Elements of Geometry

Macmillan, 1895 - Geometry - 293 pages
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Contents

 An angle 5 Equality axioms 12 Parallels 21 Construction of triangles 28 CHAPTER III 35 Quadrilaterals and quadrangles 42 CHAPTER IV 51 Angles and arcs 61
 Limit axioms 131 Intersections of planes 175 CHAPTER X 188 CHAPTER XI 205 Cylinders 217 Surface of a sphere 227 Areas of similar surfaces 234 Volume of a pyramid 241

 CHAPTER V 69 Proportional division 75 Medians 83 Squares on segments 89 Areas of similar polygons 96 CHAPTER VII 103 CHAPTER VIII 117
 Volume of a sphere 249 Area of a parabola 262 PROBLEMS 267 Area of an ellipse 271 Particular cases 281 Copyright

Popular passages

Page 27 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 28 - If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal.
Page 19 - The sum of two sides of a triangle is greater than the third side, and their difference is less than the third side.
Page 174 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Page 174 - Find the equation of the locus of a point which moves so that the sum of the squares of its distances from the x- and z-axes equals 4.
Page 102 - The sum of the squares of the sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.
Page 293 - F') ; the diameter drawn through them is called the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point...
Page 132 - A conic is the locus of a point which moves in a plane so that the ratio of its...
Page 135 - The areas of circles are to each other as the squares of their radii.