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altitude axis base called centre circle circular cone circumscribed coincide common Conclusion cone cone of revolution congruent constructed cube cylinder cylinder of revolution DEFINITION denote diagonals diameter dihedral angle distance divided Draw drawn element equal equidistant equivalent face angles faces figure Find the volume formed formula four frustum given given plane given point greater half Hence homologous Hypothesis included inscribed intersection lateral area lateral edges lateral faces length less lune meet method oblique opposite parallel parallel planes parallelogram perpendicular placed plane plane determined plane MN plane parallel polar pole polyhedron prism projection Proof Prop Proposition prove pyramid radii radius respectively right angles segment sides similar solid sphere spherical triangle square straight line surface tangent tetrahedron Theorem third total area triangular trihedral truncated vertex vertices zone
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 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.