Chapter III Modern or Analytical Geometry 232
The analytical Representation of Figures 232
Reduction of Figure to Position 233
Determination of the position of a Point 234
Plane Curves 237
Expression of Lines by Equations 237 Expression of Equations by Lines 238 Any change in the Line changes the Equation 240 Every “Definition” of a Line is an Equation 241 Choice of Co-ordinates 245 Two different points of View 245
1. Representation of Lines by Equations 246
2. Representation of Equations by Lines 246 Superiority of the rectilinear System 248
Advantages of perpendicular Axes 249
Surfaces 251
Determination of a Point in Space 251
Expression of Surfaces by Equations 253
Expression of Equations by Surfaces 253
Curves in Space 255
Imperfections of Analytical Geometry 258
Relatively to Geometry 258
Relatively to Analysis 258
THE
PHILOSOPHY OF MATHEMATICS.