By a line we mean a straight line in its entirety, extending both ways to infinity; and by a plane, a plane surface, extending in all directions to infinity.
We accept the three-dimensional space of experience—the space assumed by Euclid—which has for its properties (among others):—
Through any two points in space one and only one line may be drawn;
Through any three points which are not in a line, one and only one plane may be placed;
The intersection of two planes is a line;
A line which has two points in common with a plane lies in the plane, hence the intersection of a line and a plane is a single point; and
Three planes which do not meet in a line have one single point in common.
These results may be stated differently in the following form:—
| I. A plane is determined— | A point is determined— |
| 1. By three points which do not lie in a line; 2. By two intersecting lines; 3. By a line and a point which does not lie in it. | 1. By three planes which do not pass through a line; 2. By two intersecting lines 3. By a plane and a line which does not lie in it. |
| A line is determined— | |
| 1. By two points; | 2. By two planes. |