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

INTRODUCTIO AD COHÆRENTIAM momentum = arxx. quod ponatur æquale momento dimidiati
cylindri { 2 /3} ar 3 . utraque quantitate diviſa per ar, remanet {2/3} rr = xx. unde {2/3} r. x: : x. r. cum igitur A O ſit = x, mediæ proportionali
inter {2/3} r & r. habebit parallelopipedum A B C K O idem momentum
gravitatis, quod dimidiatus cylindrus.

Corol. 3. Si, adb, fuerit chorda circuli, cujus arcus, a E b, vo-
cetur {p/e}, & chorda, a d b = c. etiam cognoſcetur ſinus verſus
dE, qui ſit = k. ductis rectis D b, Da, erit Sector circuli D b E a
= {pr/2e}. ſed Triangulum D b a, eſt {1/2} cr - {1/2} ck, quo ſubducto ex Se-
ctore {pr/2e}, remanet area, a d b E a = {pr/2e}-{ 1 /2} cr + {1/2} ck, quæ
multiplicata per B C = a, dabitSolidum a d b fe a = {apr/2e}+{1/2}ack-{1/2}acr. Centrum vero gravitatis in Segmento b Ead, diſtat a centro D, in recta
D E = {cek. /3p-3ce} adeoque cum Dd ſit = r-k, diſtabit â d quan-
titate {cek/3p+3ce}-r+k, quæ diſtantia ducta in magnitudinem ab d E e f,
dabitmomentum ex gravitate ={apr/2e}+{1/2}ack-{1/2}acrX{cek/3p-3ce}
{/-r+k. }

534. PROPOSITIO LV.

Tab. XXV. fig. 10. Sit parallelopipedum, conſideratum abſque
gravitate, ope diagonalis bifariam ſectum in duo priſmata, quo-
rum unum ſit C A B M N, cujus latus unum A M horizonti paral-
lelum ponatur, baſis C A B muro, ad horizontem perpendiculari,
affixa, pondus, æquabiliter ſupra latus A M diſper ſum, habebit ad
Cohærentiam baſeos A B C eandem rationem, quam pondus incum-
bens parti a M, habet ad Cobærentiam ſuæ baſeos, abc, ubicunque
baſis, abc, ponatur.

Concipiatur fluidum grave æquabiliter impoſitum plano A M ad

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