Proposition 3.

Let AB, C be the two unequal straight lines, and let AB be the greater of them. Thus it is required to cut off from AB the greater a straight line equal to C the less.

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At the point A let AD be placed equal to the straight line C

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and with centre A and distance AD let the circle DEF be described

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Now, since the point A is the centre of the circle DEF, AE is equal to AD.

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But C is also equal to AD.

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Therefore each of the straight lines AE, C is equal to AD; so that AE is also equal to C. Therefore, given the two straight lines AB, C, from AB the greater AE has been cut off equal to C the less. (Being) what it was required to do.

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Q.E.F

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Ralph H. Abraham, 28 April, 1996.