Let AD, DB be the given two straight lines, and let it be required to find the straight line the square on which is equal to the sum of the squares on them.
Let them be placed so as to contain a right angle, that formed by AD, DB; and let AB be joined.
It is again manifest that the straight line the square on which is equal to the sum of the squares on AD, DB is AB. [I. 47]
Q. E. D.