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

INTRODUCTIO AD COHÆRENTIAM peripheria circuli D G E = {bc/r}. Eſt vero Conoidis parabolicæ A B C
ſoliditas = {acr/4} per Prop. XIII. Carrei de Dimenſione Solidorum. & quia centrum gravitatis eſt ad {1/3} F B a puncto F, in axe F B, per
Prop. XVIII. Carrei de Centro Gravitatis, erit momentum Conoi-
dis parabolicæ A B C = {aacr/12}. ſed ſolidum D B E eſt = {ab 4 c/4r 3 } cujus
momentum ex gravitate eſt = {aab 6 c/12r 5 }. datur in Propoſitione. {aab 6 c/12r 5 }. {aacr/12}: : {a 3 b 6 /r 6 }a 3 .

Quod patet multiplicando hujus Proportionis terminos medios & extremos per ſe, proveniuntque producta æqualia, nempe {a 5 b 6 c. /12r 5 }.

Coroll. Sunt quadrata momentorum Cohærentiæ harum Conoi-
dum Parabolicarum inter ſe, uti momenta gravitatis ipſarum Co-
noidum. Nam ſunt Cohærentiæ inter ſe uti r 3 ad b 3 , quarum qua-
drata ſunt r 6 , b 6 . eſt vero {aab 6 c/12r 5 } {aacr/12}: : b 6 , r 6 . nam multipli-
catis extremis mediisque terminis per ſe, habentur producta utrim-
que æqualia, nempe{aab 6 cr/12}

544. PROPOSITIO LXV.

Tab. XXVI. fig. 2. Datis duabus Conoidibus Parabolicis gravi-
bus D E F, A B C, ejusdem altitudinis ſed diverſarum baſium, at-
que pondere dato Q appenſo ex vertice F Conoidis gracilioris,
invenire pondus P appendendum ex vertice C Conoidis craſſioris,
ita ut momenta propriarum gravitatum inconoidibus, & ponde-
rum appenſorum earum verticibus, ſint ad cohærentias baſium in
eadem proportione.

Vocetur A F, r. C F, b. peripheria baſeos, c, pondus P quæſitum

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