Proposition 7.
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point, there cannot be constructed on the same straight line (from its extremities), and on the same side of it, two other straight lines meeting in
another point and equal to the former two respectively, namely each to that which has the same extremity with it.
For, if possible, given two straight lines AC, CB constructed on the straight line AB and meeting at the point C, let two other straight lines
AD, DB be constructed on the same straight line AB, on the same side of it, meeting in another point D and equal to the former two respectively, namely each to that which has the same extremity with it, so that CA is
equal to DA which has the same extremity A with it, and CB to DB which has the same extremity B with it; and let CD be joined. Then, since AC is equal to AD,
But it was also proved much greater than it:
Q. E. D. 1 2 3