Chapter XII: Historical Criticism

From a problem in Diophantus's _Arithmetic_ about the price of some wine it would seem that the wine was of poor quality, and Paul Tannery has suggested that the prices mentioned for such a wine are higher than were usual until after the end of the second century. He therefore rejected the view which was formerly held that Diophantus lived in that century.[40]

The same method applied to a problem given by the ancient Hindu algebraist Brahmagupta, who lived in the seventh century after Christ, might result in placing Brahmagupta in prehistoric times. This is the problem:[41] "Two apes lived at the top of a cliff of height _h_, whose base was distant _mh_ from a neighbouring village. One descended the cliff and walked to the village, the other flew up a height _x_ and then flew in a straight line to the village. The distance traversed by each was the same. Find _x_."

FOOTNOTES:

[40] W. W. Rouse Ball, _A Short Account of the History of Mathematics_, 4th edition, London, 1908, p. 109.

[41] _Ibid._, pp. 148-9.