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

CORPORUM FIRMORUM. erecta ſit perpendicularis P A, ſitque P quædam particula attracta ab
omnibus circuli partibus; â P ad quodcunque punctum radii A D,
ducatur recta P E, in recta P A ducatur P F = P E, ex F ducatur
F K parallela ad A D, quæ repræſentet vires, quibus punctum E at-
trahit particulam P, ſitque I K L curva linea, quam punctum K
perpetuo tangit: Occurrat eadem circuli plano in L. in P A capia-
tur P H æqualis P D, & erigatur perpendiculum H I cur væ oc-
currens in I. demonſtravit Newtonus Lib. 1. prop. 90. Princ. Philoſ. corpuſculi P attractionem eſſe, ut area A H I L. eſt ducta in alti-
tudinem A P.

Vocetur P F x. F K y, & ſit F K, vel vis quâ punctum E
attrahit corpus P, reciproce ut aliqua potentia ipſius P F, ſit
hæc n. tum æquatio curvæ erit y = {1/X n } & area A H I K L uti
{1/PA n - 1 } - {1/PH n - 1 } unde attractio corpuſculi P in circulum erit
ut {1/PA n - 2 } - {PA/PH n - 1 }.

Hæc Cl. Chynæus in Philoſophical Principles of Natural reli-
gion eleganter explicuit §. 44. Si n = i, & P A = 0. tum radius cir-
culi attrahentis productus coincidet cum Aſy mptoto P O, in quo
caſu area A H I L erit infinita, cum curva ſit Hyperbola vulgaris; & P A = 0, ſive evaneſcente intervallo inter particulam & circu-
lum attrahentem, erit attractio = P A X A H I L = 0 X ? = i.

Si n = 1, & P A = ? , hoc eſt quando planum attrahens A D
poſitum eſt ad concurſum Hyperbolæ, cum ſuâ Aſymptoto P H,
tum arcus D H, cujus centrum eſt P, & cujus radius eſt P D = P A
= ? , coincidet cum A D, & ideo A L coincidet cum H I, unde
P A X A H I L = ? X 0 = i.

Si n = i. & P A = a tum A H vocetur y, & P H = x = a + y,
unde corpuſculum P a circulo attrahetur vi = P A X A H I L =
{y-yy/2a} + {y 3 /3aa} - {y 4 /4a 3 } & c.

Si n = 2 & P A = 0. tum area A H I L erit plus quam infinita,
unde attractio erit A P X A H I L = 0 multiplicato per pluſquam
infinitum, unde liquet attractionem in hoc caſu, poſito P A = 0.

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