Solid Geometry |
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AABC ABCD altitude Analysis and construction angles are equal axis bisector bisects circular cylinder congruent spheres conical surface corresponding cube diameter dihedral angle equal chords equal segments EXERCISES face angles Find the area Find the total Find the volume frustum given plane given point Hypothesis increased indefinitely inscribed intersecting planes isosceles lateral area lateral edges lateral faces locus of points lune Mathematical measure number of lateral Outline of proof parallel planes parallelogram plane angle plane containing Plane Geometry plane parallel plane perpendicular points equally distant polar pole polyhedral angle polyhedrons prismatoid prove radii radius rectangle regular polygon regular polyhedrons revolves right angles right circular cone right section segment joining segments or angles semicircle skew lines slant height spherical angle spherical polygon spherical surface spherical triangle square straight line symmetric tangent tetrahedron THEOREM total area triangular prism trihedral vertex vertices
Popular passages
Page 87 - The distance between two points on the surface of a sphere is the length of the minor arc of a great circle between them.
Page 183 - Square Measure 144 square inches (sq. in.) = 1 square foot (sq. ft.) 9 square feet = 1 square yard (sq.
Page 197 - The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse: a2 + b2 = c2.
Page 50 - A Plane Surface, or a Plane, is a surface in which, if any two points be taken, the straight line joining these points will lie wholly in the surface.
Page 20 - A line perpendicular to one of two parallels is perpendicular to the other also.
Page 197 - The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle, and likewise the external bisector externally.
Page 200 - The area of a trapezoid is equal to one-half the product of the altitude and the sum of the bases. THEOREM 116. Two parallelograms or two triangles are equivalent if 1. They have equal bases and are between the same parallels. 2. a = a
Page 198 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 25 - 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 195 - Multiplying or dividing both terms of a ratio by the same number does not change the value of the ratio.