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). |
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.
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.
Book I: Euclid, Elements, Book I (ed. Dionysius Lardner, 11th Edition, 1855)
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This proposition in other editions:
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.