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

CORPORUM FIRMORUM. unde eruitur x = {cddrr/aacr + 12ap}

## 547.PROPOSITIO LXVIII.

Tab. XXVI. fig I. Data Conoide Parabolica D B E, datoque
pondere appenſo P, cujus momentum ſimul cum momento Conoidis
ex gravitate, ad momentum Cobærentiæ ejuſdem ſolidi quamlibet
babeat rationem; Conoidem datam ita producere in F, ut ejus pon-

Ponatur G D radius = r. peripheria circuli baſeos = c. G B = a. pondus P = p. B F quæſita = x. erit C F radius baſeos = {rrx/a}. & peripheria circuli baſeos = c {x/a}.

Eſt ſolidum DBE = {acr/4}. ejus momentum ex gravitate = {aacr/12}. & momentum ponderis P = ap. Cohærentia = 8r 3 . Eſt autem
ſolidum A B C = {1/4} crx{x/a}, ejusque momentum {crxx/12}{x/a}. & Cohæ-
rentia = 8 {r 6 x 3 /a 3 }. Quia igitur ambo momenta Conoidum ad ſuas
Cohærentias ſupponuntur eſſe in eadem ratione, erit {aacr/12} + ap. 8r 3 : : {crxx/12} {x. /a}. {8r 3 x/a} {x/a}.

Quorum extremis mediisque terminis per ſe multiplicatis, at-
que diviſione facta per 8 {x/a}. fit {cr 4 xx/12} = {aacr 4 x/12a} + {apr 3 x/a}. & inſtituta diviſione per {cr 4 /12}. fit
x x = ax + 12{px/cr}. unde per tranſpoſitionem.

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