# New Plane and Solid Geometry

Ginn, 1899 - Geometry - 382 pages
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### Contents

 ELEMENTARY DEFINITIONS 1 THE DEMONSTRATIONS OF GEOMETRY 9 PRELIMINARY PROPOSITIONS 13 PLANE GEOMETRY 14 RECTILINEAR FIGURES 21 TRIANGLES 33 PARALLELS AND PARALLELOGRAMS 47 PROBLEMS 67
 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 PAGE 283

 LOCI OF POINTS 80 EQUALITY OF POLYGONS 90 PROBLEMS 109 PRACTICAL MENSURATION 112 CIRCLES DEFINITIONS 114 CENTRAL ANGLES 117 CHORDS AND TANGENTS 133 ANGLES FORMED BY CHORDS SECANTS AND TANGENTS 4 INSCRIBED AND CIRCUMSCRIBED TRIANGLES AND QUADRILAT ERALS 136 Two CIRCLES 151 METHODS 152 RATIO AND PROPORTION 159 THE THEORY OF LIMITS 167 A PENCIL CUT BY ANTIPARALLELS OR BY A CIRCUMFERENCE 177 PROBLEMS 194 THE PARTITION OF THE PERIGON 205 THE MENSURATION OF THE CIRCLE 216
 PAGE 1 286 PRISMATIC AND PYRAMIDAL SPACE PRISMS AND PYRAMIDS 291 THE MENSURATION OF THE PRISM 298 9 299 THE MENSURATION OF THE PYRAMID 308 THE CYLINDER CONE AND SPHERE 317 THE SPHERE 326 THE MENSURATION OF THE SPHERE 355 SIMILAR SOLIDS 364 TABLES 371 INDEX 379 67 381 136 146 Copyright

### 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.