An introduction to mathematics, by A. N. Whitehead.

238 INTRODUCTION TO MATHEMATICS
of similarity (cf. Chapter XIII), which is
another type of correlation.
Again, to take another example, consider
the internal structure of the triangle ABC.
Its sides and angles are inter-related-the
greater angle is opposite to the greater side,
and the base angles of an isosceles triangle
are equal. If we proceed to trigonometry
this correlation receives a more exact determination in the familiar shape
sin A sin B sin C
a b c '
a2 = b2 + c2- bccosA, with two similar
formula.
Also there is the still simpler correlation
between the angles of the triangle, namely,
that their sum is equal to two right angles;
and between the three sides, namely, that the
sum of the lengths of any two is greater than
the length of the third.
Thus the true method to study geometry is
to think of interesting simple figures, such as
the triangle, the parallelogram, and the circle,
and to investigate the correlations between
their various parts. The geometer has in his
mind not a detached proposition, but a figure
with its various parts mutually inter-dependent. Just as in algebra, he generalizes the
triangle into the polygon, and the side into