Mathematics in Ancient and Medieval India c6.s4.19

c6.s4.19

The theorem of square on the diagonal of a rectangle i.e. a² + b² = c², is usually known as Pythagorian theorem and is universally associated with the name of the Greek Pythagoras (c. 540 B C.). In fact the relation 3² + 4² = 5² and some such relations have been used by Pythagoras, and the evidence of any general statement regarding this is not yet available. Actual proof was first given by Euclid (c. 300 B. C.).⁷ Proclus (c 460 A. D.), the commentator of Euclid remarked : "for my part, while I admire those who first observed the truth of the theorem, I marvel more at the writer of the Elements, not only because he made it first by a most lucid demonstration, but because he compelled assent to the still more general theorem by the irrefragable arguments of science in the sixth book.¹ Heath admitted with the remarks : “it is difficult for us to be more positive than Proclus was”.² Hence it is far from conclusive that Pythagoras stated the above general theorem. Variety of evidence is at present available that the practical use of the theorem was current in old Babylonian times (c. 1800–1600 B. C.). The evidence for this is found in certain Babylonian cuneiform tablets. No general theorem was found to have been mentioned. It has been conclusively proved by Neugebauer that Pythagoras has derived his “Number theorem of Universe” as well as the so called Pythagorian Theorem from the Babylonian cuneiform tablets³. The Chinese knew a similar relation which appeared in *Chou Pei* (4th century B. C.) and the most of its credit is connected from the time of its first commentator Chao Chun Chhing (3rd century A. D.).⁴ In India, the proof first appeared in the work of Bhāskara II⁵ (c. 1150 A. D.). Needham remarks “Bhāskara’s treatment derives from the Chou Pei”.⁶ This is not however true, for the proofs of Bhāskara II and that stated to be of *Chou Pei* can readily be deduced from a number of constructions described in the *Śulbasūtras*¹.