(Edited by Dionysius Lardner, 1855)

Proposition XXXI. Problem.

[Euclid, ed. Lardner, 1855, on `Google Books`]

(123) | Through a given point (C) to draw a right line parallel to a given right line (A B). |

In the line A B take any point F, join C F, and at the point C and with the right line C F make the angle F C E equal to A F C (XXIII), but at the opposite side of the line C F; the line D E is parallel to A B.

For the right line F C intersecting the lines D E and A B makes the alternate angles E C F and A F C equal, and therefore the lines are parallel (XXVII).

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

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