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ABCD altitude base called centre chord circ circle circumference circumscribed common cone consequently construction contained convex cosine cylinder demonstration described determined diameter distance divided draw drawn equal equation equivalent evident example expressed faces fall figure follows formulas four give given greater half hence homologous inclination included inscribed join less likewise manner means measure meet multiplied namely observed opposite parallel perpendicular plane polyedron polygon prism PROBLEM Prop proportion proposed PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remain result right angles Scholium sides similar sines solid angle solution sphere spherical triangle square straight line suppose surface taken tang tangent THEOREM third triangle triangle ABC triangular vertex vertices whole
Page 152 - AMB be a section, made by a plane, in the sphere, whose centre is C. From the...
Page 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 62 - Similar triangles are to each other as the squares of their homologous sides.
Page 211 - If two angles of one triangle are equal to two angles of another triangle, the third angles are equal, and the triangles are mutually equiangular.
Page 187 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 140 - AT into equal parts .Ax, xy, yz, &c., each less than Aa, and let k be one of those parts : through the points of division pass planes parallel to the plane of the bases : the corresponding sections formed by these planes in the two pyramids will be respectively equivalent, namely, DEF to def, GHI to ghi, &c.
Page 150 - The radius of a sphere is a straight line, drawn from the centre to any point...
Page 168 - THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.