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

52 INTRODUCTION TO MATHEMATICS
We have seen that the essence of motion is
that a body was at A and is now at C. This
transference from A to C requires two distinct elements to be settled before it is completely determined, namely its magnitude
(i.e. the length AC) and its direction. Now
anything, like this transference, which is
completely given by the determination of a
D c
A B
Fig. 6.
magnitude and a direction is called a vector.
For example, a velocity requires for its definition the assignment of a magnitude and of a
direction. It must be of so many miles per
hour in such and such a direction. The existence and the independence of these two
elements in the determination of a velocity
are well illustrated by the action of the
captain of a ship, who communicates with
different subordinates respecting them: he
tells the chief engineer the number of knots
at which he is to steam, and the helmsman