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

CHAPTER XVI
GEOMETRY
GEOMETRY, like the rest of mathematics, is
abstract. In it the properties of the shapes
and relative positions of things are studied.
But we do not need to consider who is observing the things, or whether he becomes acquainted with them by sight or touch or
hearing. In short, we ignore all particular
sensations. Furthermore, particular things
such as the Houses of Parliament, or the
terrestrial globe are ignored. Every proposition refers to any things with such and
such geometrical properties. Of course it
helps our imagination to look at particular
examples of spheres and cones and triangles
and squares. But the propositions do not
merely apply to the actual figures printed in
the book, but to any such figures.
Thus geometry, like algebra, is dominated
by the ideas of "any" and "some" things.
Also, in the same way it studies the interrelations of sets of things. For example, consider any two triangles ABC and DEF.
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