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
ponderis momentum ad ſuam Cobærentiam ſit in eadem propor-
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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