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

GEOMETRY 239
the conic section. Or, pursuing a converse
route, he classifies triangles according as they
are equilateral, isosceles, or scalene, and
polygons according to their number of sides,
and conic sections according as they are
hyperbolas, ellipses, or parabolas.
The preceding examples illustrate how the
fundamental ideas of geometry are exactly
the same as those of algebra; except that
algebra deals with numbers and geometry
with lines, angles, areas, and other geometrical entities. This fundamental identity
is one of the reasons why so many geometrical truths can be put into an algebraic
dress. Thus if A, B, and C are the numbers
of degrees respectively in the angles of the
triangle ABC, the correlation between the
angles is represented by the equation
A+B+C= 180~;
and if a, b, c are the number of feet respectively in the three sides, the correlation between the sides is represented by a <b+ c,
b < c+ a, c < a + b. Also the trigonometrical
formule quoted above are other examples of
the same fact. Thus the notion of the variable and the correlation of variables is just as
essential in geometry as it is in algebra.
But the parallelism between geometry and
algebra can be pushed still further, owing to
the fact that lengths, areas, volumes, and