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

DIFFERENTIAL CALCULUS 221
and "slowly" gain their meaning from a tacit
reference to rates of change. Thus the differential calculus is concerned with the very
key of the position from which mathematics
can be successfully applied to the explanation of the course of nature.
This idea of the rate of change was certainly
in Newton's mind, and was embodied in the
y~
P
/ (xY).......A.
O T N M x
Fig. 32.
language in which he explained the subject.
It may be doubted, however, whether this
point of view, derived from natural phenomena, was ever much in the minds of the
preceding mathematicians who prepared the
subject for its birth. They were concerned
with the more abstract problems of drawing
tangents to curves, of finding the lengths of
curves, and of finding the areas enclosed by
curves. The last two problems, of the recti