the halfpennyworth of
bread to many gallons of sack. Many more methods might be given, all ending
in the same result, let that result mean what it may.

Now since dozens of methods, to which dozens more might be added at
pleasure, concur in giving one and the same result; and since these methods
are declared by all who have shown knowledge of mathematics to be
_demonstrated_: it is not asking too much of a person who has just a little
knowledge of the first elements that he should learn more, and put his hand
upon the error, before he intrudes his assertion of the existence of error
upon those who have given more time and attention to it than himself, and
who are in possession, over and above many demonstrations, of many
consequences verifying each other, of which he can know nothing. This is
all that is required. Let any one square the circle, and persuade his
friends, if he and they please: let him print, and let all read who choose.
But let him abstain from intruding himself upon those who have been
satisfied by existing demonstration, until he is prepared {214} to lay his
finger on the point in which existing demonstration is wrong. Let him also
say what this mysterious 3.14159... really is, which comes in at every door
and window, and down every chimney, calling itself the circumference to a
unit of diameter. This most impudent and successful impostor holds false
title-deeds in his hands, and invites examination: surely those who can
find out the rightful owner are equally able to detect the forgery. All the
quadrators are agreed that, be the right what it may, 3.14159... is wrong.
It would be well if they would put their heads together, and say what this
wrong result really means. The mathematicians of all ages have tried all
manner of processes, with one object in view, and by methods which are
admitted to yield demonstration in countless cases. They have all arrived
at one result. A large number of opponents unite in declaring this result
wrong, and all agree in two points: first, in differing among themselves;
secondly, in declining to point out what that curious result really is
which the mathematical methods all agree in giving.

Most of the quadrators are not aware that it has been fully demonstrated
that no two numbers whatsoever can represent the ratio of the diameter to
the circumference with perfect accuracy. When therefore we are told that
either 8 to 25 or 64 to 201 is the true ratio, we know that it i