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

118 INTRODUCTION TO MATHEMATICS
Again we generalize x2+y2 1 into ax2 +
by2 =c, or still further into ax2 +2hxy +by2
= c, or, still further, into ax2 +hxy +by2 +2gx
+2fy =c.
Here again we are led to variable correlations which are indicated by their various
algebraic forms.
Now let us turn to geometry. The name
of the science at once recalls to our minds
the thought of figures and diagrams exhibiting
triangles and rectangles and squares and
circles, all in special relations to each other.
The study of the simple properties of these
figures is the subject matter of elementary
geometry, as it is rightly presented to the
beginner. Yet a moment's thought will show
that this is not the true conception of the
subject. It may be right for a child to commence his geometrical reasoning on shapes,
like triangles and squares, which he has cut
out with scissors. What, however, is a triangle? It is a figure marked out and bounded
by three bits of three straight lines.
Now the boundary of spaces by bits of
lines is a very complicated idea, and not at
all one which gives any hope of exhibiting
the simple general conceptions which should
form the bones of the subject. We want
something more simple and more general. It
is this obsession with the wrong initial ideas
-very natural and good ideas for the creation