New Plane and Solid Geometry |
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Common terms and phrases
a₁ ABCD altitude angles are equal angles equal b₁ bisected bisectors C₁ called central angles chord circle circumcenter circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder Definitions diagonals diameter dihedral angle divided draw drawn edges equal angles equal bases Exercises exterior angles faces figure of prop frustum geometry given line given point greater Hence hypotenuse inscribed intersecting lines isosceles triangle line-segment locus of points meet mid-points oblique opposite sides parallel lines parallelepiped parallelogram perigon perimeter perpendicular plane polyhedral angle prism prismatic space Prismatoid produced Proof prop proportional PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively rhombus right angle segments Similarly slant height sphere spherical polygon square straight angle straight line Suppose symmetric tangent tetrahedron Theorem transverse section trihedral vertex vertices
Popular passages
Page 40 - Theorem. If two triangles have the three sides of the one respectively equal to the three sides of the other, the triangles are congruent.
Page 161 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 118 - In the same circle, or in equal circles, if two arcs are equal, their central angles are equal; and conversely.
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 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 46 - Two intersecting straight lines cannot both be parallel to the same straight line.
Page 162 - If the product of two numbers is equal to the product of two other numbers, either two may be made the means, and the other two the extremes of a proportion.
Page 111 - To construct a parallelogram equal to a given triangle and having one of its angles equal to a given angle.