Euclid, Elements
Thomas L. Heath, Sir Thomas Little Heath, Ed.

I say that LN is the irrational straight line called minor.

For, since AK is rational and is equal to the squares on LP, PN, therefore the sum of the squares on LP, PN is rational.

Again, since DK is medial, and DK is equal to twice the rectangle LP, PN, therefore twice the rectangle LP, PN is medial.

And, since AI was proved incommensurable with FK, therefore the square on LP is also incommensurable with the square on PN.

Therefore LP, PN are straight lines incommensurable in square which make the sum of the squares on them rational, but twice the rectangle contained by them medial.

Therefore LN is the irrational straight line called minor; [X. 76] and it is the “side” of the area AB.

Therefore the “side” of the area AB is minor. Q. E. D.

PROPOSITION 95.

For let the area AB be contained by the rational straight line AC and the fifth apotome AD; I say that the “side” of the area AB is a straight line which produces with a rational area a medial whole.

For let DG be the annex to AD; therefore AG, GD are rational straight lines commensurable in square only, the annex GD is commensurable in length with the rational straight line AC set out, and the square on the whole AG is greater than the square