href="@public@vhost@g@gutenberg@html@files@39702@[email protected]#Page_70" class="pginternal" tag="{http://www.w3.org/1999/xhtml}a">70

CHAPTER III.

• TRANSCENDENTAL ANALYSIS: its different conceptions    88
• 1. Preliminary Remarks    88
  2. Its early History    89
• Method of Leibnitz    91
• 1. Infinitely small Elements    91
  2. Examples:
  3. 1. 1. Tangents    93
     2. 2. Rectification of an Arc    94
     3. 3. Quadrature of a Curve    95
     4. 4. Velocity in variable Motion    95
     5. 5. Distribution of Heat    96
  4. Generality of the Formulas    97
  5. Demonstration of the Method    98
  6. 1. Illustration by Tangents    102
• Method of Newton    103
• 1. Method of Limits    103
  2. Examples:
  3. 1. 1. Tangents    104
     2. 2. Rectifications    105
  4. Fluxions and Fluents    106
• Method of Lagrange    108