It also follows, as was pointed out in § 3, in discussing the definitions of Book I., that a plane is determined already by one straight line and a point without it, viz. if all lines be drawn through the point, and cutting the line, they will form a plane.
This may be stated thus:—
A plane is determined—
1st, By a straight line and a point which does not lie on it;
2nd, By three points which do not lie in a straight line; for if two of these points be joined by a straight line we have case 1;
3rd, By two intersecting straight lines; for the point of intersection and two other points, one in each line, give case 2;
4th, By two parallel lines (Def. 35, I.).
The third case of this theorem is Euclid’s
Prop. 2. Two straight lines which cut one another are in one plane, and three straight lines which meet one another are in one plane.
And the fourth is Euclid’s