FIRST BOOK OF MATHEMATICS.
I. ELEMENTARY DEFINITIONS.
Point—Line—Plane—Circle—Angle—Parallel Lines.
1. Each page or side of this leaf is a surface. It has a certain shape or form. It has a certain size or magnitude, depending on its length and breadth. It may be quite flat, or more or less bent—that is, curved.
2. The edges or boundaries of the leaf are lines. Each line has length, but not breadth, or next to none. In geometry, we speak of lines as if they had no breadth, though we cannot draw any line entirely without breadth. But we may reason about them as if they had no breadth. Also, the edges of the leaf may be straight or curved.
3. But the book has more than length and breadth. It has also thickness or depth. In geometry, a thing that has these three properties is called a solid. A solid, in a geometrical sense, need not have body or substance all through. An empty room, a vessel from which the air has been taken out, or a portion of space considered by itself, are solids, speaking geometrically.
4. The boundary of a solid is a surface, or surfaces.
