Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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200125HOROLOG. OSCILLATOR.
PROPOSITIO II.
11De centro
OSCILLA-
TIONIS.
TAB. XVIII.
Fig. 1.
POſitis quæ prius, ſi pondera omnia A, B, C,
ſint æqualia;
dico ſummam omnium perpendi-
cularium A D, B E, C F, æquari perpendicula-
ri, à centro gravitatis ductæ, G H, multiplici
ſecundum ponderum numerum.
Quum enim ſumma productorum, à ponderibus ſingulis
in ſuas perpendiculares, æquetur producto ex G H in pon-
dera omnia;
ſitque hìc, propter ponderum æqualitatem,
ſumma illa productorum æqualis producto ex uno pondere
in ſummam omnium perpendicularium;
itemque productum
ex G H in pondera omnia, idem quod productum ex pon-
dere uno in G H, multiplicem ſecundum ponderum nume-
rum:
patet ſummam perpendicularium neceſſario jam æquari
ipſi G H, multiplici ſecundum ponderum numerum.
quod
erat demonſtrandum.
PROPOSITIO III.
SI magnitudines quædam deſcendant omnes, vel
aſcendant, licet inæqualibus intervallis;
alti-
tudines deſcenſus vel aſcenſus cujusque, in ipſam
magnitudinem ductæ, efficient ſummam producto-
rum æqualem ei, quæ fit ex altitudine deſcenſus
vel aſcenſus centri gravitatis omnium magnitudi-
num, ducta in omnes magnitudines.
Sunto magnitudines A, B, C, quæ ex A, B, C, deſcen-
22TAB. XVIII.
Fig. 2.
dant in D, E, F;
vel ex D, E, F, aſcendant in A, B, C.
Sitque earum centrum gravitatis omnium, dum ſunt in
A, B, C, eadem altitudine cum puncto G;
cum vero ſunt in
D, E, F, eadem altitudine cum puncto H.
Dico ſummam
productorum ex altitudine A D in A, B E in B, C F in C,
æquari producto ex G H in omnes A, B, C.

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