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

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10888GEOMETRI Æ circulus eum ſecat, producetur ergo ab hoc ſecante plano in ipſis ſo-
lidis circulus centrum in axehabens, cuius diameter erit, BD, ha-
1134. huius. bemus igitur duos circulos in eodem plano, circa eandem diametrum,
22Corol. 34
huius. ergo illi erunt congruentes, periphæria autem circuli dicto ſecante
plano in dicto ſolido producti eſt in ſuperficie ambiente dictum ſoli-
dum, ergo, & periphęria circuli, BNDE, deſcripti, vt dictum eſt,
erit in tali ſuperficie, ſcilicet in ſuperficie ſphæræ in figura circuli,
ſphæroidis in figura ellipſis, conoidis parabolici in figura parabolæ,
& hyperbolici in figura hyperbolę, idem oſtendemus de alijs quibuſ-
cumque ſic deſcriptis circulis ab ordinatim applicatis ad dictos axes
tanquam à diametris, qui ſint erecti eiſdem ſectionibus, igitur quod
proponebatur demonſtratum fuit.

THEOREMA XLIV. PROPOS. XLVII.

INFRASCRIPTIS poſitis, eadem adhuc ſequi oſten-
demus.

Ijſdem enim expoſitis figuris, præter circulum, ſupponamus ip-
fam, AC, non eſſe axem, ſed diametrum, & ad ipſam ordinatim ap-
plicari vtcumque, BD, intelligatur autem, BD, diameter cuiuſdam
ellipſis ab eadem deſcriptæ, quæ ſit erecta plano propoſitæ figuræ,
ſit autem, in figura ellipſis, deſcriptæ ellipſis ſecunda diameter per-
pendicularis ipſi, BD, & æqualis ductæ à puncto, B, parallelę tan-

61[Figure 61] genti ellipſim, ABCD, in ex-
tremitate eiuſdem axis (quæ
tangat in, S,) interiectæ in-
ter, BD, & eam, quę ducitur
3344. huius. à puncto, D, parallela iun-
genti puncta, S, A. In figura
verò hyperbolæ ſit ſecunda
diameter perpendicularis, BD,
& æqualis ei, quæ ducitur à
puncto, D, parallela tangenti
hyperbolam in extremitate a-
xis (vt in, S,) interiectæ in-
ter, BD, & eam, quę ducitur
à puncto, B, parallela iungenti
puncta, S, A, & tandem in párabola ſit ſecunda diameter perpendi-
cularis quoque ipſi, BD, & æqualis diſtantiæ parallelarum eiuſdem
4442. huius. axi, quę ducuntur ab extremitatibus ip ſius, B, D. Intelligantur

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