623606INTRODUCTIO AD COHÆRENTIAM
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.
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. ={a4cr+7a3bcr+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 Dq, H Fq, 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
{crx4+5bcrx3+6bbcx3/6aax+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{crx6+9bcrx5+26bbcrx4+24b3crx3/24aaxx+48abxx+120aabx+720abbx+144aabb+1728ab3. }
quod eſt æquale momento ſegmenti F A G.
Propoſitione LXXXV. ={a4cr+7a3bcr+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 Dq, H Fq, 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
{crx4+5bcrx3+6bbcx3/6aax+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{crx6+9bcrx5+26bbcrx4+24b3crx3/24aaxx+48abxx+120aabx+720abbx+144aabb+1728ab3. }
quod eſt æquale momento ſegmenti F A G.
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.
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.
zoom in
zoom out
zoom area
full page
page width
set mark
remove mark
get reference
digilib