New Plane and Solid Geometry |
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Common terms and phrases
a₁ ABCD angles are equal angles equal b₁ b₂ bisected bisectors C₁ called central angles chord circle circumference circumscribed cone congruent construct convex COROLLARIES corresponding cylinder Definitions diagonals diameter dihedral angle divided draw drawn edges equal angles equals the sum 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 n-gon oblique opposite sides orthocenter parallel lines parallelepiped 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 Similarly sphere spherical polygon square straight angle straight line subtend Suppose tangent Theorem trapezoid trihedral vertex vertices XVII
Popular passages
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 161 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
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 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.
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 65 - The lines joining the mid-points of the opposite sides of a quadrilateral bisect each other.
Page 40 - If two triangles have the three sides of the one respectively equal to the three sides of the other, the triangles are congruent, C Given A ABC, AB'C, with AB = AB', BC = B'C, and AC = AC.