# The Elements of Coordinate Geometry, Part 2

Macmillan & Company, 1896 - Coordinates - 416 pages
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### Contents

 INTRODUCTION ALGEBRAIC RESULTS 1 General EquATION TRACING OF CURVES 24 GENERAL EQUATION 36 OBLIQUE COORDINATES 66 EQUATIONS REPRESENTING TWO OR MORE STRAIGHT 88 TRANSFORMATION OF COORDINATES 109 CHAP PAGE 118 Equation to a tangent 126
 THE HYPERBOLA 271 322 290 329 297 338 310 349 323 356 329 364 338 367 344

 Pole and polar 137 Equation to a circle in polar coordinates 145 SYSTEMS OF CIRCLES 160 Conic Sections THE PARABOLA 174 THE PARABOLA continued 206 THE ELLIPSE 225 The director circle 245 MISCELLANEOUS PROPOSITIONS 269
 378 354 19 392 Circles of curvature and contact of the third order 398 24 400 Envelopes 407 31 417 109 417

### Popular passages

Page 118 - A conic section is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line.
Page 195 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 158 - A straight line moves so that the product of the perpendiculars on it from two fixed points is constant. Prove that...
Page 156 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 29 - This equation tells us that the square of the distance of the point (x, y) from the...
Page 3 - The sum of the products of the roots, taken two at a time, is equal to the coefficient of the third term, thus, Zl*2 + XiX3 + XiX4 + X2X3 + X2X4 + X3Xt = pi.
Page 182 - ... the tangent of the angle which the tangent makes with the axis of abscissas, this coefficient must have as many values as there are intersecting branches.
Page 303 - If a right-angled triangle be inscribed in a rectangular hyperbola, prove that the tangent at the right angle is the perpendicular upon the hypothenuse.