Book 1 — CHAPTER V.
W. M. (William Mitchell) Gillespie translation
THE CALCULUS OF VARIATIONS 151
Problems giving rise to it 151
Ordinary Questions of Maxima and Minima 151 A new Class of Questions 152 Solid of least Resistance; Brachystochrone; Isoperimeters 153
Analytical Nature of these Questions 154
Methods of the older Geometers 155
Method of Lagrange 156
Two Classes of Questions 157 1. Absolute Maxima and Minima 157 Equations of Limits 159 A more general Consideration 159 2. Relative Maxima and Minima 160 Other Applications of the Method of Variations 162
Its Relations to the ordinary Calculus 163