## Solid Geometry |

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altitude arcs base called circle circumference circumscribed common concurrent congruent contains convex coplanar COROLLARIES corresponding cube cylinder Definitions determine diagonal diameter dihedral angle distance divided draw drawn edges elements entire equal equidistant equilateral Exercises face angles faces figure Find formula four frustum Geometry given given plane given point greater Hence intersecting lateral area length less lies lune measure meet oblique opposite parallel planes pass perpendicular polar pole polyhedral angle polyhedron portion prism prismatic space projection Proof prop proportional PROPOSITION prove pyramid radii radius ratio rectangular parallelepiped regular Required respectively segment sides similar Similarly slant height solid sphere spherical polygon spherical surface spherical triangle square step straight line Suppose symmetric tetrahedron Theorem transverse section triangular trihedral vertex vertices volume

### Popular passages

Page 297 - If a pyramid is cut by a plane parallel to the base, (1) the edges and altitude are divided proportionally, (2) the section is similar to the base.

Page 317 - A plane surface, or a plane, is a surface in which, if any two points are taken, the straight line joining these points lies wholly in the surface.

Page 309 - The lateral area of a regular pyramid equals half the product of its slant height and the perimeter of its base. For in the above theorem, let B' = 0 ; then s' and p

Page 260 - Theorem. 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 O, A'B' the projection of AB on P, and XX' any other line in P, through O.

Page 283 - If a polyhedron is such that no straight line can be drawn to cut its surface more than twice, it is said to be convex; otherwise it is said to be concave. Unless the contrary is stated, the word polyhedron means convex polyhedron.

Page 268 - Theorem. If each of two intersecting planes is perpendicular to a third plane, their line of intersection is also perpendicular to that plane. Given two planes, Q, R, intersecting in OP, and each perpendicular to plane M. To prove that OP _L M.

Page 252 - I, prop. XII 3. .'.by folding A ACP over AC as an axis, it can be brought to coincide with A A CP'. § 57 339. Definitions. A line is said to be perpendicular to a plane when it is perpendicular to every line in that plane which passes through its foot, — ie the point where it meets the plane. The plane is then said to be perpendicular to the line. If a line meets a plane, and is not perpendicular to it, it is said to be oblique to the plane. COROLLARIES. 1. If a line is perpendicular to each of...

Page 267 - If two planes are perpendicular to each other, a line drawn in one of them perpendicular to their intersection is perpendicular to the other.

Page 313 - A polyhedron is called a prismatoid if it has for bases two polygons in parallel planes, and for lateral faces triangles or trapezoids with one side common with one base and the opposite vertex or side common with the other base.

Page 251 - O'A', OB = O'B', AB = AB'. I, prop. XXIV 7. .'. A ABO .£ A A'B'O', and Z AOB = Z A'O'B'. I, prop. XII 2. THE RELATIVE POSITION OF A LINE AND A PLANE. PROPOSITION VI. 338. Theorem. If a line is perpendicular to each of two intersecting lines, it is perpendicular to every other line lying in their plane and passing through their point of intersection.