# Plane and Solid Geometry

American Book Company, 1899 - Geometry - 384 pages

### Contents

 Lines and Surfaces 10 Demonstration or Proof 17 Parallel Lines 27 Triangles 33 Area and Equivalence 74 Supplementary Exercises 78 Measurement 98 Summary 122
 BOOK VI 213 Maxima and Minima 230 BOOK VII 243 Dihedral Angles 257 Polyhedral Angles 267 BOOK VIII 273 Pyramids 287 Similar and Regular Polyhedrons 299

 BOOK III 135 BOOK IV 147 Supplementary Exercises 169 BOOK V 173
 Cylinders and Cones 309 Supplementary Exercises 325 Copyright

### Popular passages

Page 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...
Page 33 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Page 219 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 217 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.
Page 136 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Page 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
Page 374 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 176 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.