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

178 INTRODUCTION TO MATHEMATICS
Geometrical similarity may be defined thus:
Two figures are similar (i) if to any point
in one figure a point in the other figure
corresponds, so that to every line there is a
corresponding line, and to every angle a
corresponding angle, and (ii) if the lengths
of corresponding lines are in a fixed proportion, and the magnitudes of corresponding
angles are the same. The fixed proportion
of the lengths of corresponding lines in a map
(or plan) and in the original is called the scale
of the map. The scale should always be
indicated on the margin of every map and
plan. It has already been pointed out that
two triangles whose angles are respectively
equal are similar. Thus, if the two triangles
A
//\ \ /\D
B E' C E o
Fig. 24.
ABC and DEF have the angles at A and D
equal, and those at B and E, and those at C
and F, then DE is to AB in the same propor