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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 382, page id 1066518432:0410
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82
A P P F N D
I X.
tio y = ax =aa, in qua abscisae a lumantur à centro, lemilatere
transverlo existente =a, sintque tenacitates aut Airmitates currae
proportionales distantiis punctorum currae a centro, hoc eAt, t=
V (X L yy). FF S. 26T. praebebit r = 1: aa, et B (=ardt: td5) = 2 ∞y
nec non k =Ht: a; hinc aequatio prima de =hdg: R praebebit dg =
trdt: 2∞7 = 2t∞d∞: 2∞) = td∞: Y; aEqui FdN =7d5, ersodq (= t dx: y
=7d5: γ = ds, Tdcirco potentix BFI, Ceu dq. Cunt ut elementa currX
Bb, carum que directiones in centro hyverbolae coeunt, quoniam tan-
Sens anguli DBFI inventa eAt = 2∞7: a, et haec exprestio etiam tan-
sentem ansuli, quem normalis trperbolae BD cum recta ex puncto B
ad centrum hyperbolae ducta continet. Propterea est hyperbola 
quilatera catenaria. s srarium directiones in centro hyperbolae con-
currere supponuntur, uc lupra circa tinem 3. 205. Sine demonstra-
tione diccum est. Pariter si poluissem dg = ds et h =2∞y: a in hy-
perbola cadem, invenissemus t =V Xx L yy.
Generalius, si directiones grarium conrersunt in punctum, abscis-
Exeque lumantur in axe ab hoc centro grarium, crit h = axdx L aydy:
xdy -yda, ec hujus ac alterius di =hdg: k opC, in suppositione dq=
ds inrenissemus t =V ax L yy e 7y = ∞∞ = aa.
Si directiones grarium axi AC parallelae sunt, erit h = ad x: dy,
ac substituendo loco da, et dy carum proportionales n de m, fiet
h (=adX: dy) = an: m. Item in requatione quarta, Currosando m de
dn pror et ds, quibus proportionales TunE, AeT an: m =amat: tdn,
et at: t=nan: mm (aUE, Quia Mm + nn = aa, eC
nan = -mam) = - mdm: nm = - dm: M, CFGO
It =I (aa: M), id CA, t = aa: m = ads: dy, ut ha-
bet aequatio nona. Substicuendo isitur ralorem
inrentum ipsius t in aequatione secunda invenie.
tur xquatio septima, et ex hac ope analosix dp:
dg = a: R, = aV: ds, elicietur aequatio octava.
5. B = adio: a
6. k = ads: dy
7. dp = ads: rdy
8. aq = ad5: rdy
9. t = ad5: dy
Tlinc, ex hisce tribus ap, dq e t una data in indeterminatis curvX
ee constantibus utlibet inricem permixtis. Facile inrenientur reli-
quae dux, si non algebraice, laltem transcendenter.
Si directiones Potentiarum BFI (unt currae normales, crit B =0,
et k = a, et Pola aequatio secunda sufticie; hunc casum particula-
rem Celeb. Joh. Bernoullius solutum dedit jam pridem in Commen-
tariis Academiae Res. Paris. Scientiarum 1706, et nuper adhuc in
Li