Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER I.
"/>
de conſtituta conoides, & </
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<
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xml:space
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">ſphæroides, in quibus planis per eorum
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axes ductis, productæ ſint figuræ iam dictæ, ſecentur deinde planis
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ad axem obliquis, ſed erectis ad dictas figuras, & </
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<
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xml:space
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deſcriptarum ellipſium dicta ſolida ſecantia, erunt ergo ex his ſecan-
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tibus planis conceptæ in ipſis figuræ pariter ellipſes, quarum diame-
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trierunt, BD, quidem prima, ſecunda autem in ſpha roide æqualis
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ductæ à puncto, B, parallelæ tangenti ellipſim in, S, interiectæ in-
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ter ipſam, BD, & </
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<
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xml:space
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">ductam à puncto, D, parallelam iungenti pun-
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cta, S, A, (in cęteris autem ſolidis eadem ſuo modo verificabuntun)
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note
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ergo in ſphæroide ipſa, BD, eſt prima diameter dictæ ellipſis, quæ
<
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à dicto ſecante plano producitur, & </
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<
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xml:space
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">eſt etiam prima diameter ellipſis,
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quę deſcribitur modo ſupradicto, ſunt autem ſecundę diametri vtriuſ-
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que ellipſis ęquales, immo communes, quia ad rectos angulos ſecant
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ipſam, BD, ergo habemus in eodem plano duas ellipſes circa ea-
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ſdem diametros coniugatas, ergo neceſſario erunt congruentes, ſed
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linea ellipſis, quę eſt communis ſectio dicti plani, & </
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<
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xml:space
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ex Corol.
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25. huius.</
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roidis eſt in ſuperficie ſphæroidis, ergo, & </
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<
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ſcriptæ erit in ſuperficie dicti ſphæroidis. </
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<
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xml:space
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">Eodem modo idem de cæ-
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teris ellipſibus ſimiliter deſcriptis demonſtrabimus tum in ſphæroide,
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tum etiam in conoidibus parabolicis, & </
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<
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opus erat.</
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">_H_Inc patet propoſito aliquo ex ſupradictis ſolidis, eoq; </
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<
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vtcumque parallelis ad axem rectis, ſiue obliquis figuras, quæ ex
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ſectione planorum in ipſis ſolidis producuntur, eaſdem eſſe illis, quæ de-
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ſcribuntur lineis rectis, tamquam homologis diametris, & </
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<
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inquam, quæ-ſunt communes ſectiones dictarum æquidiſtantium figura-
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rum, & </
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<
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">figuræ, quæ produceretur ducto plano per axem rectè eas ſecan-
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te, quæ deſcribentes eſſent, quæ ondinatim applicantur ad axes, vel dia-
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metros dictarum figurarum, ſecundis autem diametris deſcriptarum fi-
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gurarum exiſtentibus, ijs, quæ ſupradictæ ſunt, prout poſtul at varietas
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ſolidorum, iuxta Prop.</
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<
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">_A_Duerte tamen licet ſupra vocentur diametri, quæ dictas figuras de-
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ſcribunt, deberetamen intelligi ſemper eſſe axes deſeriptarum fi-
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gurarum, cum .</
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quando vice axis vtimur nomine diametri, vt in circulo apparet, cuius
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tamen omnes diametri ſunt axes: </
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