Page:Carroll - Euclid and His Modern Rivals.djvu/67

---

greater than the interior opposite angle on the same side.[I. 16.]

Cor. 3. The pair of interior angles, which are on the side, of the transversal, next to the point of intersection, are together less than two right angles.[I. 17.]

5. A Pair of Lines, which have a common point and are equally inclined to a certain transversal, are coincidental.

6. A Pair of Lines, which have a separate point and are equally inclined to a certain transversal, are separational.[I. 27, 28.]

7. If there be given a Line and a point without it, it is possible to draw a Line, through the given point, separational from the given Line.[I. 31.]

8. A Pair of intersectional Lines are such that any two points on one, which are on the same side of the other, are not equidistant from it.

Cor. That which is the more remote from the point of intersection has the greater distance.

9. A Pair of Lines, which have a common point and of which one has two points on the same side of and equidistant from the other, are coincidental.

10. A Pair of Lines, which have a separate point and of which one has two points on the same side of and equidistant from the other, are separational.

11. Each of a Pair of intersectional Lines has, in each portion of it, a point whose distance from the other exceeds any given length.

or

A Pair of intersectional Lines diverge without limit.