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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 93, page id 1066518432:0121
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DE VTRTBOS ET NOTEBOS CORPORDM. L. IB. I. 93
C Peu ppR: T= CTIE RCCIPROCCUE R 2n -1. Proinde sI CONatUS Centri-
Fugus Fuerit reciproce ut T2, erit tempus periodicum in ratione
sesquiplicata radii R, e in hoc consistit celebre Kepleri theore-
ma. Reliqua, qua eadem Facilitate ex tribus praecedentibus Formu-
lis elici possunt, Lectoris industrix relinquimus, at que adeo ad con-
templationem pendulorum conicorum absque ulterioribus ambagi-
bus accedimus.
284. Si Elum AMI motu conieo moreatur circa axem AD hori-
zonti rectum, adoo ut pondus ipsi annexum M circumferentiam cir-
culi MOR describat; id feri non potest, quin praeter graritatem
secundum directionem ipsi AD parallelam in corpus M agentem ci-
dem mobili insit conatus alius secundum directionem DM agCnS.
NTam uE AIum AMI in Situ hoc CUb angulo D AMI ad axem inclina-
to detineatur duabus riribus aut solicitationibus lateralibus AB e
BC opus est, quarum prior graritatem exponit, altera vero BC
nonnisi a motu circulari provenire potest, ex motu rero centrali
relultat conatus centrifuxus, ergo BC repraelentat ejusmodi cona-
cum centrifusum. Agatur isitur BB aequidictans lateri AM, Aet-
que EM = BC. PONaNEUE inSuIPeF AD = A, AM =L, AB =G
et BC = RM = C, FadiuS DM =R, peripheria MRO = PR, e
Perinde ac supra V celeritas mobilis in circumterentia MO: quibus
Draeluppolitis, erit iterum, ut in antecedenti paragrapho, tempus
unius circuicus T mobilis M in Peripheria MOR, dum silum AM
superticiem conicam deseribit = pr (R: C) verum ob parallelas AM
eE BE, eA AD: AB = DM: FM, hoc CA; A: G =R: C, crooctiam
I =DY (A: C), haec vero exprectio etiam significat (5. 175. 178.
tempus duarum oscillationum minimarum lateralium penduli cujus
A sit lonsitudo; magnitudo rero V (A: C) Significat tempus delcen-
Cus perpendicularis alicujus sraris ex altitudine : A. Proptereatem-
Pora circuitus pendulorum conicorum sunt in subduplicata ratione
alticudinum A conorum. SuperAuum duco reliqua, circa ejusmodi
Dendula ab Flugenio indicata, theoremata operose demonstrare, cum
ex hisce posicis principiis sponte lua Facillime Auant, ceu quilibet
ridebit, qui animum iis adrertere relit. Priusquam tamen ad alia
transeam, contemplabimur paulisper problema ab ingeniositimo Ton.
Bernoullio olim propositum quodque ab IIlustr. Hlospitalio solutio-
nem nactum est; sed quoad arguendi Formam a nostra disferentissi-
BTaM.