The Elements of Solid Geometry
Leach, Shewell & Sanborn, 1893 - Geometry, Solid - 95 pages
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ABC and DEF altitude axis base base and altitude bounded called centre circle circumference coincide common cone construct COROLLARY corresponding cube cutting cylinder DEFINITIONS diagram diameter diedral angle distance divided draw drawn equal with respect equivalent face angles feet follows formed frustum greater Hence included inscribed intersection lateral edges lateral faces lateral surface less limit lune manner measure mutually equal oblique opposite parallel parallel planes parallelopiped pass perimeter perpendicular plane plane MN polar triangle pole polyedral angle polygon prism Problem PROPOSITION prove pyramid radius regular regular polyedrons represent respect right angles right prism right section SCHOLIUM shown sides similar solid sphere spherical triangle squares straight line surface symmetrical termed THEOREM triangles ABC triedral vertex vertices volume wedge
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 30 - The lateral or total areas of two similar cglinders of revolution are to each other as the squares of their altitudes, or as the squares of the radii of their bases ; and their volumes are to each, other as the cubes of their altitudes, or as the cubes of the radii of their bases. Let S and s...
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 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.
Page 29 - The lateral area of a prism is equal to the product of the perimeter of a right section and a lateral edge.
Page 61 - 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...