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

INTRODUCTIO AD COHÆRENTIAM vitate = {aacr/12}. momentum ponderis = ap. Cohærentia = 8r 3 . ſed Conoidis quæſitæ ſoliditas erit = {bbcx/4r}. ejuſque momentum
= {bbcxx/12r}. & Cohærentia = 8b 3 . ponitur in Propoſitione
{aacr/12} + ap, 8r 3 : : {bbcxx/12r}. 8b 3
unde eruitur x = 8aab 3 cr + 96b 3 ap - 8bbcrr.

Cognita longitudine parabolæ x, dataque ejus ordinata = b. fa-
cile invenitur parameter = {bb/x}. quâ erutâ deſcribetur parabola per
Prop. VII. vel VIII. Hoſpitalii Lib. I. Sect. Coniq. deſcriptâ Para-
bolâ circa axin circumvolutâ, generabitur Conois parabolica quæ-
ſita.

546. PROPOSITIO LXVII.

Tab. XXVI. fig. 2. Data Conoide parabolica gravi A B C dato-
que pondere P, cujus momentum ſimul cum momento ponderis dati
ſolidi ſit in quacunque ratione data, invenire aliam Conoidem pa-
rabolicam, quæ datam quamlibet babeat longitudinem, & cujus
momentum ex gravitate ad Cohærentiam ſuam ſit in eadem ratione.

Quantitatibus Conoidis A B C vocatis ut in præcedenti Propoſi-
tione, erit Conoidis momentum = {aacr/12}. momentum ponderis
= ap. Cohærentia = 8r 3 .

Sit longitudo Conoidis quæſitæ data G F = d. radius baſeos quæ-
ſitus G D = x. erit ejus peri pheria = {cx/r}, ſolidum = {cdxx/4r}. cujus mo-
mentum = {cddxx/12r}. Cohærentia = 8x 3 . quare ordinanda hæcpro-
portio, cum momenta gravitatis ad Cohærentias ſuas debent habe-
re eandem rationem, {cddxx/12r}. 8x 3 : : {aacr/12} + ap. 8r 3 .

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