### Contents

 ANGLES 13 AXIOMS 19 TRIANGLES 28 EXERCISES 69 THE CIRCLE LOCI PROBLEMS 78 TANGENT AND SECANTS 90 PLANE LOCI 102 PAGE 111
 EXERCISES 221 PLANES AND POLYHEDRAL ANGLES 225 PLANES AND PARALLELS 234 DIHEDRAL ANGLES 240 POLYHEDRAL ANGLES 251 EXERCISES 258 PYRAMIDS 275 THE REGULAR POLYHEDRONS 286

 LIMITS 117 PROPORTIONAL ANGLES AND LINES 128 EXERCISES 136 SIMILAR POLYGONS 144 RATIOS OF CERTAIN LINES 151 CONSTRUCTIONS 157 AREAS AND THEIR COMPARISON 165 EXERCISES 186 EXERCISES 194 AREA OF THE CIRCLE 210
 THE THREE ROUND BODIES 293 SPHERES 300 SPHERICAL ANGLES AND POLYGONS 309 EXERCISES 330 CONES 336 EXERCISES 342 EXERCISES 352 SYMMETRICAL POLYHEDRONS 360 INDEX 371 Copyright

### Popular passages

Page 308 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 298 - Sphere is a body bounded by a uniformly curved surface, all the points of which are equally distant from a point within called the center.
Page 283 - 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 113 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Page 373 - The object of these primers is to convey information in such a manner as to make it both intelligible and interesting to very young pupils, and so to discipline their minds as to incline them to more systematic after-studies. They are not only an aid to the pupil, but to the teacher, lightening the task of each by an agreeable, easy, and natural method of instruction.
Page 178 - ... the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 123 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 118 - If the product of two numbers is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Page 179 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Page 272 - Two prisms are to each other as the products of their bases by their altitudes ; prisms having equivalent bases are to each other as their altitudes; prisms having equal altitudes are to each other as their bases ; prisms having equivalent bases and equal altitudes are equivalent.