Elements of Geometry: Geometry of spaceHarper & Brothers, 1898 - Geometry |
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Common terms and phrases
ABCD altitude angles are equal bisecting bisector circumference circumscribed coincide cone of revolution conical surface Construct cube cylinder of revolution Def.-The Defs.-A diagonals diameter diedral angles distance divided equiangular polygon equilateral triangle equivalent Exercise.-The face angles Find the locus formed frustum geometry given circle given plane given point given straight line Hence Hint.-Let inscribed lateral area lateral edges lateral faces lune meet middle points octaedron opposite parallelogram parallelopiped pass a plane perimeter perpendicular perpendicular to MN plane MN point of intersection pole polyedral angle polyedron prismatic surface PROVE Q. E. D. PROPOSITION quadrilateral radical axis radii radius ratio of similitude rectangular parallelopiped regular polygon regular pyramid regular tetraedron right angles right section right triangle slant height spherical polygon spherical surface spherical triangle square symmetrical tangent THEOREM triangle ABC triangular prism triedral truncated vertices
Popular passages
Page 389 - 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...
Page 472 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 386 - Two triangles are congruent if (a) two sides and the included angle of one are equal, respectively, to two sides and the included angle of the other...
Page 305 - The volume of any prism is equal to the product of its base and altitude. GIVEN— the prism ABCDE-R with base ABCDE and altitude RO.
Page 422 - The lateral area of a frustum of a cone of revolution is equal to half the sum of the circumferences of its bases multiplied by its slant height.
Page 307 - A regular pyramid is a pyramid whose base is a regular polygon, and whose vertex lies in the perpendicular erected at the centre of the base.
Page 296 - Two rectangular parallelopipeds having equal bases are to each other as their altitudes. Let AB and A'B' be the altitudes of the two rectangular parallelopipeds P and P', which have equal bases.
Page 251 - PQ, and therefore cuts MN, by the first part of the proposition. Therefore the plane CD, in which BC lies, will cut MN.
Page 374 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.
Page 266 - Theorem. The acute angle which a line makes with its own projection on a plane is the least angle which it makes with any line in that plane. Given the line AB, cutting plane P at 0, A'B' the projection of AB on P, and XX' any other line in P, through 0.