true of relation, of form and quantity, is often grossly false in regard
to morals, for example. In this latter science it is very usually untrue
that the aggregated parts are equal to the whole. In chemistry, also,
the axiom fails. In the consideration of motive it fails; for two
motives, each of a given value, have not, necessarily, a value, when
united, equal to the sum of their values apart. There are numerous other
mathematical truths which are only truths within the limits of relation.
But the mathematician argues from his finite truths, through habit, as
if they were of an absolutely general applicability, as the world indeed
imagines them to be. Bryant, in his very learned _Mythology_, mentions
an analogous source of error when he says that 'although the pagan
fables are not believed, yet we forget ourselves continually and make
inferences from them as existing realities.' With the algebraists,
however, who are pagans themselves, the 'pagan fables' are believed, and
the inferences are made, not so much through lapse of memory as through
an unaccountable addling of the brains. In short, I never yet
encountered the mere mathematician who could be trusted out of equal
roots, or one who did not clandestinely hold it as a point of his faith
that _x squared+px_ was absolutely and unconditionally equal to _q_. Say
to one of these gentlemen, by way of experiment, if you please, that you
believe occasions may occur where _x squared+px_ is not altogether equal
to _q_, and, having made him understand what you mean, get out of his
reach as speedily as convenient, for, beyond doubt, he will endeavour to
knock you down.

"I mean to say," continued Dupin, while I merely laughed at his last
observations, "that if the Minister had been no more than a
mathematician, the Prefect would have been under no necessity of giving
me this check. I knew him, however, as both mathematician and poet, and
my measures were adapted to his capacity with reference to the
circumstances by which he was surrounded. I knew him as a courtier, too,
and as a bold intriguant. Such a man, I considered, could not fail to be
aware of the ordinary policial modes of action. He could not have failed
to anticipate--and events have proved that he did not fail to
anticipate--the waylayings to which he was subjected. He must have
foreseen, I reflected, the secret investigations of his premises. His
frequent absences from home at night, which were hailed by the Pre