### Contents

 GEOMETRY 1 PLANE GEOMETRY 7 THE CIRCLE 75 PROPORTION 135 AREAS OF POLYGONS 184 REGULAR POLYGONS AND CIRCLES 211
 LINES AND PLANES IN SPACE 251 POLYHEDRONS CYLINDERS AND CONES 289 THE SPHERE 360 CONIC SECTIONS 409 TABLE OF FORMULAS 460 Copyright

### Popular passages

Page 66 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Page 274 - If two planes are perpendicular to each other, a straight line drawn in one of them perpendicular to their intersection is perpendicular to the other plane.
Page 372 - Each side of a spherical triangle is less than the sum of the other two sides. Let ABC be a spherical triangle, AB the longest side.
Page 385 - If two angles of a spherical triangle are unequal, the sides opposite are unequal,, and the greater side is opposite the greater angle...
Page 191 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 360 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 383 - Hence the two last are right angles ; hence the arc drawn from the vertex of an isosceles spherical triangle to the middle of the base, is at right angles to the base, and bisects the vertical angle.
Page 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 150 - If two triangles have an angle of the one equal to an angle of the other, and the including sides proportional, they are similar. In the triangles ABC and A'B'C', let ZA = Z A', and let AB : A'B' = AC : A'C'. To prove that the A ABC and A'B'C
Page 376 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180� and less than 540�. (gr). If A'B'C' is the polar triangle of ABC...