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||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.]
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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.]
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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.]
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Playfair's Axiom.
A pair of intersectional Lines cannot both be separational from the same Line.
[This is II. 16 (a).]
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