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

TRIGONOMETRY 173
tion as EF is to BC, and as FD is to CA.
But it is not true of other figures that similarity is guaranteed by the mere equality of
angles. Take, for example, the familiar cases
of a rectangle and a square. Let ABCD be
a square, and ABEF be a rectangle. Then
all the corresponding angles are equal. But
A D F
B C E
Fig. 25.
whereas the side AB of the square is equal to
the side AB of the rectangle, the side BC of
the square is about half the size of the side
BE of the rectangle. Hence it is not true
that the square ABCD is similar to the rectangle ABEF. This peculiar property of the
triangle, which is not shared by other rectilinear figures, makes it the fundamental
figure in the theory of similarity. Hence in
surveys, triangulation is the fundamental
process; the hence also arises the word "tri