Elements of the philosophy of the human mind. By Dugald Stewart. Rev. and abridged, with critical and explanatory notes, for the use of colleges and schools. By Francis Bowen ...

68 ATTENTrON.
which is obvious almost to sense; such as, that any two sides
of a triangle are greater than the third side; or that one circle
cannot cut another circle in more than two points; but to some
propositions with respect to quantity, considered abstractly, (to
some, for example, in the fifth book of Euclid,) which almost
every student would be ready to admit without a demonstration.
These propositions, however, do by no means belong to. the class
of axioms; for their evidence does not strike every person
equally, but requires a certain degree of quickness to perceive
it. At the same time, it frequently happens, that although we
are convinced the proposition is true, we cannot state immediately to others upon what our conviction is founded. In such
cases, I[ think it highly probable, that before we give our assent
to the theorem, a process of thought has passed through the mind,
but has passed through it so quickly, that we cannot, without difficulty, arrest our ideas in their rapid succession, and state them
to others in their proper and logical order. It is some confirmation of this theory, that there are no propositions of which it is
more difficult to give a legitimate proof fiom first principles,
than of those which are only removed a few steps from the class
of axioms; and that those men who are the most remarkable
for their quick perception of mathematical truth, are seldom
clear and methodical in communicating their knowledge to
others. A man of a moderate degree of quickness, the very
first time he is made acquainted with the fundamental principles
of the method of fluxions, or of the method of prime and ultimate ratios, is almost instantaneously satisfied of their truth;
yet how difficult is it to demonstrate these principles rigorously!
aWhat I have now said with respect to mathematics, may be
applied in a great measure to the other branches of knowledge.
How many questions daily occur to us, in morals, in politics, and
in common life; in considering which we almost instantaneously
see where the truth lies, although we are not in a condition, all
at once, to explain the grounds of our conviction! Indeed, I
apprehend, there are few, even among those who have devoted
themselves to study, but why) have not been habituated to com