Full text: Musschenbroek, Petrus: Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes

564. De Corporibus Hyperbolicis.
PROPOSITIO LXXXV.

Tab. XXVI. fig. 10. Corporis Hyperbolici generati ex circum-
gyrata Hyperbola A B D circa axin A D, cujus baſis E D B eſt pa-
rieti perpendiculari ad horizontem affixa, determinare momentum
ex gravitate, & Cohærentiam baſeos B D E reſpectivam.

Vocetur A D, a. & axis Hyperbolæ primus A L, 2 b. B D radius
baſeos, r. circumferentia circuli a puncto B deſ [?] cripti, c. tum erue-
tur ſoliditas corporis Hyperbolici = {a a c r + 3 a b c r. /6 a + 12 b} Centri
gravitatis in axe A D diſtantia â puncto D eſt = {a a + 4 a b. /4 a + 12 b}
Soliditate igitur per hanc diſtantiam â D multiplicata, habebitur
momentum corporis Hyperbolici
{a 4 c r + 7 a 3 b c r + 12 a a b b c r. /24 a a + 120 a b + 144 b b}
Cohærentia autem baſeos eſt = 8 r 3 .

565. PROPOSITIO LXXXVI.

Tab. XXVI. fig. 10. Corporis Hyperbolici A B E Cohærentia, eſt
ad Cohærentiam ſegmenti F A G, in ratione compoſita ex D A X
D L X B E. ad H A X H L X G F.

A L ſupponitur axis Hyperbolæ primus, ponatur pondus I pen-
dens ex vertice Hyperbolæ A B E eſſe ſummum, quod appendi poſ-
ſit, adeoque æquale Cohærentiæ baſeos B D E. & pondus K pen-
dens ex vertice ſegmenti F A G etiam ſummum, ſeu æquale Co-
hærentiæ baſeos F G, tum pondus I eſt ad pondus K in ratione
Cubi B E ad Cubum F G, ſive B E q X B E ad F G X F G. ſed eſt
B E ad F G q ex natura Hyperbolæ, uti D A X D L ad H A
X H L. adeoque his loco quadratorum poſitis, erit pondus I ad pon-
dus K, uti D A X D L X B E, ad H A X H L X F G.

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