New Plane and Solid Geometry

Ginn, 1899 - Geometry - 382 pages
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Contents

 THE DEMONSTRATIONS OF GEOMETRY 9 RECTILINEAR FIGURES 21 PARALLELS AND PARALLELOGRAMS 43 PROBLEMS 67 LOCI OF Points 80 EQUALITY OF POLYGONS 90 PROBLEMS 109 CENTRAL ANGLES 116
 APPENDIX TO PLANE GEOMETRY 226 CONCURRENCE AND COLLINEARITY 238 SOLID GEOMETRY 244 THE RELATIVE POSITION OF A LINE AND A PLANE 251 PENCIL OF PLANES 265 POLYHEDRAL ANGLES 274 PROBLEMS 280 GENERAL AND REGULAR POLYHEDRA 283

Popular passages

Page 100 - The projection of a point on a line is the foot of the perpendicular from the point to the line. Thus A
Page 157 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 293 - 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 25 - 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 182 - 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 117 - The perpendicular bisector of a chord passes through the center of the circle and bisects the arcs subtended by the chord.
Page 198 - 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 313 - 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 34 - If two triangles have two sides of the one respectively equal to two sides of the other, and the...
Page 32 - 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.