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.

COROLLARIVM.

_H_Inc patet propoſito aliquo ex ſupradictis ſolidis, eoq; ſecto planis
vtcumque parallelis ad axem rectis, ſiue obliquis figuras, quæ ex
ſectione planorum in ipſis ſolidis producuntur, eaſdem eſſe illis, quæ de-
ſcribuntur lineis rectis, tamquam homologis diametris, & primis, ĳs,
inquam, quæ-ſunt communes ſectiones dictarum æquidiſtantium figura-
rum, & figuræ, quæ produceretur ducto plano per axem rectè eas ſecan-
te, quæ deſcribentes eſſent, quæ ondinatim applicantur ad axes, vel dia-
metros dictarum figurarum, ſecundis autem diametris deſcriptarum fi-
gurarum exiſtentibus, ĳs, quæ ſupradictæ ſunt, prout poſtul at varietas
ſolidorum, iuxta Prop. 42. 43. & 44. huius.

SCHOLIVM.

_A_Duerte tamen licet ſupra vocentur diametri, quæ dictas figuras de-
ſcribunt, deberetamen intelligi ſemper eſſe axes deſeriptarum fi-
gurarum, cum . n. nomen diametri ſit commune diametro, & axi, @li-
quando vice axis vtimur nomine diametri, vt in circulo apparet, cuius
tamen omnes diametri ſunt axes: Inſuper ſciendum eſt etiam, quæ

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