Philo of Gadara[21] is asserted by Montucla,[22] on the {41} authority of
Eutocius,[23] the commentator on Archimedes, to have squared the circle
within the _ten-thousandth_ part of a unit, that is, to _four_ places of
decimals. A modern classical dictionary represents it as done by Philo to
_ten thousand_ places of decimals. Lacroix comments on Montucla to the
effect that _myriad_ (in Greek _ten thousand_) is here used as we use it,
vaguely, for an immense number. On looking into Eutocius, I find that not
one definite word is said about the extent to which Philo carried the
matter. I give a translation of the passage:
"We ought to know that Apollonius Pergaeus, in his Ocytocium [this work is
lost], demonstrated the same by other numbers, and came nearer, which seems
more accurate, but has nothing to do with Archimedes; for, as before said,
he aimed only at going near enough for the wants of life. Neither is Porus
of Nicaea fair when he takes Archimedes to task for not giving a line
accurately equal to the circumference. He says in his Cerii that his
teacher, Philo of Gadara, had given a more accurate approximation ([Greek:
eis akribesterous arithmous agagein]) than that of Archimedes, or than 7 to
22. But all these [the rest as well as Philo] miss the intention. They
multiply and divide by _tens of thousands_, which no one can easily do,
unless he be versed in the logistics [fractional computation] of Magnus
[now unknown]."
Montucla, or his source, ought not to have made this mistake. He had been
at the Greek to correct Philo _Gadetanus_, as he had often been called, and
he had brought away {42} and quoted [Greek: apo Gadaron]. Had he read two
sentences further, he would have found the mistake.
We here detect a person quite unnoticed hitherto by the moderns, Magnus the
arithmetician. The phrase is ironical; it is as if we should say, "To do
this a man must be deep in Cocker."[24] Accordingly, Magnus, Baveme,[25]
and Cocker, are three personifications of arithmetic; and there may be
more.