Euclid, Elements of Geometry, Book I, Proposition 30
(Edited by Dionysius Lardner, 1855)

Proposition XXX. Theorem.
[Euclid, ed. Lardner, 1855, on Google Books]

(121) If two right lines (A B, C D) be parallel to the same right line (E F), they are parallel to each other.

Let the right line G K intersect them; the angle A G H is equal to the angle G H F (XXIX); A B C D E F G H K and also the angle H K D is equal to G H F (XXIX); therefore A G H is equal to G K D; and therefore the right lines A B and C D are parallel.

(122)   Cor.—Hence two parallels to the same line cannot pass through the same point. This is, in fact, equivalent to the twelfth axiom (115).

Book I: Euclid, Elements, Book I (ed. Dionysius Lardner, 11th Edition, 1855)

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