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

114 INTRODUCTION TO MATHEMATICS
seem, after all, to be very simple, almost
childishly so, and to lie well within the
province of philosophical thought. Probably
their very simplicity is the cause of error; we
are not used to think about such simple
abstract things, and a long training is necessary to secure even a partial immunity from
error as soon as we diverge from the beaten
track of thought.
The discovery of coordinate geometry, and
also that of projective geometry about the
same time, illustrate another fact which is
being continually verified in the history of
knowledge, namely, that some of the greatest
discoveries are to be made among the most
well-known topics. By the time that the
seventeenth century had arrived, geometry
had already been studied for over two thousand years, even if we date its rise with the
Greeks. Euclid, taught in the University of
Alexandria, being born about 330 B.c.; and he
only systematized and extended the work of a
long series of predecessors, some of them men
of genius. After him generation after generation of mathematicians laboured at the improvement of the subject. Nor did the
subject suffer from that fatal bar to progress,
namely, that its study was confined to a
narrow group of men of similar origin and
outlook-quite the contrary was the case;
by the seventeenth century it had passed