New Plane and Solid Geometry |
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Common terms and phrases
a₁ ABCD altitude angles are equal angles equal b₁ b₂ bisect 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 altitudes equal angles equal bases equidistant Exercises exterior angles face angles frustum geometry given line given point greater Hence hypotenuse inscribed intersecting lateral area line-segment lune mid-points oblique opposite sides parallel lines 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 right angle segments similar Similarly slant height sphere spherical excess spherical polygon spherical surface spherical triangle square straight angle straight line Suppose symmetric tangent tetrahedron Theorem transverse section trihedral vertex vertices
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 118 - In the same circle, or in equal circles, if two arcs are equal, their central angles are equal; and conversely.
Page 147 - To draw a tangent to a given circle from a given point.
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 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 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 39 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included angle.
Page 46 - Two intersecting straight lines cannot both be parallel to the same straight line.
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.