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### Contents

 REFERENCES TO PLANE GEOMETRY 257 LINES AND PLANES IN SPACE 267 DIHEDRAL ANGLES 292 POLYHEDRAL ANGLES 307 POLYHEDRONS 318 PYRAMIDS 334 THE PRISMATOIDAL FORMULA 346 REGULAR POLYHEDRONS 354
 THE CONE 376 CAVALIERIS THEOREM 387 THE SPHERE 395 SPHERICAL ANGLES 407 POLAR TRIANGLES 417 CONGRUENCE AND SYMMETRY OF TRIANGLES 423 MENSURATION OF THE SPHERE 429 TABLE OF FORMULAS 453

### Popular passages

Page 260 - If two triangles have two sides of 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.
Page 264 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 261 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 280 - If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane.
Page 263 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.
Page 385 - The volume of a frustum of a circular cone is equivalent to the sum of the volumes of three cones whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and the mean proportional between the bases of the frustum. Let V denote the volume, B the lewer base, b the upper base, H the altitude of a frustum of a circular cone.
Page 383 - The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. S TrR2 R* If1' = ~R^ = "cT* = -D'*
Page 266 - 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 266 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 385 - The lateral area of a frustum of a cone of revolution is equal to the circumference of a section equidistant from its bases multiplied by its slant height.