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ABCD altitude angles are equal axis base bisector bisects called centre chord circumference circumscribed coincide cone construct curve cylinder denote diagonals diameter dihedral angles directrix distance divide draw ellipse equal respectively equiangular equidistant equilateral triangle equivalent exterior angle face angles feet Find the area frustum given circle given line given point given straight line greater Hence homologous sides hyperbola hypotenuse inches intersection lateral area lateral edges latus rectum locus measured middle point number of sides opposite parabola parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedron prism Proof proportional Proposition prove pyramid radii radius ratio rectangle regular polygon right angle right triangle Scholium secant segment similar polygons slant height sphere spherical polygon spherical triangle square surface tangent tetrahedron Theorem trapezoid triangle ABC trihedral vertex vertices volume
Page 96 - Any two sides of a triangle are together greater than the third side.
Page 187 - Two triangles having 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 64 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 141 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 134 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Page 304 - The frustum of a triangular pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum and whose bases are the lower base, the upper base, and a mean proportional between the two bases of the frustum.
Page 352 - 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 403 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.