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A₁ A₂ ABCDE altitude approach a limit axis b₁ b₂ C₁ C₂ called circle circular sector circumference coincide congruent conical surface contains convex COROLLARY cube cylindrical surface d₁ d₂ Definition Denote dihedral angle distance element equal face angles figure frustum geometry given line given point greatest number h₂ homothetic intersecting lines irrational number l₁ lateral area lateral edges least number less line segment locus of points m₁ m₂ number of sides octahedron parallel lines parallelepiped pencil of planes placed in reverse plane perpendicular points equidistant pole polyhedral angle polyhedron prismatic surface Proof prove R₂ radius ratio of similitude rational numbers real numbers respectively right circular cone right section S-ABC side approaches zero skew lines slant height sphere spherical angle spherical polygon spherical surface spherical triangle straight line surface of revolution symmetrical tangent THEOREM transverse section trihedral vertex vertices volume
Page 144 - If two spherical triangles on the same sphere, or equal spheres, have two sides and the -included angle of one equal respectively to two sides and the included angle of the other, I. They are equal if the equal parts occur in the same order. II. They are symmetrical if the equal parts occur in the reverse order. D
Page 118 - The lateral area of a frustum of a cone of revolution is equal to one half the sum of the circumferences of its bases multiplied by its slant height. Given L the lateral area, C and C...
Page 93 - Assuming that 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 155 - The shortest line that can be drawn on the surface of a sphere between two points is the arc of a great circle, not greater than a semicircumference, joining the two points.
Page 43 - If two triangles have two sides of the 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. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 161 - The surface of a sphere is equal to four times the area of a circle...
Page 166 - The volume of a spherical sector is equal to the product of the zone which forms its base into one-third the radius of the sphere.
Page 153 - The area of a lune is to the surface of the sphere as the angle of the lune is to four right angles, or as the arc which measures that angle is to the circumference.