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1. A material body, as, for example, a block of wood, occupies a limited portion of space.
The boundary which separates such a body from surrounding space is called the surface of the body.
If the material which composes such a body could be conceived as taken away from it, without altering the form of the bounding surface, we should have a portion of space, with the same bounding surface as the material body.
We call this portion of space a geometrical solid, or simply a solid.
We call the surface which bounds it a geometrical surface, or simply a surface; it is also called the surface of the solid.
2. If two surfaces intersect each other, we call that which is common to both a geometrical line, or simply a line.
Thus, if surfaces AB and CD cut each other,
their common part, EF, is a line.
3. If two lines intersect each other, we call that which is common to both a geometrical point, or simply
Thus, if lines AB and CD cut each other, their common part, O, is a point.
4. A solid has extension in every direction; but this is not the case with surfaces and lines.
A point has extension in no direction.
We may conceive a surface 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 existing independently in space.
A line is produced by the motion of a moving point, a surface by the motion of a moving line, and a solid by the motion of a moving surface.
5. We define a straight line as a line which has the same direction throughout its length.
A straight line is designated by two letters anywhere upon its length, or by a single letter; thus, the straight line in the figure may be designated either AB or a.
We define a curve as a line no portion of which is straight; as CD.
We define a broken line as a line which is composed of different successive straight lines; as EFGH.
The word "line," without qualification, will be used hereafter as signifying a straight line.
6. We define a plane as a surface such that if a straight line be drawn between any two of its points, it lies entirely in the surface.
Thus, if P and Q are any two points in surface MN, and the straight line PQ lies entirely
in the surface, then MN is a plane.
7. We may conceive a straight line as being of unlimited length; we may also conceive a plane as being of unlimited extent in regard to length and breadth.
8. We define a geometrical figure as any combination of points, lines, surfaces, and solids.