Page:Carroll - Euclid and His Modern Rivals.djvu/72

34 {| 1. A Pair of separational Lines are equally inclined to any transversal. ∗2. A Pair of Lines, which are unequally inclined to a certain transversal, are intersectional. 3. Through a given Point, without a given Line, a Line may be drawn such that the two Lines are equally inclined to any transversal. 4. A Pair of Lines, which are equally inclined to a certain transversal, are so to any transversal. 5. A Pair of Lines, which are unequally inclined to a certain transversal, are so to any transversal. 6. A Pair of separational Lines are equidistantial from each other. ∗7. A Pair of Lines, of which one has two points on the same side of, and not equidistant from, the other, are intersectional.
 * II.
 * Containing eighteen Propositions, of which no one is an undisputed Axiom, but all are real and valid Theorems, which, though not deducible from undisputed Axioms, are such that, if any one be admitted as an Axiom, the rest can he proved.
 * [N. B. Those marked ∗ have been, or parts of them have been, proposed as Axioms.
 * [N. B. Those marked ∗ have been, or parts of them have been, proposed as Axioms.
 * [N. B. Those marked ∗ have been, or parts of them have been, proposed as Axioms.
 * }
 * }
 * }