New Plane and Solid Geometry |
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Common terms and phrases
A₁ ABCD altitude angles are equal angles equal b₁ b₂ bisected bisectors C₁ called central angles chord circumference circumscribed congruent construct convex COROLLARIES corresponding Definitions diagonals diameter dihedral angle divided draw drawn edges equal angles equals the sum equilateral Exercises exterior angles figure of prop frustum geometry given line given point greater Hence hypotenuse inscribed intersecting isosceles triangle line joining line-segment locus of points meet mid-points oblique opposite sides orthocenter parallel parallelogram perigon perimeter perpendicular plane plane geometry polyhedral angle prism Prismatoid Proof prop proportional PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular polygon respectively rhombus right angle right-angled triangle similar Similarly sphere spherical spherical polygon square straight angle straight line subtend Suppose surface tangent Theorem transversal trapezoid 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 29 - The distance from a point to a line is the length of the perpendicular from that point to that line.
Page 27 - If two triangles have two sides and the included angle of the one respectively equal to two sides and the included angle of the other, the triangles are congruent.
Page 121 - The perpendicular bisector of a chord passes through the center of the circle and bisects the arcs subtended by the chord.
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 162 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Page 118 - In the same circle, or in equal circles, if two arcs are equal, their central angles are equal; and conversely.
Page 46 - Two intersecting straight lines cannot both be parallel to the same straight line.