Solid Geometry, with Problems and Applications
Allyn and Bacon, 1919 - Geometry, Solid - 211 pages
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altitude APPLICATIONS approximate arcs base bounded called center of similitude circle circumscribed computed cone construct contains COROLLARY corresponding cube cylinder defined definite determined diameter difference dihedral angle dimensions distance draw edges element equal EXERCISES face angles faces figure Find fixed follows formed four frustum geometry Give given plane greater Hence inches incommensurable increasing inscribed intersection lateral area length less limit line-segment locus manner measure meet Note oblique opposite parallel parallel planes parallelopiped pass perimeter perpendicular placed plane geometry polar pole polygon polyhedral angle polyhedrons prism PROBLEM projection Proof prove pyramid radius ratio rectangular regular relation respectively right circular cone right section segment sequence Show sides SIGHT similar slant height solid sphere spherical triangle square straight line Suggestion surface tangent tetrahedrons THEOREM trihedral unit variable vertex vertices volume
Page 6 - If a line is perpendicular to one of two parallel lines, it is perpendicular to the other also.
Page 45 - The sum of the face angles of any convex polyhedral angle is less than four right angles.
Page 199 - COR. 2. The volume of a rectangular parallelopiped is equal to the product of its base by its altitude.
Page 44 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 65 - The volume of any parallelopiped is equal to the product of its base and altitude. Given any parallelopiped P with area of base b and altitude h.
Page 33 - 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.
Page 33 - The projection of a straight line on a plane is a straight line in that plane.
Page 105 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Page 17 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular...
Page 6 - Two triangles are congruent if two angles and the included side of one are equal respectively to two angles and the included side of the other.