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

Vocetur C A, a. CD, b. circumferentia deſcripta a puncto B
ſit c. invenietur ſoliditas corporis generati = {bcr/3}. centrum gravi-
tatis in axe CD diſtat a puncto D = {7/16} D C = {7/16}b. quare momen-
tum ex gravitate erit {7bbcr/48}. quia autem D B eſt = 2a a
erit Cohærentia = 8 a 3 2.

568. PROPOSITIO LXXXIX.

Tab. XXVI. fig. 12. Sit ſolidum Hyperbolicum ABCE, in quo
ſegmentum LIKM baſi parallelum, erit Cohærentia ſolidi ABC
ad eam ſegmenti LIKMC, utirectangulumex GC, GH ad rectan-
gulum ex NC, NH.

Sit C H axis Hyperbolæ primus, quo ducto erit Cohærentia
baſeos A B F E ad Cohærentiam baſeos LIKM, in ratione dupli-
cata E A ad LI. ſed eſt quadratum E A ad quadratum LI, uti re-
ctangulum ex abſciſſa G C X per G H, ad rectangulum ex abſciſſa-
N C in N H. quare patet propoſitum.

569. De Hemisphæriis.
PROPOSITIO XC.

Tab. XXVI. fig. 13. Momentum Hemisphærii inſcripti cylindro,
baſi affixa parieti, eſt dimidium momenti ipſius Cylindri habentis
eandem baſin & altitudinem.

Vocetur enim radius A D baſeos, r. & peripheria circuli, c. erit
ipſa baſis = {cr/2} hæc multiplicata per A E = r. dat ſoliditatem Cylin-
dri circumſcripti C A E = {crr/2}, cujus centrum gravitatis eſt in me-
dio ſive in {1/2} r. adeoque erit momentum cylindri ={cr 3 /4}. Eſt au-
tem ſoliditas Cylindri ad eam hemisphærii, uti 3 ad 2, adeoque

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