28
MINOS AND EUCLID.
[Act I.
Euc. We shall find the Table of Propositions, which I now lay before you, very convenient to refer to. I have placed contranominal Propositions (i.e. Propositions of the form 'All X is Y,' 'All not-Y is not-X') in the same section.
| Table I. |
| Containing twenty Propositions, of which some are undisputed Axioms, and the rest real and valid Theorems, deducible from undisputed Axioms. |
| [N.B. Those marked ∗ have been proposed as Axioms.] |
| ∗1. A Pair of Lines, which have two common points, are coincidental.
or ∗. Two Lines cannot enclose a space. [Euc. Ax.] |
|
2. (a) A Pair of Lines, which have a separate point, have not two common points. (b) A Pair of Lines, which have a common point and a separate point, are intersectional. |
| 3. If there be given a Line and a point, it is possible to draw a Line, through the given point, intersectional with the given Line. |
| 4. A Pair of intersectional Lines are unequally inclined to any transversal.
Cor. 1. In either pair of alternate angles, that, which is on the side, of the transversal, remote from the point of intersection, is the greater. [I. 16.] Cor. 2. Every exterior angle, which is on the side, of the transversal, next to the point of intersection, is |
