Full text: Volumen primum. Opera mechanica (1)

CHRISTIANI HUGENII ab aliquo angulorum ſuſpendatur, motuque hoc laterali agi-
tetur, pendulum illi iſochronum eſſe {2/3} diagonii totius.

113.1.

TAB. XXIII.
Fig. 3.
De centro
OSCILLA-
TIONIS .

114. Centrum oſcillationis Trianguli iſoſcelis.

In triangulo iſoſcele, cujuſmodi C B D, ſpatium appli-
candum æquatur parti decimæ octavæ quadrati à diametro
B E, & vigeſimæ quartæ quadrati baſeos C D. Unde, ſi
ab angulo baſeos ducatur D G, perpendicularis ſuper latus
D B, quæ occurrat productæ diametro B E in G; ſitque
A centrum gravitatis trianguli; diviſoque intervallo G A
in quatuor partes æquales, una earum A K apponatur ipſi
B A; erit B K longitudo penduli iſochroni, ſi triangulum
ſuſpendatur ex vetrice B. Cum autem ex puncto mediæ ba-
ſis E ſuſpenditur, longitudo penduli iſochroni E K æquabi-
tur dimidiæ B G.

114.1.

TAB.XXIII.
Fig. 4.

Atque hinc liquet, triangulum iſoſceles rectangulum, ſi
ex puncto mediæ baſis ſuſpendatur, iſochronum eſſe pendu-
lo longitudinem diametro ſuæ æqualem habenti. Similiterque,
ſi ſuſpendatur ab angulo ſuo recto, eidem pendulo iſochro-
num eſſe.

115. Centrum oſcillationis Parabolæ.

In parabolæ portione recta, ſpatium applicandum æqua-
tur {12/175} quadrati axis, una cum quinta parte quadrati dimi-
diæ baſis. Cumque parabola ex verticis puncto ſuſpenſa eſt,
invenitur penduli iſochroni longitudo {5/7} axis, atque inſuper
{@/3} lateris recti. Cum vero ex puncto mediæ baſis ſuſpenditur,
erit ea longitudo {4/7} axis, & inſuper {1/2} lateris recti.

116. Centrum oſcillationis Sectoris circuli.

In circuli ſectore B C D, ſi radius B C vocetur r: ſemi
arcus C F, p: ſemiſubtenſa C E, b: fit ſpatium applican-
dum æquale {1/2} rr - {4b b r r/9 p p}, hoc eſt, dimidio quadrati B C,
minus quadrato B A; ponendo A eſſe centrum gravitatis ſe-
ctoris. Tunc enim B A = {2 b r/3 p}. Si autem ſuſpendatur ſector

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