## The Princeton Colloquium: Lectures on Mathematics, Delivered September 15 to 17, 1909, Before Members of the American Mathematical Society in Connection with the Summer Meeting Held at Princeton University, Princeton, N.J., Volume 3, Part 1 |

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analytic arbitrary functions bound vector boundary point brachistochrones calculus of variations catenaries coefficients common complete system conformal transformation conic conservative field Consider constant contact transformations continuous curve convergent series corresponding curve Cxy defined denote derivatives described different from zero differential equation distinct dynamical EDWARD KASNER factor field of force finite number follows functional determinant given point Hence inequality infinite system initial point initial speed integral interior point interval inverse irreducible polynomial limit point lineal element linear locus natural family normal congruence obtained oo3 trajectories oo4 curves orthogonal osculating circles osculating parabolas osculating plane particle passing polygon polynomial problem projection radius of curvature region result root sheet simply connected single-valued solutions space space-time curves straight lines surface system of curves system of oo3 system of trajectories tangent tautochrones theory Thomson-Tait vanish identically variables velocity curves velocity system wave set xy-plane