Angeli, Stefano degli - Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna

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177165 conos eſſe in E, diuidente bifariam A D. De ex-
ceſſu conoideorum ſupra conos, patuit in ſcholio
propoſit. 6. De exceſſu portionis ſphæræ, vel ſphæ-
roidis patuit in anteced propoſit. Quare quoadom-
nia patet propoſitum.

PROPOSITIO XLVII.

Si in ſolidis antecedentis propoſitionis inſcribantur coni vt
dictum eſt, & ſect s diametris ipſorum bifariam ordi-
natim applicentur lineœ, ſecantes latus conorum inſcri-
ptorum. Diametri prœdictorum ſolidorum, & etiam
coni, ſic ſecabuntur ab ipſorum centris grauitatis, vt
partes terminatœ ad verticem ſint ad partes terminatas
ad baſim vt quadratum ordinatim applicatœ, vna cum
duobus quadratis ductœ in conis, ad quadratum ordi-
natim applicatœ.

SInt ergo ſolida vt in antecedenti propoſitione, &
inſuper etiam conus, vt in quarta figura BAC,
quorum diametri A D, ſint ſectæ bifariamin E, &
ord natim applicentur E G F, ſitque horum cen-
trum grauitatis punctum O. Dico A O, eſſe ad
O D, vt quadratum F E, cum duobus quadratis
G E, ad quadratum F E. In cono res eſt manifeſta,
quia ſicuti A O, eſt tripla O D, ſic tria quadrata
G E, ſunt tripla vnius quadrati G E. In alijs ſic
patebit. Fiat D P, quarta pars D A. Ergo P,
erit centrum grauitatis conorum. Cum ergo ex

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