Page:A budget of paradoxes (IA cu31924103990507).pdf/44

30 Philo of Gadara is asserted by Montucla, on the authority of Eutocius, 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:—

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 and quoted 🇬🇷. 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.' Accordingly, Magnus, Baveme, and Cocker, are three personifications of arithmetic; and there may be more.

Aristotle, treating of the category of relation, denies that the quadrature has been found, but appears to assume that it can be done. Boethius, in his comment on the passage, says that it has been done since Aristotle, but that the demonstration is too long for him to give. Those who have no notion of the quadrature question may look at the English Cyclopædia, art. 'Quadrature of the Circle.'