Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
Let AB, C be the two given 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.
Now, since the point A is the
centre of the
AE is equal to AD. [Def. 15]
But C is also equal to AD.
Therefore each of the straight lines AE, C is equal to AD; so that AE is also equal to C. [C.N. 1]
Therefore, given the two straight
lines AB, C,
the greater AE has been cut off
equal to C the less.
(Being) what it was required to do.
Book I: Euclid, Book I (ed. Sir Thomas L. Heath 1st Edition, 1908)
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