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

176 INTRODUCTION TO MATHEMATICS
land-surveying, angles are the chief subject
of measurements. The direct measurements
of length are only rarely possible with any
accuracy; rivers, houses, forests, mountains,
and general irregularities of ground all get in
the way. The survey of a whole country will
depend only on one or two direct measurements of length, made with the greatest
elaboration in selected places like Salisbury
Plain. The main work of a survey is the
measurement of angles. For example, A, B,
and C will be conspicuous points in the disA C
Fig. 23.
trict surveyed, say the tops of church towers.
These points are visible each from the others.
Then it is a very simple matter at A to
measure the angle BAC, and at B to measure
the angle ABC, and at C to measure the angle
BCA. Theoretically, it is only necessary to
measure two of these angles; for, by a wellknown proposition in geometry, the sum of
the three angles of a triangle amounts to two