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ABCD adjacent altitude apply base bisect called centre chord circle circumference coincide common conceive cone consequently construct contain Converse corresponding DEM.-Let demonstration describe diagonals diameter diedral difference direction distance dividers draw drawn edge equal equiangular equivalent extremities faces facial angles fall feet figure four given given line greater Hence homologous inches included inscribed intersect joining latter length less lune manner mean measured meet oblique opposite parallel parallelogram passing path perpendicular plane pole polygon position prism produced PROP proportional PROPOSITION pyramid quadrilateral radii radius ratio reason rectangle regular represent respectively revolve right angles sides similar solid sphere spherical triangle square straight line student supplement surface tangent Theorem.-The third triangle triedral unit vertex vertices volume whence
Page 219 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 141 - The area of a trapezoid is equal to the product of its altitude...
Page 233 - If two semicircumferences of great circles intersect on the surface of a hemisphere, the sum of the two opposite triangles thus formed is equivalent to a lune whose angle is that included by the semicircumferences. DEM. — Let the semicircumferences CEB and DEA intersect at E on the surface of the...
Page 209 - A sphere is a solid, bounded by one continued convex surface, every point of which is equally distant from a point within, called the centre.
Page 106 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Page 138 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 127 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 53 - Similar triangles are to each other as the squares of their homologous sides.