Euclid, Elements of Geometry, Book I, Proposition 3 (Edited by Dionysius Lardner, 1855)

Proposition III. Problem.
[Euclid, ed. Lardner, 1855, on Google Books]

 (61) From the greater (A B), of two given right lines to cut off a part equal to the less (C).

Solution.

From either extremity A of the greater let a right line A D be drawn equal to the less C (II), and with the point A as centre, and the radius A D let a circle be described (41). The part A E of the greater cut off by this circle will be equal to the less C.

Demonstration.

For A E and A D are equal, being radii of the same circle (17); and C and A D are equal by the construction. Hence A E and C are equal.

By a similar construction, the less might be produced until it equal the greater. From an extremity of the less let a line equal to the greater be drawn, and a circle be described with this line as radius. Let the less be produced to meet this circle.

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