CHAPTER V.. Page

Page

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