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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 399, page id 1066518432:0427
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A P
P F N
Y
Z2.
EE, ubi B = d A: dZ; C = dB: dZ e DF = Z, item AL = Y, 20
er - ee = 55, haec appolita Formula Factis in ea substitutionibus va-
lorum linearum DK, FA. F , prodibic aequatio circa finem 5. 169.
exhibita. Verum, quia nonnihil elegantior, uc miti videtur, solu-
tio ejusdem problematis sele mihi obtulit, cam hoc loco apponere
placet. Circa rectam AC, tanquam axem, descripta sIE currA quX-
cunque HIB, radioque etiam pro lubitu TumEo AC, atque adeo centro
C circulus AC, Cujus tangens in A crit linea recta indekinita OAII,
ac per quodlibet punctum B currae MB ductis tangente BV ordi-
nataque BR producenda usque ad occurtum ejus cum circulo in
G, diridatuE (UBEANGCNS RV in S, UE RS SIE ad FOFam RV ut 1ad
numerum quemcumque rationalem n, ac junsatur SC, tum duca-
tUT Per A recta AI cum C Aa continens angulum PAO aequalem,
ubique respectiro angulo CISR, atque hoc idem si Factum Fuerit
cum tansente ex subtangente ad punctum currae HI, relultet recta AA,
quemadmodum in ordine ad punctum B Curra HB prorenit AL.
Exxonat AI celeritatem mobilis curram API describentis in pun-
eto A existente centro solicitationum centralium D, per punctum
I ducta indesinita IK parallela AC, sumatur in An segmentum
A = AIT _E per a agaTUE aK parallela AI, rectae IR conreniens in
R, per quod punctum descripea intelligatur hyperbola RM inter
2(YIMPEOTAS Aa _E AT. POrrO in AI Cumta AO aequali respectira
OrdinaEx RB CurrX HB ducatur OP Parallela AM, quae producta
occurrat hyperbolae in M, ac denique in ordinata MO per hoc
punctum M ad alympeotam AO ducta ac deortum producta, fiat
OF equalis disferentiae ordinatarum AII, RB e punctum L erit
in scala celeritatum mobilis in curra altera AN incedentis. HIXC FiB. 160.
autem CuEVa ANI ita Comparata CA, ut radii rectOreS AD =AII, e
ND = RB, per ejus terminos ducti, angulum ADN contincat, qui siE
ad angulum in circulo ACCF, ut F ad numerum qui anFCa n. FAO
Ng CUErA AN cangens in N, suxer quam cadtat perpendicularis
Dg, aC CenErO D descripEi (InE arCUS F. N arculusque np, DOTIEO-
que in A8. 759. angulo CC8 adt ans. NDn =n: T asatur eb paral-
lela CB.
Demonstr. Ouia anGULUS INFNITESIUS NON eK ad GCG UE F ad
n, Peu (Constr.) =RS: RV, ∞ (5. 129.) arculus pn ad Cre in com
posica ratione anguli NOn ad angulum GCg, vel T ad n, (eu RS adt
RV, ec radii DN vel ordinatx RB ad radium GC, crit pn: 6
AS. RB: CC. RV; acqui eAt (8: bB (= GC: GR) =6C. RV: CR.
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