INTRODUCTION

Excerpts

In plane geometry each figure is restricted so that all of its parts lie in the same plane. Such figures are called *two-dimensional figures*.
A figure, all parts of which lie in one straight line, is a *one-dimensional figure*, while a point is of zero dimensions.
In plane geometry, two lines which do not meet are parallel, while in solid geometry, two lines which do not meet need not be parallel. That is, they may not be in the same plane. Lines which are not parallel and do not meet are called *skew* lines.
In plane geometry, “the locus of all points at a given distance from a given point” is a circle, while in solid geometry this locus is a sphere.
If all parts of the figure are not required to lie in one plane, the theorem just quoted is far from true.
A plane is designated by a single letter in it, by two letters at opposite corners of the parallelogram representing it, or by any three letters in it but not in the same straight line.
The area of a circle is one half the circumference times the radius, or in symbols:
Through a point not on a given line only one straight line can be drawn parallel to that line.

ah = bk
In any triangle, the product of one side and its altitude equals the product of another side and its altitude.
a = \tfrac{1}{2} \cdot 2\pi r \cdot r = \pi r^2.
The area of a circle is one half the circumference times the radius, which equals pi times the square of the radius.

No exercises in this chapter.