world.

Now, as the whole universe with all its parts possesses a certain form or
figure, if any part of it moves, that form or figure of the whole is
varied: hence, as MOTION is no other than a perpetual variation of figure,
our idea of motion is also a real resemblance of the motion that produced
it.

It may be said in objection to this definition of motion, that an ivory
globe may revolve on its axis, and that here will be a motion without
change of figure. But the figure of the particle _x_ on one side of this
globe is not the _same_ figure as the figure of _y_ on the other side, any
more than the particles themselves are the same, though they are _similar_
figures; and hence they cannot change place with each other without
disturbing or changing the figure of the whole.

Our idea of TIME is from the same source, but is more abstracted, as it
includes only the comparative velocities of these variations of figure;
hence if it be asked, How long was this book in printing? it may be
answered, Whilst the sun was passing through Aries.

Our idea of PLACE includes only the figure of a group of bodies, not the
figures of the bodies themselves. If it be asked where is Nottinghamshire,
the answer is, it is surrounded by Derbyshire, Lincolnshire and
Leicestershire; hence place is our idea of the figure of one body
surrounded by the figures of other bodies.

The idea of SPACE is a more abstracted idea of place excluding the group of
bodies.

The idea of NUMBER includes only the particular arrangements, or
distributions of a group of bodies, and is therefore only a more abstracted
idea of the parts of the figure of the group of bodies; thus when I say
England is divided into forty counties, I only speak of certain divisions
of its figure.

Hence arises the certainty of the mathematical sciences, as they explain
these properties of bodies, which are exactly resembled by our ideas of
them, whilst we are obliged to collect almost all our other knowledge from
experiment; that is, by observing the effects exerted by one body upon
another.

3. _Of the Penetrability of Matter._

The impossibility of two bodies existing together in the same space cannot
be deduced from our idea of solidity, or of figure. As soon as we perceive
the motions of objects that surround us, and learn that we possess a power
to move our own bodies, we experience, that those objects, which excite in
us the idea of solidity and of figure, oppose this