# 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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