(Edited by Sir Thomas L. Heath, 1908)

[Euclid, ed. Heath, 1908, on

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.

At the point A let
AD be placed equal to the straight
line C;
[I. 2]

and with centre A and
distance AD let the circle
DEF be described.
[Post. 3]

Now, since the point A is the
centre of the
circle DEF,

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,
from AB
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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