g that wonderful nation the Greeks,
followed the safe road of a science. Still it is not to be supposed
that it was as easy for this science to strike into, or rather to
construct for itself, that royal road, as it was for logic, in which
reason has only to do with itself. On the contrary, I believe that it
must have remained long in the stage of groping (chiefly among the
Egyptians), and that this change is to be ascribed to a _revolution_,
due to the happy thought of one man, through whose experiment the path
to be followed was rendered unmistakable for future generations, and
the certain way of a science was entered upon and sketched out once
for all.... A new light shone upon the first man (Thales, or whatever
may have been his name) who demonstrated the properties of the
isosceles triangle; for he found that he ought not to investigate
that which he saw in the figure or even the mere conception of the
same, and learn its properties from this, but that he ought to produce
the figure by virtue of that which he himself had thought into it _a
priori_ in accordance with conceptions and had represented (by means
of a construction), and that in order to know something with certainty
_a priori_ he must not attribute to the figure any property other than
that which necessarily follows from that which he has himself
introduced into the figure, in accordance with his conception."[12]

[12] B. x-xii, M. xxvi.

Here Kant's point is as follows. Geometry remained barren so long as
men confined themselves either to the empirical study of individual
figures, of which the properties were to be discovered by observation,
or to the consideration of the mere conception of various kinds of
figure, e. g. of an isosceles triangle. In order to advance, men had
in some sense to produce the figure through their own activity, and in
the act of constructing it to recognize that certain features were
necessitated by those features which they had given to the figure in
constructing it. Thus men had to make a triangle by drawing three
straight lines so as to enclose a space, and then to recognize that
three angles must have been made by the same process. In this way the
mind discovered a general rule, which must apply to all cases, because
the mind itself had determined the nature of the cases. A property B
follows from a nature A; all instances of A must possess the property
B, because they have solely that nature A which the mind has given