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

GEOMETRY 237
What relations must exist between some of
the parts of these triangles, in order that the
triangles may be in all respects equal? This
is one of the first investigations undertaken
in all elementary geometries. It is a study
A D
B C E F
Fig. 33.
of a certain set of possible correlations between the two triangles. The answer is that
the triangles are in all respects equal, if:Either, (a) Two sides of the one and the included angle are respectively equal to two
sides of the other and the included angle:
Or, (b) Two angles of the one and the side
joining them are respectively equal to two
angles of the other and the side joining them:
Or, (c) Three sides of the one are respectively equal to three sides of the other.
This answer at once suggests a further enquiry. What is the nature of the correlation
between the triangles, when the three angles
of the one are respectively equal to the three
angles of the other? This further investigation leads us on to the whole theory