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 ...

452 REASONING AND DEDUCTIVE EVIDENCE.
And is not a universal affirmation made with respect to a fact
which experience is equally incompetent to disprove or to confirm?
In like manner, when it is said, that "triangles on the same
base, and between the same parallels are equal," do we feel ourselves the less ready to give our assent to the demonstration, if
it should be supposed, that the one triangle is confined within
the limits of the paper before us, and that the other, standing
on the same base, has its vertex placed beyond the sphere of
the fixed stars? In various instances, we are led, with a force
equally imperious, to acquiesce in conclusions, which not only
admit of' no illustration or proof from the perceptions of sense,
but which, at first sight, are apt to stagger and confound the
faculty of imagination. It is sufficient to mention, as examples
of this, the relation between the hyperbola and its asymptotes,
[which are constantly approaching each other, and yet will not
meet till they are extended to infinity]; and the still more obvious truth of the infinite divisibility of extension. What analogy is there between such propositions as these, and that which
announces, that the mercury in the Torricellian tube will fall,
if carried up to the top of a mountain; or that the vibrations
of a pendulum of a given length will be performed in the same
time, while it remains in the same latitude? Were there, in
reality, that analogy between mathematical and physical propositions, which Beddoes and his followers have fancied, the
equality of the square of the hypothenuse of a right angled triangle to the squares described on the two other sides, and the
proportion of 1, 2, 3, between the cone and its circumscribed
hemisphere and cylinder, might, with fully as great propriety,
be considered in the light of physical phenomena, as of geometrical theorems. Nor would it have been at all inconsistent with
the logical unity of his work, if Mr. Leslie had annexed to his
Elements of Geometry, a scholium concerning the final causes
of circles and of straight lines, similar to that which, with such
sublime effect, closes the Principia of Sir Isaac Newton.*
* In the course of my own experience, I have met with one person, of
no common ingenuity, who seemed seriously disposed to consider the
truths of geometry very nearly in this light. The person I allude to was