1. A material body, such as a block of wood, occupies a limited or bounded portion of space. The boundary which separates such a body from surrounding space is called the surface of the body. 2. If the material composing such a body could be conceived as taken away from it, without altering the form or shape of the bounding surface, there would remain a portion of space having the same bounding surface as the former material body; this portion of space is called a geometrical solid, or simply a solid. The surface which bounds it is called a geometrical surface, or simply a surface; it is also called the surface of the solid. 3. If two geometrical surfaces intersect each other, that which is common to both is called a geometrical line, or simply a line. Thus, if surfaces AB and CD cut each other, their common intersection, EF, is a line. E C D F B 4. If two geometrical lines intersect each other, that which is common to both is called a geometrical point, or simply a point. B Thus, if lines AB and CD cut each other, their common intersection, O, is a point. 5. A solid has extension in every direction; but this is not true of surfaces and lines. A point has extension in no direction, but simply position in space. 6. A surface may be conceived as existing independently in space, without reference to the solid whose boundary it. forms. In like manner, we may conceive of lines and points as having an independent existence in space. 7. A straight line, or right line, is a line which has the same direction throughout its length; as AB. A curved line, or curve, is a line no portion of which is straight; as CD. A broken line is a line which is composed of different successive straight lines; as EFGH. 8. The word "line" will be used hereafter as signifying a straight line. 9. A plane surface, or plane, is a surface such that the straight line joining any two of its points lies entirely in the surface. M Thus, if P and Q are any two points in P surface MN, and the straight line joining N P and Q lies entirely in the surface, then MN is a plane. 10. A curved surface is a surface no portion of which is plane. |