Solid Geometry

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Page xxxv - If two triangles have two sides of the one equal to two sides of the...
Page 312 - The area of a lune is to the area of the surface of the sphere as the angle of the lune is to four right angles.
Page 224 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 303 - 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 258 - Aa, and let k be one of those parts ; through the points of division pass planes parallel to the plane of the bases ; the corresponding sections...
Page 220 - If a line is perpendicular to each of two lines at their point of intersection, it is perpendicular to their plane. Given FB perpendicular at B to each of two straight lines AB and BC of the plane MN. To prove FB perpendicular to the plane MN.
Page 254 - A truncated pyramid is the portion of a pyramid included between the base and a plane not parallel to the base.
Page xlii - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Page 319 - The volumes of two spheres are to each other as the cubes of their radii, or as the cubes of their diameters.
Page 308 - ... respectively equal to two face angles and the included dihedral angle of the other.

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