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

CHAPTER XVII
QUANTITY
IN the previous chapter we pointed out
that lengths are measurable in terms of some
unit length, areas in term of a unit area, and
volumes in terms of a unit volume.
When we have a set of things such as
lengths which are measurable in terms of any
one of them, we say that they are quantities
of the same kind. Thus lengths are quantities
of the same kind, so are areas, and so are
volumes. But an area is not a quantity of
the same kind as a length, nor is it of the
same kind as a volume. Let us think a little
more on what is meant by being measurable,
taking lengths as an example.
Lengths are measured by the foot-rule. By
transporting the foot-rule from place to place
we judge of the equality of lengths. Again,
three adjacent lengths, each of one foot, form
one whole length of three feet. Thus to measure lengths we have to determine the equality
of lengths and the addition of lengths. When
some test has been applied, such as the transporting of a foot-rule, we say that the lengths
are equal; and when some process has been
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