Table III. |
Containing five Propositions, taken from Table II, which have been proposed as Axioms. |
Euclid's Axiom. A Pair of Lines, which have a separate point and make, with a certain transversal, two interior angles on one side of it together less than two right angles, are intersectional on that side. [This is one case of II. 2, with an additional statement as to the side of the transversal on which the Lines will meet.] |
T. Simpson's Axiom. A Pair of Lines, which have a separate point and of which one has two points on the same side of, and not equidistant from, the other, are intersectional. [This is II. 7.] |
Clavius' Axiom. Through a given Point, without a given Line, a Line may be drawn equidistantial from the given Line. [This is part of II, 8.] |
Playfair's Axiom. A pair of intersectional Lines cannot both be separational from the same Line. [This is II. 16 (a).] |
Page:Carroll - Euclid and His Modern Rivals.djvu/75
Jump to navigation
Jump to search
Sc. II. § 4.]
PAIRS OF LINES.
37
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/9c/Carroll_-_Euclid_and_His_Modern_Rivals.djvu/page75-1024px-Carroll_-_Euclid_and_His_Modern_Rivals.djvu.jpg)