Page:A History of Mathematics (1893).djvu/93

 P were $$\scriptstyle{(\frac{1}{6}+\frac{1}{7})}$$ of the W and Y. (2) Of Cows, which had the same colors (w, b, y, p),

$\begin{align}\scriptstyle{w=(\frac{1}{3}+\frac{1}{4})(B+b)}&\scriptstyle{:b=(\frac{1}{4}+\frac{1}{5})(P+p):p=(\frac{1}{5}+\frac{1}{6})(Y+y)}\\&\scriptstyle{:y=(\frac{1}{6}+\frac{1}{7})(W+w)\text{.}}\\\end{align}$|undefined

Find the number of bulls and cows.[6] Another problem in the Anthology is quite familiar to school-boys: "Of four pipes, one fills the cistern in one day, the next in two days, the third in three days, the fourth in four days: if all run together, how soon will they fill the cistern?" A great many of these problems, puzzling to an arithmetician, would have been solved easily by an algebraist. They became very popular about the time of Diophantus, and doubtless acted as a powerful stimulus on his mind.

Diophantus was one of the last and most fertile mathematicians of the second Alexandrian school. He died about 330 A.D. His age was eighty-four, as is known from an epitaph to this effect: Diophantus passed $$\scriptstyle{\frac{1}{6}}$$ of his life in childhood, $$\scriptstyle{\frac{1}{12}}$$ in youth, and $$\scriptstyle{\frac{1}{7}}$$ more as a bachelor; five years after his marriage was born a son who died four years before his father, at half his father's age. The place of nativity and parentage of Diophantus are unknown. If his works were not written in Greek, no one would think for a moment that they were the product of Greek mind. There is nothing in his works that reminds us of the classic period of Greek mathematics. His were almost entirely new ideas on a new subject. In the circle of Greek mathematicians he stands alone in his specialty. Except for him, we should be constrained to say that among the Greeks algebra was always an unknown science.

Of his works we have lost the Porisms, but possess a fragment of Polygonal Numbers, and seven books of his great work on Arithmetica, said to have been written in 13 books.

If we except the Ahmes papyrus, which contains the first