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

CORPORUM FIRMORUM ſit = x. deinde G D = d. F G = b. peripheria baſeos {cd/r}. pondus Q = q.

Erit ſoliditas Parabolicæ Conoidis A B C = {bcr/4} & momentum
ex gravitate = {bbcr/12}. & momentum ponderis P appenſi = b x. ita
quoque erit ſoliditas Conoidis D E F = {bcdd/4r}. & momentum ex
Gravitate = {bbcdd/12r}. atque momentum ponderis Q appenſi = bq. Cohærentia vero baſeos A B eſt = 8r 3 , & baſeos D E = 8d 3 : ſuppo-
nitur in Propoſitione {bbcdd/12r} + bq. 8d 3 : : {bbcr/12} + bx. 8r 3 . multiplicatis extremis & mediis per ſe, fit {8bbcddr 3 /12r} + 8bqr 3
= {8bbcd 3 r/12} + 8bd 3 x. & tranſponendo ac dividendo fit
{8bbcddr 3 /12r} + 8bqr 3 - {8bbcd 3 r/12}/8bd 3 } = x. ſive {bcrr/12d} + {qr 3 /d 3 } - {bcr/12}. = x.

545.PROPOSITIO LXVI.

Tab XXVI fig. 2. Data Conoide Parabolica A B C, datoque
pondere P, cujus momentum ſimul cum momento ponderis dati ſolidi
ad Cobærentiam ejuſdem ſolidi, quamlibet babeat proportionem,
ſuper data baſi aliam Conoidem Parabolicam conſtruere, cujus
tione.

Ponatur F B = r. peripheria = c. F C = a. pondus appenſum = p. baſeos datæ radius = b. peripheria baſeos datæ = {bc/r}. longitudo
quæſita = x.

Erit ſolidum A B C = {acr/4}. ejuſque momentum oriundum ex gra-

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