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

DYNAMICS 55
transportations are A to B and A to D,
complete the parallelogram ABCD, and then
the sum of the two is the diagonal AC.
All this at first sight may seem to be
very artificial. But it must be observed
that nature itself presents us with the idea.
For example, a steamer is moving in the
direction AD (cf. fig. 6) and a man walks
across its deck. If the steamer were still,
in one minute he would arrive at B; but
during that minute his starting point A on
the deck has moved to D, and his path on
the deck has moved from AB to DC. So
that, in fact, his transportation has been from
A to C over the surface of the sea. It is,
however, presented to us analysed into the
sum of two transportations, namely, one from
A to B relatively to the steamer, and one
from A to D which is the transportation of
the steamer.
By taking into account the element of time,
namely one minute, this diagram of the man's
transportation AC represents his velocity.
For if AC represented so many feet of transportation, it now represents a transportation
of so many feet per minute, that is to say, it
represents the velocity of the man. Then
AB and AD represent two velocities, namely,
his velocity relatively to the steamer, and the
velocity of the steamer, whose "sum" makes
up his complete velocity. It is evident that