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

240 INTRODUCTION TO MATHEMATICS
angles are all measurable; so that, for example, the size of any length can be determined
by the number (not necessarily integral) of
times which it contains some arbitrarily
known unit, and similarly for areas, volumes,
and angles. The trigonometrical formule,
given above, are examples of this fact. But it
receives its crowning application in analytical
geometry. This great subject is often misnamed as Analytical Conic Sections, thereby
fixing attention on merely one of its subdivisions. It is as though the great science
of Anthropology were named the Study of
Noses, owing to the fact that noses are a
prominent part of the human body.
Though the mathematical procedures in
geometry and algebra are in essence identical
and intertwined in their development, there
is necessarily a fundamental distinction
between the properties of space and the
properties of number-in fact all the essential
difference between space and number. The
"spaciness" of space and the "numerosity"
of number are essentially different things, and
must be directly apprehended. None of the
applications of algebra to geometry or of
geometry to algebra go any step on the road
to obliterate this vital distinction.
One very marked difference between space
and number is that the former seems to be so
much less abstract and fundamental than the