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

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10989LIBER I. de conſtituta conoides, & ſphæroides, in quibus planis per eorum
axes ductis, productæ ſint figuræ iam dictæ, ſecentur deinde planis
ad axem obliquis, ſed erectis ad dictas figuras, & ſint eadem plana
deſcriptarum ellipſium dicta ſolida ſecantia, erunt ergo ex his ſecan-
tibus planis conceptæ in ipſis figuræ pariter ellipſes, quarum diame-
trierunt, BD, quidem prima, ſecunda autem in ſpha roide æqualis
ductæ à puncto, B, parallelæ tangenti ellipſim in, S, interiectæ in-
ter ipſam, BD, & ductam à puncto, D, parallelam iungenti pun-
cta, S, A, (in cęteris autem ſolidis eadem ſuo modo verificabuntun)
1144. huius. ergo in ſphæroide ipſa, BD, eſt prima diameter dictæ ellipſis, quæ
à dicto ſecante plano producitur, & eſt etiam prima diameter ellipſis,
quę deſcribitur modo ſupradicto, ſunt autem ſecundę diametri vtriuſ-
que ellipſis ęquales, immo communes, quia ad rectos angulos ſecant
ipſam, BD, ergo habemus in eodem plano duas ellipſes circa ea-
ſdem diametros coniugatas, ergo neceſſario erunt congruentes, ſed
linea ellipſis, quę eſt communis ſectio dicti plani, & ſuperſiciei ſphe-
22Elicietur
ex Corol.
25. huius. roidis eſt in ſuperficie ſphæroidis, ergo, & linea ellipſis vt ſupra de-
ſcriptæ erit in ſuperficie dicti ſphæroidis. Eodem modo idem de cæ-
teris ellipſibus ſimiliter deſcriptis demonſtrabimus tum in ſphæroide,
tum etiam in conoidibus parabolicis, & hyperbolicis, quę oſtendere
opus erat.

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