Euclid, Elements, Book I, Proposition 31 (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).

Solution.

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.

Demonstration.

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).

Euclid, Elements of Geometry, Book I, Proposition 31 (Edited by Dionysius Lardner, 1855)

Solution.

Demonstration.

Euclid, Elements of Geometry, Book I, Proposition 31
(Edited by Dionysius Lardner, 1855)