_ 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.

ON SQUARING THE CIRCLE.

Aristotle, treating of the category of relation, denies that the quadrature
has been found, but appears to assume that it can be done. Boethius,[26] 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 Cyclopaedia_,
art. "Quadrature of the Circle."

Tetragonismus. Id est circuli quadratura per Campanum, Archimedem
Syracusanum, atque Boetium mathematicae perspicacissimos adinventa.--At
the end, Impressu