The Elements of Solid Geometry
Leach, Shewell & Sanborn, 1893 - Geometry, Solid - 95 pages
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Common terms and phrases
axis base and altitude bounded called centre circle circumference coincide common common altitude cone construct COROLLARY corresponding cube curve cutting cylinder DEFINITIONS diagram diameter diedral angle distance divided draw drawn elements equivalent face angles feet formed frustum given greater Hence included increasing inscribed intersection lateral edges lateral faces lateral surface less limit lune manner measure meet mutually equal oblique one-half opposite parallel parallel planes parallelogram parallelopiped pass perimeter perpendicular plane plane MN pole polyedral angle polygon Problem PROPOSITION prove pyramid radius regarded represent respectively revolved right angles right prism right section SCHOLIUM shown sides similar slant height solid sphere spherical triangle squares straight line symmetrical taken termed THEOREM tion triangular prism triedral vertices volume
Page 48 - 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 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Page 4 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Page 49 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 94 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Page 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Page 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Page 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Page 56 - 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.