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ABCD altitude axis base bisects called centre chord circle circular circumference circumscribed coincide common cone construct contained curve cylinder denote describe diagonals diameter difference dihedral angles distance divide draw drawn element ellipse equal equidistant equilateral equivalent faces fall feet figure Find formed four frustum given line given point greater height Hence homologous inches included indefinitely inscribed intersection isosceles joining lateral edges length less limit measured meet middle point opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane MN polygon polyhedron prism PROBLEM Proof proportional PROPOSITION prove pyramid radii radius ratio rectangle regular respectively right angles segment sides similar solid sphere spherical triangle square straight line surface symmetrical tangent tetrahedron THEOREM third touches triangle trihedral unit vertex vertices volume
Page 46 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 250 - ... of two oblique lines meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 148 - 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' are similar. In this case we prove the A similar by proving them mutually equiangular. Proof. Place the A A'B'C...
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 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 333 - The volume of a frustum of a 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 a mean proportional between the 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.
Page 356 - 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...
Page 45 - Two triangles are equal if two sides and the included angle of the one are equal, respectively, to two sides and the included angle of the other...