whatever may have been his name) who demonstrated the properties of
the isosceles triangle. For he found that it was not sufficient to
meditate on the figure, as it lay before his eyes, or the conception
of it, as it existed in his mind, and thus endeavour to get at the
knowledge of its properties, but that it was necessary to produce
these properties, as it were, by a positive a priori construction;
and that, in order to arrive with certainty at a priori cognition,
he must not attribute to the object any other properties than those
which necessarily followed from that which he had himself, in accordance
with his conception, placed in the object.

A much longer period elapsed before physics entered on the highway
of science. For it is only about a century and a half since the wise
Bacon gave a new direction to physical studies, or rather--as others
were already on the right track--imparted fresh vigour to the
pursuit of this new direction. Here, too, as in the case of
mathematics, we find evidence of a rapid intellectual revolution. In
the remarks which follow I shall confine myself to the empirical
side of natural science.

When Galilei experimented with balls of a definite weight on the
inclined plane, when Torricelli caused the air to sustain a weight
which he had calculated beforehand to be equal to that of a definite
column of water, or when Stahl, at a later period, converted metals
into lime, and reconverted lime into metal, by the addition and
subtraction of certain elements; [Footnote: I do not here follow
with exactness the history of the experimental method, of which,
indeed, the first steps are involved in some obscurity.] a light broke
upon all natural philosophers. They learned that reason only perceives
that which it produces after its own design; that it must not be content