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

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10686GEOMETRIE dem ſecantis figuram, & alterius acti per axem recto ad pla-
num ſecans. Archim. ibid. Propoſ. 14.

THEOREMA XLI. PROPOS. XLIV.

SI ſphæroides plano ſecetur non recto ad axem, ſectio erit
ellipſis, diameter verò ipſius maior erit concepta in ſphę-
roide ſectio duorum planorum, eius ſcilicet, quod ſecat figu-
ram, & eius, quod ducitur per axem recto ad planum ſecans.
Arch. ibid. Propoſ. 15.

Minor verò diameter ſic habetur. Sit Sphæroides, vel conoides
hyperbolicum, BDMF, axis, BM, centrum, A, ellipſis verò per

59[Figure 59] axem tranſiens in
ſphæroide, BDM
F, in conoide verò
hyperbola, NCO.
Secetur autem ſphę-
roides, vel conoides
plano non recto ad
axem, ſed erecto fi-
guræ, BDMF, ex
quo fiat in ipſis ſe-
ctio, DF, hæc erit
ellipſis, cuius maior
diameter, DF. In-
ueniatur nunc ver-
tex ellipſis, ſeu hy-
perbolæ, BDMF,
reſpectu ipſius, DF, qui ſit, C, & iungatur, CB, ac per, B, aga-
tur, BG, tangens in, B, ipſam ellipſim, ſeu hyperbolam, tandem à
puncto, D, parallela ipſi, BG, & à puncto, F, parallela ipſi, CB,
produc antur, DE, FE, quæ inuicem concurrent vt in, E. Dico
igitur, quod erit, ED, minor diameter eiuſdem ellipſis, DF.

Hoc autem demonſtrat ibid. Dauid Riualtus in Commentarijs in
Archim. ad Propoſ. 14. & 15.

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