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

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10787LIBERI.

THEOREMA XLII. PROPOS. XLV.

SI ſphæroides, vel conoides parabolicum, ſeu hyperboli-
cum ſecentur quomodocumq; planis parallelis ad axem
rectis, ſiue inclinatis, communes ſectiones ſimiles erunt, &
diametri eiuſdem rationis erunt omnes in eadem figura per
axem tranſeunte, rectè eaſdem ſecante.

Hæc colliguntur in Coroll. 2. Prop. 15. lib. Arch. de Conoidibus,
& Sphæroidibus, & ibidem etiam à Federico Commandino in ſuis in
Arch. Comment. demonſtrantur. Hęc verò circa ipſas ſectionum fi-
guras verificari pariter manifeſtum eſt, hoc autem dico, vtor enim
ijſdem ſectionum nominibus tamquam figuras ſub ipſis comprehen-
fas ſignificantibus.

THEOREMA XLIII. PROPOS. XLVI.

EXpoſitis prædictis coni ſectionibus, circulo nempè, El-
lipſi, Parabola, & Hyperbola, ſi, quę ad earundem axes
ordinatim applicantur, diametri eſſe intelligantur circulo-
rum ab ipſis deſcriptorum, qui ſint erecti pianis ipſarum figu-
rarum, periphærię deſcriptorum circulorum in ſectione, quę
eſt circulus, erunt omnes in ſuperficie ſphęrę, in Ellipſi verò
in ſuperficie ſphæroidis, in Parab. in ſuperficie conoidis pa-
rabolici, & in Hyperbola in ſuperficie conoidis Hyperbolici.

Sint prædictę ſectiones figurę

60[Figure 60] ſcilicet, ipſæ, ABCD, earum
axes, AC, vna ex ordinatim ad
axim applicatis, BD, quæ in-
telligatur eſſe diameter ab ea
deſcripti circuli, BNDE. Di-
co circumferentiam, BNDE,
eſſe in dicta ſuperficie. Intelli-
gantur dictę figuræ reuolui circa
ſuos axes, vt ex circulo fiat ſphę-
ra, ex ellipſi ſphæroides, ex pa-
rabola conoides parabolicum,
& ex hyperbola hyperbolicum,
ſecentur autem planis ad axem
rectis, eundem axem ſecantibus in eodem puncto, in quo

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