Full text: Volumen primum. Opera mechanica (1)

HOROLOG. OSCILLATOR. numerum particularum ſolidi A B C, æquale quadratis di-
ſtantiarum à plano A D . Apparet autem, fieri ſpatium Z æquale {1/20} quadrati B C.

122.1.

Figure 1. Pag. 166.
TAB.XXV.
Fig. 1.
A O C G D L N
Figure 2. Fig. 2.
A B C G D L N
Figure 3. Fig. 3.
O C D A K B N E F C D L M
Figure 4. Fig. 4.
O A C D F E K B N C L D M
Figure 5. Fig. 5.
E A G F H K B D C
De centro
OSCILLA-
TIONIS.
Prop. 15.
huj.

Itaque, totum ſpatium applicandum, æquatur hic {3/80} qua-
drati A D, cum {1/20} quadrati B C. Unde, ſi ſuſpenſio, ut
hic, poſita fuerit in A, vertice pyramidis, ideoque diſtan-
tia, ad quam applicatio facienda, A E æqualis {3/4} A D; fiet
hinc E S, intervallum quo centrum agitationis inferius eſt
centro gravitatis, æquale {1/20} A D, atque inſuper {1/15} tertiæ
proportionalis duabus A D, B C. ſive tota A S æqualis {4/5}
A D, præter dictam {1/15} tertiæ proportionialis.

123. Centrum oſcillationis Coni.

Quod ſi A B C conus fuerit, omnia eodem modo @e habe-
bunt, niſi quod ſpatium Z hic fit æquale rectangulo Δ Ρ Φ , hoc eſt {3/2@} quadrati P V vel B D, ſive {3/80} quadrati B C. Quare, totum ſpatium applicandum, in cono erit {3/80} qua-
drati A D, una cum {3/80} quadrati B C. Ac proinde, poſita
ſuſpenſione ex vertice A, fiet E S, qua centrum agitationis
inferius eſt centro gravitatis, æqualis {1/20} A D, & {1/20} tertiæ
proportionalis duabus A D, B C. ſive tota A S æqualis {4/5}
A D, una cum {1/5} tertiæ proportionalis duabus A D, D B. Atque hinc manifeſtum eſt, ſi A D, D B æquales ſint, hoc
eſt, ſi conus A B C ſit rectangulus, fieri A S æqualem axi
A D.

123.1.

Prop. 15.
huj.

Sequitur quoque porro, ex propoſitione 20, conum hunc
rectangulum, ſi ex D centro baſeos ſuſpendatur, iſochro-
num fore ſibi ipſi ex vertice A ſuſpenſo, quemadmodum & de triangulo rectangulo ſupra oſtenſum fuit.

124. Centrum oſcillationis Sphæræ.

Si A B C ſit ſphæra, erit figura plana proportionalis, à
latere adponenda, O V H, ex parabolis compoſita, qua-
rum baſis communis O H, æqualis ſphæræ diametro A D. Sectâ vero ſphærâ planis per centrum E, quorum B C ſit

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