulus, cuius centrum, E, in axe reperitur, quod erat oſtendendum.

COROLLARIVM.

_C_olligimus autem ipſas, BD, MN, communes ſectiones figurã-
rum per axem ductarum, & circulorum, qui per ſectionem dicti
ſolidi per plana ad axem recta in eo produsuntur, eſſe eorum diametros,
cum per centrum tranſeant.

THEOREMA XXXII. PROPOS. XXXV.

SI quicunq; conus ſecetur plano baſi æquidiſtante conce-
pta in cono figura erit circulus centrum in axe habens.

Si conus ſit rectus patet hoc ex antecedenti Propoſ. cæterum ſi ſit
ſcalenus, qualis ſit conus, ACFD, qui ſecetur plano baſi, CFD,
æquidiſtante, quod in eo producat figuram, BRE. Dico ipſam eſſe
circulum, centrum in axe habentem. Secetur ergo plano per axem,
1116. huius. quod in eo producat triangulum, ACD, cuius & circuli, CFD,
communis ſectio ſit, CD, quę erit diameter dicti circuli; eius autem
& figuræ, BRE, communis ſectio, BE; ſunt igitur trianguli, AB
224. Sex. El. l, ACN, ſimiles, quia, BI, ęquidiſtat ipſi, C
N, ergo, CN, ad, NA, erit vt, BI, ad, IA,

53[Figure 53] eodem modo oſtendemus, AN, ad, ND, eſſe
vt, BI, ad, IE, ergo, ex æquo, CN, ad, N
D, erit vt, BI, ad, IE, ſed, CN, eſt ęqualis,
ND, ergo & , BI, ipſi, IE. Ducatur nunc
aliud planum per axem, quod producat trian-
gulum, ANF, quodq; ſecet figuram, BRE,
in, IR, fient ergo trianguli, AIR, ANF, æ-
quianguli, ergo, FN, NA, NC, erunt lineæ
in eadem proportione cum ipſis, RI, IA, IB,
ergo, ex ęquo, FN, ad, NC, erit vt, RI, ad,
IB, ſed, FN, eſt æqualis ipſi, NC, ergo, R
I, erit æqualis ipſi, IB, eodem modo oſtende
mus quaſcunque ductas à puncto, I, ad lineam ambientem, BRE,
eſſe æquales ipſi, BI, ergo figura, BRE, erit circulus, cuius, cen-
trum, I, quod oſtendere oportebat.

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