The following is as given in Sir Thomas L. Heath's translation, which can be found in the book The Thirteen Books of The Elements, Vol. 1.
|Book I||Book II||Book IX|
|Definitions, Postulates, and Common Notions||Definitions||Proposition 20|
|Proposition 1, Proposition 3,||Proposition 14||Proposition 36|
|Proposition 5, Proposition 6,|
|Proposition 29, Proposition 47|
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,
But C is also equal to AD.
Therefore ach 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.