One of the oldest [ca. 75-125 A.D] and most complete diagrams from Euclid’s Elements of Geometry is a fragment of papyrus found among the remarkable rubbish piles of Oxyrhynchus in 1896-97 by the renowned expedition of B. P. Grenfell and A. S. Hunt. It is now located at the University of Pennsylvania. The diagram accompanies Proposition 5 of Book II of the Elements, and along with other results in Book II it can be interpreted in modern terms as a geometric formulation of an algebraic identity – in this case, that ab + (a-b)2/4 = (a+b)2/4

“If a straight line be cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.” (from the classic translation of T. L. Heath)