An introductory text-book of logic - Mellone, Sydney - Rare Books at ...

THE GENERAL NATURE OF INDUCTION. 247
particular triangle as an example. A figure is given
which the reader is requested to regard as having two
equal sides, and it is conclusively proved that if the sides
be really equal then the angles opposite to those sides
must be equal also. But Euclid says nothing about
other isosceles triangles ;
he treats one single triangle as
a sufficient specimen of all isosceles triangles, and we
are asked to believe that what is true of that is true of
any other, whether its sides be so small as to be only
visible in a microscope, or so large as to reach to the
farthest fixed star. There may evidently be an infinite
number of isosceles triangles as regards the length of the
equal sides, and each of these may be infinitely varied
by increasing or diminishing the contained angle, so that
the number of possible isosceles triangles is infinitely
infinite ; and yet we are asked to believe of this incom
prehensible number of objects what we have only
proved
of one single specimen. We do know with as
much certainty as knowledge can possess, that if lines
be conceived as drawn from the earth to two stars
equally distant, they will make equal angles with the
and yet we can never have tried
line joining those stars ;
the experiment."
In this passage Jevons has well shown the "univer
"
sality of the results of Geometrical reasoning.
But he
does not clearly bring out what is the most essential
point, the reason why this universality is attainable. By
examination of a single case we have reached an ab
solutely universal law. How is this possible? It is
possible for two reasons. We know by
definition what
are the essential qualities of the isosceles triangle ; and
we argue from these essential qualities and from no
others. Hence we are certain that the result will be
true of every isosceles triangle; for every isosceles tri-