s no such
thing, without the necessity of examination. The point that is left open,
as not fully demonstrated to be impossible, is the _geometrical_
quadrature, the determination of the circumference by the straight line and
circle, used as in Euclid. The general run of circle-squarers, hearing that
the quadrature is not pronounced to be _demonstratively_ impossible,
imagine that the _arithmetical_ quadrature is open to their ingenuity.
Before attempting the arithmetical problem, they ought to acquire knowledge
enough to read Lambert's[355] demonstration (last given in Brewster's[356]
translation {215} of Legendre's[357] Geometry) and, if they can, to refute
it. [It will be given in an Appendix.] Probably some have begun this way,
and have caught a Tartar who has refused to let them go: I have never heard
of any one who, in producing his own demonstration, has laid his finger on
the faulty part of Lambert's investigation. This is the answer to those who
think that the mathematicians treat the arithmetical squarers too lightly,
and that as some person may succeed at last, all attempts should be
examined. Those who have so thought, not knowing that there is
demonstration on the point, will probably admit that a person who
contradicts a theorem of which the demonstration has been acknowledged for
a century by all who have alluded to it as read by themselves, may
reasonably be required to point out the error before he demands attention
to his own result.

_Apopempsis of the Tutelaries._--Again and again I am told that I spend too
much time and trouble upon my two tutelaries: but when I come to my
summing-up I shall make it appear that I have a purpose. Some say I am too
hard upon them: but this is quite a mistake. Both of them beat little
Oliver himself in the art and science of asking for more; but without
Oliver's excuse, for I had given good allowance. Both began with me, not I
with them: and both knew what they had to expect when they applied for a
second helping.

On July 31, the Monday after the publication of my remarks on my 666
correspondent, I found _three_ notes in separate envelopes, addressed to me
at "7A, University College." When I saw the three new digits I was taken
rhythmopoetic, as follows--

Here's the Doctor again with his figs, and by Heavens!
He was always at sixes, and now he's at sevens.

To understand this fully the reader must know that the greater part of
Apocalyptic interpretation has lo