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

174 INTRODUCTION TO MATHEMATICS
see at once the great contrast between conic
sections and trigonometry. The origin of
trigonometry was practical; it was invented
because it was necessary for astronomical research. The origin of conic sections was
purely theoretical. The only reason for its
initial study was the abstract interest of the
ideas involved. Characteristically enough
conic sections were invented about 150 years
earlier than trigonometry, during the very
best period of Greek thought. But the importance of trigonometry, both to the theory
and the application of mathematics, is only
one of innumerable instances of the fruitful
ideas which the general science has gained
from its practical applications.
We will try and make clear to ourselves
what trigonometry is, and why it should be
generated by the scientific studyof astronomy.
In the first place: What are the measurements which can be made by an astronomer?
They are measurements of time and measurements of angles. The astronomer may adjust
a telescope (for it is easier to discuss the
familiar instrument of modern astronomers)
so that it can only turn about a fixed axis
pointing east and west; the result is that
the telescope can only point to the south, with
a greater or less elevation of direction, or, if
turned round beyond the zenith, point to the
north. This is the transit instrument, the