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.