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

566. PROPOSITIO LXXXVII.

Tab. XXVI. fig. 10. Determinare momentum ex gravitate corpo-
ris Hyperbolici A B E, ejusque ſegmenti F A G. cujus baſis F G pa-
rallela eſt ad B E.

Momentum integri corporis Hyperbolici determinavimus in
Propoſitione LXXXV. ={a 4 cr+7a 3 bcr+12aabbcr. /24aa+120ab+144bb} Verum
nunc ſegmenti F A G momentum determinandum quoque erit: Vocetur A H, x, tum ex natura Hyperbolæ eſt D A X D L, ad
H A X H L: : B D q , H F q , ſive eſt aa+2ab, xx+2bx: : rr,
{rrxx+2bxrr: /aa+2ab} ut nunc peripheria deſcribenda a puncto F radii
H F habeatur, fiat r. c: : r {xx+2bx. /aa+2ab} c{xx+2bx. /aa+2ab}
ut ſoliditas obtineatur, multiplicanda hæc peripheria per radium,
& per{xx+3xb. /6x+12b} quod dat productum
{crx 4 +5bcrx 3 +6bbcx 3 /6aax+12abx+12aab+144abb} = ſoliditati ſegmenti F A G. & quoniam centrum gravitatis in axe H A diſtat a G F, quantitate
{xx+4xb. /4x+12b} per hanc quantitatem multiplicata ſoliditas dabit
productum{crx 6 +9bcrx 5 +26bbcrx 4 +24b 3 crx 3 /24aaxx+48abxx+120aabx+720abbx+144aabb+1728ab 3 . }
quod eſt æquale momento ſegmenti F A G.

567. PROPOSITIO LXXXVIII.

Tab. XXVI fig. 11. Sit Hyperbola AMB, & dimidium primi axis
A C, & dimidium axis conjugati C D, circa C D concipiatur circum-
volvi figura B A C D, quæritur ut determinetur momentum ſolidi
generati, & Cohærentia baſeos B D, affixæ parieti perpendiculari ad
borizontem.

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