Chicago, 1917 - Geometry, Solid - 189 pages
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altitude arcs axis base bounded circle coincide common cone of revolution construct contains corresponding cube cylinder of revolution denoted determine diagonal diameter dihedral angle dimensions distance divided draw edge equal equidistant equilateral equivalent EXERCISES faces figure Find the ratio Find the volume foot formed formula four frustum GEOMETRY given plane given point greater GROUP Hence inches included intersection lateral area lateral edges locus lune measurement meet opposite parallel parallel planes pass perpendicular plane MN plane perpendicular polar pole polygon polyhedral angle polyhedron Post principle prism Proof properties PROPOSITION prove pyramid radii radius rectangle rectangular parallelopiped regular respectively segment Show sides similar slant height solid sphere spherical triangle square straight line surface symmetrical tangent THEOREM third triangular trihedral vertex vertices zone
Page 300 - If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third.
Page 375 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 478 - In a given indefinite straight line it is required to find a point such that the sum of its distances from two given points on the same side of the straight line shall be the least possible.
Page 368 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. OM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =0= GM' . Proof. The lateral edges of GM
Page 353 - The sum of the face angles of any convex polyhedral angle is less than four right angles.
Page 303 - If two triangles have two sides of 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. If two triangles have two sides of...
Page 340 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their intersection, is perpendicular to the other.
Page 307 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.
Page 449 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...