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

180 INTRODUCTION TO MATHEMATICS
gonometry," derived from the two Greek
words trigonon, a triangle, and metria, measurement. The fundamental question from
which trigonometry arose is this: Given the
magnitudes of the angles of a triangle, what can
be stated as to the relative magnitudes of the
sides. Note that we say "relative magnitudes
of the sides," since by the theory of similarity
it is only the proportions of the sides which
are known. In order to answer this question, certain functions of the magnitudes of
an angle, considered as the argument, are introduced. In their origin these functions
were got at by considering a right-angled triangle, and the magnitude of the angle was
defined by the length of the arc of a circle.
In modern elementary books, the fundamental position of the arc of the circle as defining the magnitude of the angle has been
pushed somewhat to the background, not to
the advantage either of theory or clearness
of explanation. It must first be noticed
that, in relation to similarity, the circle holds
the same fundamental position among curvilinear figures, as does the triangle among
rectilinear figures. Any two circles are similar figures; they only differ in scale. The
lengths of the circumferences of two circles,
such as APA' and A 1PiA' in the fig. 26 are
in proportion to the lengths of their radii.
Furthermore, if the two circles have the same