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# Title: [Christiani Hugenii Zulichemii, Const. F. Horologium Oscillatorium. Sive De Motu Pendulorum Ad Horologia Aptato Demonstrationes Geometricae] Christiani Hvgenii Zvlichemii, Const. F. Horologivm Oscillatorivm. Sive De Motv Pendvlorvm Ad Horologia Aptato Demonstrationes Geometricæ (shelfmarks Leibn. Marg. 70; ZEN Leibn. Marg. 70)
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FTOKOLOb. OSCILLATOR.
242
a F aqualis : a D; Rec hinc E S, incerrallum quo cenrrum agia
I. E.
tionis inferius est centro graritatis, aquale: AD, atque insu-F2ONLB.
Per: cerrix proportionalis duabus A D, B C. CirC FOTa A S aqua-
lis = AD, Praecer dictam tertix proxorrionalis.
Centrum oscillationis Coni.
Ouod Tia B C conusfuerie, omnia eodem modo sc habebune,
nili quod sparium 2 hic sic ae quale rectangulo a e p F, hoc est : - + PrOP. 15. hui.
quadrari e v velB D, Tire 2 quadrati B c. Ouare, torum spacium
appplicandum, in conoerit quadrati a D, una cum ; quadrari
BC. Ac proinde, Polira luspentione ex verrice A, ACE F S, qua
centrum agirarionis interius est centro gravicatis, aequalis AD,
et terrix proportionalis duabus AD, BC. Sirc tota asaequalis :
A D, una cum : tertix proportionalis duabus A D, D B. AEque hinc
manifectum cAt, si A D, DB aequalessint, hoc Cst, (I COnUS A B CFIE
rectangulus, tieri a saqualem axi aD.
Sequitur quoque Porro, ex propolitione 20, conum hunc re-
ctanoulum, si ex Dcentro baleos luspendatur, ilochronum Fore
Sibi ipsi exvertice a Cuspenso, quemadmodum de decriangulo re-
ctangulo supra ostenlum fuir.
Centrum oscillationis Sphara.
Si AB C Scsphaera, erir figura plana proporrionalis, à larere ad
ponenda, ov_, ex parabolis compotica, quarum basis communis
Om, aequalis Sphara diametro a D. Sect a vero sphera planis per
centrum E, quorum BC c horizonti parallelum, A D veroverri
cale: ut inveniatur lumma quadrarorum à distantiis à plano a D,
nolcenda est distantia centri or. para bola O V H ab OE, qux lic P P,
estque: V P. Deinde, dirisa Pr bitariam in A, constat rectangu-
lum a x ∞, multiplex per numerum parricularum spherx A B C,
aequari quadratis distantiarum a plano X D F. F. A aurem rectangu - + ProP. 15. in
lum a P o aequale: quadrati e V, vel quadrati BF.
fine.
Acqui, quadraca diltantiarum à plano B C, aequalia esse liguer
quadratis dictantiarum à plano nD, ac proinde cidem rectangu-
loaro, mulcipliciper dictum parricularum numerum. Ergo spa-
cium applicandum, in sphera aBc, erit duplum rectanguli A P P;
ideoque aequale: quadrari aradio EB.
lraque, si sphera suspensa sir ex puncto in supertieie lua a, exir
is
ECLHTEO