Page:Carroll - Euclid and His Modern Rivals.djvu/73

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Sc. II. § 4.]
PAIRS OF LINES.
35

∗8. Through a given point, without a given Line, a Line may be drawn such that the two Lines are equidistantial from each other.

9. A Pair of Lines, of which one has two points on the same side of, and equidistant from, the other, are equally inclined to any transversal.

10. A Pair of Lines, which are unequally inclined to a certain transversal, are such that any two points on one, which are on the same side of the other, are not equidistant from it.

11. A Pair of Lines, which are equally inclined to a certain transversal, are equidistantial from each other.

12. A Pair of Lines, of which one has two points on the same side of, and not equidistant from, the other, are unequally inclined to any transversal.

13. A Pair of Lines, of which one has two points on the same side of, and equidistant from, the other, are equidistantial from each other.

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

15. (a) A Pair of Lines, which are separational from a third Line, are not intersectional with each other.

(b) A Pair of Lines, which have a common point

D 2