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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 385, page id 1066518432:0413
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1
P
P F N D I X.
sectionibus conicis. Et hxc est demonstratio Celebris K epleri ca-
nOniS.
VTII. De Centro Oscillationis. In cheoria centri oscillationis. C aP.
V. Lib. L. CxPOSITA BTCVITaLIS FaNEUM GraTI DOlUI, NON VeTO ex ne-
cellitate, centrum olcillationis reperiri in linca centri, hoc est, in re-
cta ex puncto sulpensionis per centrum graritatis figurx oscillantis
ducta. Mechodus enim nostra perinde valet quae cunque linea acci-
piatur per punctum suspentionis, in qua centrum oscillationis exi-
ctat, inrenietur semper hanc lineam per cenerum sraritatis Agurx
oscillantis transire debere, prortus ut idem etiam Celeb. Toh. Ber-
noullius in eleganti suo Schediasmate Aet. LipP. 27Fq. menl. Junii
S. 28. Octendit. Nam si in (9. 46. pendulum simplex CN com-
Polito ilochronum per aliud punctum in quam per centrum srari-
catis M fisurx oscillantis transire ponatur, quod tamen ita com-
Paratum, leu positum, esse debet, ut linca ex hoc puncto m (in A-
sura quidem non signato sed calamo aut mente Facile (upplendo)
Per centrum graritatis M ducta horizontali CY ad angulos rectos
Semper occurrat, invenietur, semper, ut in 5. 206, NVC = (P. PC + Fig. 46.
O. OC +_C.). G: M. mC, ubi M, ut in citato locO, SigniHICAE F.
P + F. O. + ecC. Seu aggregatum ponderum omnium Agurx oscillan-
eis partium. Jam vero, mucato utlibet angulo YCN, mucabitur simul
magnitudo ipsius mC, aC proPterCa quanLItAS NC = (P. PO2 +.
OC2 + XC.). G: MI. mC constans e inrariata fieri nequit, nisi coin-
cidente mC, cum MC, atque adeo puncta m e M ubique confundan-
tur, adco ut hinc appareat centrum olcillationis neceslario inlinca
centri existere. Ouod crat demonstrandum.
TX. Applicatio hujus norae theorix centrioscillationis nunc pau-
louberius declaranda est, quam in 5. 208, ubi Formula tantum exhibe
tur protisuris uniformis graritatis. Delignando particulas P, ( ecc.
ut ibi per dp, carumque pondus per Bdp, ita ut B gradtum grarita-
tis denotet, ex, si s signiticet gravitatem, qua simplex pendulum agi-
Tatur, _ 2 diltantiam particulae olcillantis ab axe olcillationis, ca-
non5. 206. CN = (P. PO +_C.). Cr: MI. MIC Prabebit + =95ZZap:
Bxdp. Flinc, (I B = 2ZZ: aX, Het t = aC (ZZ dp: C (22dp = a.
Oscilletur jam Aigura BAD in planum, Ccu ita ut axis oscillationis Fi8. 154.
semper maneat in plano tisurx olcillantis, at que adeo ordinatae Agu.
ra BD axi oscillationis  constanter parallelae sint; crunt hOc
calu ipla 2, seu distantix punctorum ordinatx, BD =DC = ∞, 2t-
que adeo s2Z dp = saxdp, et, quia dp = BC. C0 =)d_, exit sZ Z dp =
SareydX