CHAPTER III.

• MODERN OR ANALYTICAL GEOMETRY    232
• The analytical Representation of Figures    232
• 1. Reduction of Figure to Position    233
  2. Determination of the position of a Point    234
• Plane Curves    237
• 1. Expression of Lines by Equations    237
  2. Expression of Equations by Lines    238
  3. Any change in the Line changes the Equation    240
  4. Every "Definition" of a Line is an Equation    241
  5. Choice of Co-ordinates    245
  6. Two different points of View    245
  7. 1. 1. Representation of Lines by Equations    246
     2. 2. Representation of Equations by Lines    246
  8. Superiority of the rectilinear System    248
  9. 1. Advantages of perpendicular Axes    249
• Surfaces    251
• 1. Determination of a Point in Space    251
  2. Expression of Surfaces by Equations    253
  3. Expression of Equations by Surfaces    253
• Curves in Space    255
• Imperfections of Analytical Geometry    258
• 1. Relatively to Geometry