nd candor
worthy of a better value of [pi].

Mr. Smith's method of proving that every circle is 3-1/8 diameters is to
assume that it is so,--"if you dislike the term datum, then, by hypothesis,
let 8 circumferences be exactly equal to 25 diameters,"--and then to show
that every other supposition is thereby made absurd. The right to this
assumption is enforced in the "Nut" by the following analogy:

"I think you (!) will not dare (!) to dispute my right to this hypothesis,
when I can prove by means of it that every other value of [pi] will lead to
the grossest absurdities; unless indeed, you are prepared to dispute the
right of Euclid to adopt a false line hypothetically for the purpose {118}
of a '_reductio ad absurdum_'[216] demonstration, in pure geometry."

Euclid assumes what he wants to _disprove_, and shows that his _assumption_
leads to absurdity, and so _upsets itself_. Mr. Smith assumes what he wants
to _prove_, and shows that _his_ assumption makes _other propositions_ lead
to absurdity. This is enough for all who can reason. Mr. James Smith cannot
be argued with; he has the whip-hand of all the thinkers in the world.
Montucla would have said of Mr. Smith what he said of the gentleman who
squared his circle by giving 50 and 49 the same square root, _Il a perdu le
droit d'etre frappe de l'evidence_.[217]

It is Mr. Smith's habit, when he finds a conclusion agreeing with its own
assumption, to regard that agreement as proof of the assumption. The
following is the "piece of information" which will settle me, if I be
honest. Assuming [pi] to be 3-1/8, he finds out by working instance after
instance that the mean proportional between one-fifth of the area and
one-fifth of eight is the radius. That is,

if [pi] = 25/8, sqrt(([pi]r^2)/5 . 8/5) = r.

This "remarkable general principle" may fail to establish Mr. Smith's
quadrature, even in an honest mind, if that mind should happen to know
that, a and b being any two numbers whatever, we need only assume--

[pi] = a^2/b, to get at sqrt(([pi]r^2)/a . b/a) = r.

We naturally ask what sort of glimmer can Mr. Smith have of the subject
which he professes to treat? On this point he has given satisfactory
information. I had mentioned the old problem of finding two mean
proportionals, {119} as a preliminary to the duplication of the cube. On
this mention Mr. Smith writes as follows. I put a few words in capitals;
and I write rq[218] for the sign of the square ro