# Plane and Solid Analytic Geometry

Ginn & Company, 1897 - Geometry, Analytic - 371 pages
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### Contents

 Equation of the Straight Line in Polar Co�rdinates 59 Equation of a Line through a Given Point Perpendicular to 68 Equations of Higher Degree than the First representing 74 CHAPTER IV 86 Transformation from one Set of Oblique Axes to a new 90 CHAPTER V 97 Equation of a Tangent to a Circle when the Point of Contact 103 59 110 62 118 Conjugate Diameters 120 66 127 The Parabola e 133 ARTICLE PAGE 135 CHAPTER VII 161 To find the Tangents from a Point not on the Conic Section 169 CHAPTER VIII 177 Perpendicular from Focus to Tangent 183 Parabola with Focus at the Origin 189 CHAPTER IX 199 Focal Distances 200 Sum of Focal Distances 96 Constructions PAGE 199 199 200 201 202 202 210 209
 Ellipse referred to Conjugate Diameters as Axes 220 Polar Equation of the Ellipse 222 Examples 223 CHAPTER X 229 To find the Foci when the Axes are given 231 Focal Distances 232 Difference of Focal Distances 233 117 Constructions 233 Angle between Tangent and Focal Radii 234 Equation of a Diameter 234 236 Propositions on Conjugate Diameters 238 CHAPTER XI 251 132 258 Oblique Co�rdinates 267 PART II 273 5 288 CHAPTER II 290 CHAPTER III 301 24 308 Projection 313 ARTICLE 316 The Paraboloids 330 FORMULAS 343 Copyright

### Popular passages

Page 229 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 22 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 133 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 23 - ... four times the square of the line joining the middle...
Page 132 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides. Show that the locus is a circle. 50. Prove that the two circles z2 + y2 + 2 G,z + 2 Ftf + Cj = 0 and x2 + y...
Page 23 - The sum of the squares of the other two sides is equal to twice the square of half the base, plus twice the square of the median.
Page 23 - Prove analytically that in any right triangle the straight line drawn from the vertex to the middle point of the hypotenuse is equal to one half the hypotenuse.
Page 86 - Prove analytically that the medians of a triangle meet in a point. 71. Prove analytically that the perpendicular bisectors of the sides of a triangle meet in a point. 72. Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 326 - The coordinates of the vector in the ox'y' system are (x',y') and, furthermore, as may be verified, x' = x cos 6 + y sin 6 y
Page 197 - The locus of the point of intersection of two tangents to a parabola which...