DISCOURSE ONMETAPHYSICS 595
the height CD of four fathoms. Hence (by the second supposition), the forces of the two
bodies are equal.
Now let us see whether the quantity of motion is also the same in both cases: but
it is here that there will be surprise at finding a very great difference. For it has been
demonstrated by Galileo that the speed acquired in the fall CD is twice that acquired in
the fall EF, though the height is quadruple. If then, we multiply the body (A), in the pro-
portion 1, by the speed, in the proportion 2, the product or quantity of motion will be as
2, and if on the other hand, we multiply the body (B), which is as 4, by its speed, which
is as 1, then the product or quantity of motion will be as 4. Hence the quantity of motion
of body (A) at point D is half the quantity of motion of body (B) at point F, though their
forces are equal. Hence there is a great difference between the quantity of motion and
the force, as was to be proved.
From this it is seen that the force must be measured by the quantity of the effect it
can produce, e.g. by the height to which a heavy body of a particular size and kind can
be raised, something very different from the speed that can be given it, and that to give
it twice the speed more than twice the force is needed.
Nothing is simpler than this proof. Descartes only fell into error here because he
trusted too much in his thoughts before they had matured enough with a confidence
based on the happy success of some of his thoughts and on his experience of the pene-
tration of his mind, which rendered him rather too rash in the end. But I am astonished
that his followers have not recognised this error since, and I fear that little by little they
begin to imitate the Peripatetics they so make fun of, and that like them they grow
accustomed to consulting the books of their master rather than reason and nature.
- IMPORTANCE OF THEDISTINCTIONBETWEENFORCE
ANDQUANTITY OFMOTIONINTERALIA INDECIDING THAT
WEMUSTHAV ERECOURSE TOMETAPHYSICALCONSIDERATIONS
DISTINCT FROMEXTENSION TOEXPLAIN THENATURE OFBODIES
This consideration of the distinction of force from quantity of motion is important
enough, not only in physics and mechanics in the discovery of the true laws of nature
and rules of motions, and even in the correction of several practical errors that have
A(A)(B)B EF14CD