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.
