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

INTRODUCTIO AD COHÆRENTIAM erit Cohærentia ſegmenti I H ad Cohærentiam ſegmenti B D, in
ratione compoſita ex A G q ad A E X E C & ex ratione I H c ad
B D c. adeoque erunt Cohærentiæ ſegmentorum I H, B D: : A G q
X I H c ad A E X E C X B D c .

615. PROPOSITIO CXII.

Tab. XXVII. fig. 14. Sit parabolois A C E utrimque fulta in
A & E, cujus axis borizontalis ſecetur ſegmentis L K, F H per-
pendicularibus ad axin A B. erit Cohærentia ſegmenti L K ad Co-
bærentiam ſegmenti F H, in ratione compoſita ex A G X I L, ad
I B X F G.

Nam eſt Cohærentia ſegmenti L K ad eam ſegmenti F H, uti
A G q X I L c , ad A I X I B X F G c . ſed eſt Cubus I L = I L q X I L. ita
F G c = F G q X F G. eſt vero I L q , F G q : : A I, A G adeoque A I X I L,
A G X F G: : I L c , F G c . hinc erit Cohærentia ſegmenti L K, ad
eam ſegmenti F H: : A G q X A I X I L, A I, X I B X A G X F G. factaque utriuſque quantitatis diviſione per A G X A I, erit Cohæ-
rentia L K ad eam in F H: : A G X I L ad I B X F G.

616. PROPOSITIO CXIII.

Tab. XXVII. fig. 5. Solidum ſemicirculare A C E B F D, utrim-
que in A & B ſuffultum, eſt ubivis æqualis reſiſtentiæ.

Ducatur enim quælibet D C, E F perpendicularis in diametrum
A B, eritque Cohærentia C D ad E F in ratione duplicata altitudi-
nis D C ad E F, quatenus altitudinem ſolidi ſpectamus: verum
eſt momentum ponderis maximi ſuſpenſi ex D, ad momentum
ſuſpenſi ex F, uti rectangulum A D X D B, ad rectangulum A F X F B. verum ex natura circuli, uti A D X D B ad A F X F B: : D C q , ad
F E q : : Cohærentia in D C ad Cohærentiam in F E. adeoque erit
momentum ponderis maximi idem in E F ac in C D, erit igitur hoc
ſolidum ubivis æqualis reſiſtentiæ.

Tab. XXVII. fig. 6. Corol. 1. Si A C E B D F ſit circulus, & proinde
ſolidum fuerit diſcus circularis, qui utrimque ad extremum dia-

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