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

COORDINATE GEOMETRY 115
through the minds of Egyptians and Greeks,
of Arabs and of Germans. And yet, after all
this labour devoted to it through so many
ages by such diverse minds its most important
secrets were yet to be discovered. No one
can have studied even the elements of elementary geometry without feeling the lack
of some guiding method. Every proposition
has to be proved by a fresh display of ingenuity; and a science for which this is true
lacks the great requisite of scientific thought,
namely, method. Now the especial point of
coordinate geometry is that for the first
time it introduced method. The remote
deductions of a mathematical science are not
of primary theoretical importance. The
science has not been perfected, until it consists
in essence of the exhibition of great allied
methods by which information, on any desired
topic which falls within its scope, can easily
be obtained. The growth of a science is not
primarily in bulk, but in ideas; and the more
the ideas grow, the fewer are the deductions
which it is worth while to write down. Unfortunately, mathematics is always encumbered by the repetition in text-books of
numberless subsidiary propositions, whose importance has been lost by their absorption
into the role of particular cases of more
general truths-and, as we have already insisted, generality is the soul of mathematics.