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ABCD adjacent altitude applied base bisect called centre chord circle circumference coincide common conceived construct COROLLARY corresponding DEMONSTRATION determine diagonals diameter diedral difference direction distance divided draw drawn edges equal equivalent exterior angles extremities faces fall figure four given given angle given line greater Hence homologous hypothesis inscribed intersect joining latter length less Let ABC manner measured meet oblique lines opposite sides parallel parallelogram pass path perimeter perpendicular placed plane polygon position prism produced proportional PROPOSITION prove pyramid Q. E. D. PROPOSITION quadrilateral radii radius ratio reason rectangle regular polygon respectively revolve right angles segment sides similar solid SOLUTION sphere square straight line supplemental surface tangent Theorem.-The third triangle triedrals vertex vertices volume whence
Page 284 - A Sphere is a solid bounded by a surface every point in which is equally distant from a point within called the Centre.
Page xii - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.
Page 301 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 296 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 167 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 321 - A spherical sector is the portion of a sphere generated by the revolution of a circular sector about any diameter of the circle of which the sector is a part.
Page 104 - In an isosceles triangle the angles opposite the equal sides are equal.