Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

poſitio vniuerſalis in qualibet portione parabolæ
quadraticæ.

98. PROPOSITIO XLVIII.

Si in quacunque portione parabolœ quadraticœ reſectœ linea
diametro parallela inſcribatur triangulum, & baſis por-
tionts parabolœ ſecetur bifariam, & per punctum biſſe-
ctionis ducatur parallela diametro. Centrum œquilibrij
ſecundum baſim prœdictœ portionis ſic ſecabit baſim,
vt pars ad curuam terminata ſit ad reliquam, vt pa-
rallela diametro ducta à puncto biſſectionis, vna cum tn-
tercepta inter punctum bißectionis, & latus trianguli,
ad prœdictam parallelam diametro.

ESto parabola A B C, quadratica, cuius baſis
A C, diameter B D, & ſit quælibet eius por-
tio E F B C, reſecta F E, diametro B D, paralle-
la, & in portione ſit in ſciiptum triangulum CFE; ſit-
que C E, ſecta bifariam in G, & per G, ducatur
GIH, parallela diametro, ſitque K, centrum æ-
quilibrij in baſi portionis E F B C. Dico C k, eſſe
ad k E, vt H G, cum G I, ad H I. In tertia figura
ſchematis anteced. propoſ. intelligatur portio ſphæ-
ræ, vel ſphæroidis B A C, proportionalis E F B C,
portioni parabolæ, & intelligantur in ea omnia,
quæ ſupra, Ergo C K, erit ad k E, in portione pa-
rabolæ, vt A O, ad O D, in portione ſphæræ; nem-
pe ex propoſit. anteced. vt duplum quadratum G E,

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