Kitap 1
2
And things which are equal to the same thing are also equal to one another; [C.N. 1] therefore AL is also equal to BC.
2
Therefore at the given point A the straight line AL is placed equal to the given straight line BC.
2
QED. (Being) what it was required to do.
Proposition 3.
3
Enunciation Given two unequal straight lines, to cut off from the greater a straight line equal to the less.
3
Proof. Let AB, C be the-two given unequal straight lines, and let AB be the greater of them.
3
Thus it is required to cut off from AB the greater a straight line equal to C the less.
3
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]
3
Therefore, given the two straight lines AB, C, from AB the greater AE has been cut off equal to C the less.
3
QED. (Being) what it was required to do.
Proposition 4.
4
Enunciation If two triangles have the two sides equal to two sides respectively, and have the angles contained by the equal straight lines equal, they will also have the base equal to the base, the triangle will be equal to the triangle, and the remaining angles will be equal to the remaining angles respectively, namely those which the equal sides subtend.
