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Fermat Newton Leibniz and
Lagrange and Legendre
5 other sections not shown
analysis arbitrary constants arc-length assumes axis Bliss Bolza brachystochrone problem calculus of variations Carathéodory Clebsch coefficient concludes conjugate points considers const continuous continuous function coordinates cycloid defined determinant discussion elegant end-conditions end-points envelope envelope theorem Euler Euler equation evaluated expression extremum family of extremals Fermat Figure finds fixed follows frustum function F geodesics given curve hence Hilbert implies integral integrand interval isoperimetric problem James Bernoulli John Bernoulli Kneser Lagrange Lagrange’s Legendre Legendre’s Leibniz maximum or minimum Mayer minimizing arc necessary condition Newton notation notes Osgood paper parameter partial derivatives partial differential equation point conjugate positive proceeds proof quantities relation remarks resistance result right-hand member satisfy says second variation Section side-conditions solution solve Suppose surface tangent theorem transversal vanish variable velocity Weierstrass writes