SECTION I. FUNDAMENTAL IDEAS. SPACE, SURFACE, LINE, POINT, FIGURE. 1. ANYTHING which is material occupies space. Whatever we can touch, or move, is material; anything to which we can apply force is material. We may also define space as that in which movement is possible in any direction whatever. 2. DEFINITION. A limited portion of space is called a solid. Thus a solid is the space occupied by a material thing. For example a cubic lump of iron occupies a portion of space called a cube. The cube and the lump of iron are quite distinct ideas. We can think of the cube without thinking of the lump of iron. The cube is the portion of space occupied, the lump of iron that which happens to occupy that portion of space. Thus a solid is the space occupied by anything, not the thing itself; the thing itself is called a body. L. E. 1 3. DEFINITION. A solid is bounded by a surface. Thus a surface is quite different from a solid; a surface occupies no space; it is only the boundary of space; a very thin solid is not a surface; a solid, no matter how thin it may be, is enclosed by its surface. When a solid is very thin, there are two portions of its surface very close together. The paper on which this is printed is a thin solid. The ink upon the paper is a thin solid; each letter is a solid lump of printer's ink and has two parts of its surface very near each other, one on the paper, another which we see. The student must notice that a number of surfaces which are close together do not make up a solid. If the surfaces coincide they make up a surface only. If they are not exactly coincident they have a thin solid between them. 4. DEF. A portion of a surface is bounded by a line. Thus a line is a boundary of a portion of surface, just as a surface is a boundary of a portion of space. A very narrow portion of surface is not a line. When a portion of surface is very narrow, there are two portions of its bounding line which are very close together. The edge of the paper on which this is printed when it was first . cut was a narrow surface bounded by two lines. A printed 'line' is a very thin rod of printer's ink, the upper surface of which is bounded by two lines. A printed 'line' is a solid. The student must notice that a number of lines which are close together do not make up a surface; if the lines coincide they are one line simply; if they do not exactly coincide they have a narrow surface between them. 5. DEF. A portion of a line is bounded by points. Thus a point is a boundary of a portion of a line, just as a line is a boundary of a portion of surface. When two lines intersect, their intersection is a point. Thus a point is a position. The student must notice that a number of points which are close together do not make up a line; if the points coincide they are one point merely; if they do not exactly coincide, they have a short portion of line between them. |