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

CORPORUM FIRMORUM. ad horizontem perpendiculari, erit momentum gravitatis in ſolido
A T C K B, ad momentum gravitatis in ſegmento A O F M B, poſi-
tâ ſectione O F M parallela ad T C K, uti Cohærentia baſeos
T C K ad Cohærentiam baſeos O F M.

Vocetur C T, r. A T, a. O A, b. O F, {b br. /a a} C K, c. Eſt ſpatium
O F A = {1/3} O F X O A = {1/3} {b 3 r,/a a} & ſpatium T C A = {1/3} a r: adeo-
que ſoliditas O F M A B eſt = {b 3 c r. /3 a a} & ſoliditas T C K A B = {1/3} a r c. diſtantia autem centri gravitatis ab O F in plano O F A eſt = {3/10} A O. adeoque erit in corpore O F A M. a ſectione O F M remotum {3/10} A O. hinc momentum ſolidi O A B M F, erit = {b 4 c r. /10 a a} & momentum ſo-
lidi T C K A B ex gravitate erit = {a a r c. /10} Eſt autem Cohærentia
baſeos O F M = {b 4 r r c. /a 4 } & Cohærentia baſeos T C K = r r c: ordi-
nentur momenta gravitatis & Cohærentiæ in proportionem, erit
{b 4 c r. /10 a a} {b 4 r r c/a 4 }: : {a a r c. /10} r r c. multiplicando enim extrema & media per ſe habentur producta
utrimque æqualia. {b 4 c c r 3 /10 a a} = {a a b 4 c c r 3 . /10 a 4 } adeoque quantitates an-
tea fuerunt proportionales, unde momenta gravium ſunt inter
ſe veluti Cohærentiæ: hoc etiam alio modo demonſtravit Cl. Leibnitſius.

562. PROPOSITIO LXXXIII.

Tab. XXVI. fig. 8. Sit ſolidum B R S A a D C parallelopipedum
rectangulum, cujus latus B D C E ad horizontem perpendiculare: ſit ſolidum parabolicum A a B E R S ex priori abſciſſum, atque ver-
tex parabolæ in a & A, axes in a R, A S. ordinatæ B R, E S: tum
ſolidum reliquum B D C E a A baſi B D C E applicatum parieti per-

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