The Essentials of Geometry
D.C. Heath & Company, 1899 - Geometry - 395 pages
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ABCD altitude approaches the limit axis base bounded called centre circle circumference circumscribed coincide common cone cone of revolution construct convex cube denote determined diameter diedral angle dimensions distance divided Draw lines drawn equally distant equilateral equivalent faces Find foot frustum Given Given line given point Hence homologous indefinitely inscribed intersection lateral area lateral edges lateral surface lies line drawn lune measure meet multiplied mutually Note parallel parallelopiped passing perimeter perpendicular plane MN polar pole polyedral polyedron prism produced Proof PROP Prove pyramid radii radius rectangular regular respectively revolved sector sides similar slant height solid sphere spherical triangle squares straight line surface tangent tetraedron THEOREM total surface triangular triedral unit vertex vertices volume Whence
Page 371 - A zone is a portion of the surface of a sphere included between two parallel planes.
Page 261 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Page 336 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The...
Page 328 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 237 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Page 243 - The perpendicular is the shortest line that can be drawn from a point to a straight line.
Page 353 - 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.
Page 375 - S7rR = 4WR1. (789) Therefore, the area of the surface of a sphere is equal to the area of four great circles. 791. COR. 2. TJie areas of the surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters.
Page 297 - Pyramids are to each other as the products of their bases by their altitudes.
Page 347 - If two angles of a spherical triangle are unequal, the sides opposite are unequal,, and the greater side is opposite the greater angle...