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

VARIABLES 23
OP to represent p units of pressure. Then
the point Q, which is found by completing the
parallelogram MONQ, represents the state of
the gas when its volume is v cubic feet and its
pressure is p lb. weight per square inch. If
the circumstances of the portion of gas considered are such that pv=l, then all these
points Q which correspond to any possible
state of this portion of gas must lie on the
curved line ABC, which includes all points
for which p and v are positive, and pv=l.
Thus this curved line gives a pictorial representation of the relation holding between the
volume and the pressure. When the pressure
is very big the corresponding point Q must
be near C, or even beyond C on the undrawn
part of the curve; then the volume will be
very small. When the volume is big Q will
be near to A, or beyond A; and then the
pressure will be small. Notice that an engineer or a physicist may want to know the
particular pressure corresponding to some
definitely assigned volume. Then we have
the case of determining the unknown p when
v is a known number. But this is only in
particular cases. In considering generally
the properties of the gas and how it will behave, he has to have in his mind the general
form of the whole curve ABC and its general
properties. In other words the really fundamental idea is that of the pair of variables