Proclus, the old Greek commentator on Euclid, has this to say of the history: "If we listen to those who wish to recount ancient history, we may find some of them referring this theorem to Pythagoras and saying that he sacrificed an ox in honor of his discovery. But for my part, while I admire those who first observed the truth of this theorem, I marvel more at the writer of the 'Elements' (Euclid), not only because he made it fast by a most lucid demonstration, but because he compelled assent to the still more general theorem by the irrefragable arguments of science in Book VI. For in that book he proves, generally, that in right triangles the figure on the side subtending the right angle is equal to the similar and similarly placed figures described on the sides about the right angle." Now it appears from this that Proclus, in the fifth century A.D., thought that Pythagoras discovered the proposition in the sixth century B.C., that the usual proof, as given in most of our American textbooks, was due to Euclid, and that the generalized form was also due to the latter. For it should be made known to students that the proposition is true not only for squares, but for any similar figures, such as equilateral triangles, parallelograms, semicircles, and irregular figures, provided they are similarly placed on the three sides of the right triangle. Besides Proclus, Plutarch testifies to the fact that Pythagoras was the discoverer, saying that "Pythagoras sacrificed an ox on the strength of his proposition as Apollodotus says," but saying that there were two possible propositions to which this refers. This Apollodotus was probably Apollodorus, surnamed Logisticus (the Calculator), whose date is quite uncertain, and who speaks in some verses of a "famous proposition" discovered by Pythagoras, and all tradition makes this the one. Cicero, who comments upon these verses, does not question the discovery, but doubts the story of the sacrifice of the ox. Of other early writers, Diogenes Laertius, whose date is entirely uncertain (perhaps the second century A.D.), and Athenaeus (third century A.D.) may be mentioned as attributing the theorem to Pythagoras, while Heron (first century A.D.) says that he gave a rule for forming right triangles with rational integers for the sides, like 3, 4, 5, where 3^2 + 4^2 = 5^2. It should be said, however, that the Pythagorean origin has been doubted, notably in an article by H. Vogt, published in the _Bibliotheca Mathematica_ in 1908 (Vol. IX (3), p. 15), entitled "Die Geometrie des Pythagoras," and by G. Junge, in his work entitled "Wann haben die Griechen das Irrationale entdeckt?" (Halle, 1907). These writers claim that all the authorities attributing the proposition to Pythagoras are centuries later than his time, and are open to grave suspicion. Nevertheless it is hardly possible that such a general tradition, and one so universally accepted, should have arisen without good foundation.