New Plane and Solid Geometry |
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Common terms and phrases
a₁ ABCD altitude angles equal b₁ bisect bisectors C₁ called central angles chord circle circumcenter circumference circumscribed concurrent cone congruent construct convex coplanar COROLLARIES corresponding cylinder Definitions diagonals diameter dihedral angle divided draw drawn edges equal angles equal bases equidistant equilateral Exercises exterior angles face angles frustum geometry given line given point Hence inscribed intersecting planes isosceles lateral area line-segment lune measure meet mid-points oblique opposite sides parallel lines parallelogram pencil perigon perimeter perpendicular Plane Geometry polyhedral angle prism prismatic space Prismatoid produced Proof prop PROPOSITION prove pyramid quadrilateral radians radii radius ratio rectangle regular polygon respectively right angle segments similar Similarly slant height sphere spherical polygon spherical surface square straight angle straight line Suppose symmetric tangent tetrahedron Theorem transverse section trihedral vertex vertices XVII
Popular passages
Page 104 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 161 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
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 a polygon similar to the base. Let V-ABCDE be cut by a plane parallel to its base, intersecting the lateral edges in a, b, c, d, e, and the altitude in o.
Page 29 - The third side is called the base of the isosceles triangle, and the equal sides are called the sides. A triangle which has no two sides equal is called a scalene triangle. The distance from one point to another is the length of the straight line-segment joining them. The distance from a point to a line is the length of the perpendicular from that point to that line. That this perpendicular is unique will be proved later.
Page 186 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 121 - The perpendicular bisector of a chord passes through the center of the circle and bisects the arcs subtended by the chord.
Page 202 - II, cor. 1. 2. The area of a rectangle equals the product of its base and altitude. That is, the number which represents Its square units of area is the product of the two numbers which represent its base and altitude. For in prop. II, if R' = 1, the square unit of area, then a' and 6' must each equal 1, the unit of length.
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 38 - If two triangles have two sides of the one respectively equal to two sides of the other, and the...
Page 36 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.