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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 72, page id 1066518432:0100
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F18. 37.
72 DE VEREDUS ET MIOTFBUS CORPORUM. L IB. I.
reliquis manentibus, ut Cupra, (5. 258) Triangula Similia Amp. et
IILiq suppeditane p = Zdt: ds, at que ad eo 8 = dp: p dZ = (d5 dtd z +
245. dat = 2dSdtdds): 2dt. Duae Formula non, nili in nominibus, dit.
Tert a Formulis Varignonianis, quales in Commentariis Academix
Resixe Paril. Scientiarum 17OL. ex 1706. habentur, in quibus nOn
masis quam in praelenti ullum differentialium. dt, d2, ds constans
altumtum est, led omnia rariabilia.
T6T. Fadem Facilieate habetur, aut Paltem invenitur insistendo
principiis supra politis, Formula admodum expedita ex generalis pro
radiis erolutarum. Nam criansula NNZm et ghr, quae (upra (5. 155.)
Simitia eNe ostensa TunE, praebent hy vel Ng: gr = NZ: Nm, X trian-
sula similia Ampo ac NgD hanc alteram analosiam ND: N9 =Wm:
Ap, erSO ex aquo NI: gr. =NZ: Ap, acque adco H L =ND. Ap:
or, id cst in Cymbolis supra altumtis, ec vocando insuper NL, r;
erit r = 2d2: dp, nam gr’in Aisura eAt ap in hisce Ermbolis; unde
cum p (IF = Zdi: ds, invenietur F = ZdZ: dp = Zd Zds: dSdtdZ + Zdsddt
2didas Formula generalis radii olculatoris, in qua nullum differen.
tialo constans astumtum es, quae proinde in infinitas alias facile
transformari porest. Atque deleco membro in denominatore dsdidz,
habebitur r = a5.dZ: dsaat -atdas Formula itidem generalis pro Cur.
vis quarum ordinatxe parallela axique perpendiculares funt, in qui-
bus de lune elementa abscistarum.
PROPOSITIO XXTII. PROBLEMA
262. Datis scala solicitationum centralium GBb, celeritate AI, e
directione jactus AR, desinire ex construere curvam, quam missile in
vacuo describet, concessis ficurarum quadraturis.
L. Centro D interralloque arbitrario DP describatur. circulus
PO radios De, Dn Secans in punctis O, o; altumatur que O quar-
ta proportionalis ad DN, DR, _ AI, ita ut DN. O (=DR. AI)
=EF. D9, hOC CA DN: D9 = EF: O, _E DN: D92 =F F 2: O.
ut diridendo habeatur Ng: Dg = F F= -Q: O atque adco Ng:
Dg = Y (F F = 03): 9, Scd Ng: Dg sicut radius ad tangentem an-
ruli DNg. qux tansens dicatur P, e radius DP vel DO, hinc
(FF. = 2: Q = DP: Z atque adco T =O. DP: V(FF-
de
TI. PrOpter arcus similes np e O0, est O0: pn =DP: DN, et
p: NP = Z: DP, ergo ex aquo Oo: Dp = T: DN, hinc O0=T.