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A'B'C and D'E'F ABC and DEF ABC-B axis base and altitude bases are equal bisect called centre circle circumference coincide common altitude common vertex conical surface Corollary cube cuboid cylinder DEFINITIONS diagram diameter dicular diedral angle dodecaedron Draw equal with respect equivalent feet Find the volume frustum Hence hexaedron icosaedron intersection lateral edges lateral faces lateral surface Let the line lune mutually equal mutually equiangular mutually equilateral number of faces octaedron parallelogram parallelopiped pass perimeter perpen perpendicular to MN plane angle plane PQ polar triangle pole polyedral angle prismoid Q. E. D. Proposition radii radius regular polyedrons regular polygon right angles right circular cone right prism right section Scholium sides slant height spherical angle spherical excess spherical polygon spherical triangle straight line symmetrical Theorem tri-rectangular triangle triangles are equal triangular prism triangular pyramids triedral vertices 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.