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

IMAGINARY NUMBERS 111
new science whenever a new equation appears?
Now, if this were the case, the whole of our
preceding investigations, though to some
minds they might be amusing, would in truth
be of very trifling importance. But the great
fact, which has made modern analysis possible,
is that, by the aid of this calculus of vectors,
every formula which arises can receive its
proper interpretation; and the "unknown"
quantity in every equation can be shown to
indicate some vector. Thus the science is now
complete in itself as far as its fundamental
ideas are concerned. It was receiving its final
form about the same time as when the steam
engine was being perfected, and will remain
a great and powerful weapon for the achievement of the victory of thought over things
when curious specimens of that machine
repose in museums in company with the
helmets and breastplates of a slightly earlier
epoch.