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Book I, Proposition 2 Given a point and a straight line, to draw from the point a straight line of equal length to the given straight line.
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Proof. Construct the equilateral triangle ADB (proposition I.1). Extend the straight lines DA and DB indefinitely in one direction. Draw a circle with center B and radius BC. Notice F. Draw a circle with center D and radius DF. Notice G. Since DA is equal to DB, AG must be equal to BF (because DG was equal to DF). Hence AG is equal to BF, which was equal to BC.
Drag e.g. A, B and C. |
