The Shulbasutras of Baudhayana, Apastamba, Katyayana and Manava: With Text, English Translation and Commentary c5.s3.15

c5.s3.15

The tradition attributing the theorem to Pythagoras is due to Cicero (*c.* 50 B.C.) Diogenes Laertius (second century A.D.), Athenaeus (*c.* A.D. 300), Heron (third century A.D.), and Proclus (*c.*A.D. 460), and therefore started about five centuries after the death of Pythagoras. Junge pointed out that the Greek literature of the first five centuries after Pythagoras contained no mention of the discovery of this or any other important geometrical theorem by the great philosopher and furthermore emphasized uncertainties in the statements of Plutarch and Proclus. Although various attempts have been made to justify the tradition and trace the proof to Pythagoras, no record of proof has come down to us earlier than that given by Euclid (Theorem 47, BK 1). As to the relation 4²+3²=5² from which the theorem of rational triangle is derivable, very ancient Egyptian knowledge is attested by the Kahun papyrus of the twelfth dynasty (*c.* 2000 B.C.), but its association with rational triangles does not seem indicated in this or other Egyptian papyrii.a As to the antiquity of Pythagorean theorem in China, it is stated, though not proved, in the arithmetical classic *Chou Pei Suan Ching* (third or fourth century B.C.); the numerical relationship 4, 3 and 5 between the sides and the diagonal of a rational rectangle is also given in this text. The old Babylonians of the second millennium B.C. left records on their cuneiform tablets of similar squared relationships indicating practical use of the theorem of squares. No general statement in the form of a theorem is of course found. Neugebauer is of the view that Pythagoras derived his number theorem of the universe as well as the theorem known after his name from such Babylonian cuneiform tablets.b