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CHAPTER V.

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

CHAPTER VI.

• THE CALCULUS OF FINITE DIFFERENCES    167
• 1. Its general Character    167
  2. Its true Nature    168
• General Theory of Series    170
• 1. Its Identity with this Calculus    172
• Periodic or discontinuous Functions    173
• Applications of this Calculus    173
• 1. Series    173
  2. Interpolation    173
  3. Approximate Rectification, &c.    174

BOOK II.
GEOMETRY.

CHAPTER I.

• A GENERAL VIEW OF GEOMETRY    179
• 1. The true Nature of Geometry    179
  2. Two fundamental Ideas    181
  3. 1. 1. The Idea of Space    181
     2. 2. Different kinds of Extension    public@vhost@g@gutenberg@html@files@39702@[email protected]#Page_182" class="pginternal"