594 GOTTFRIEDLEIBNIZ
things that surpass the powers of our natures, and even those of every limited nature.
Consequently, to speak more clearly, I say that miracles and the extraordinary acts of
God’s concurrence have the particular character that they could not be foreseen by the
reasoning of any created mind, however enlightened it might be, since the comprehen-
sion of the general order surpasses them all, while everything called natural depends on
the less general norms creatures can understand. Hence, in order to say nothing of these
norms or laws of nature that might cause offence, it would be good to link particular
ways of speaking with particular thoughts: whatever includes everything we express
could then be called our essence or idea, and since it expresses our union with God, it
has no limits and nothing exceeds it. But what is limited in us could be called our nature
or power, and in this respect what exceeds the natures of all created substances is super-
natural.
- EXAMPLE OF ASUBALTERNNORM ORLAW O FNATURE;
INWHICHITISSHOWN THATGODALWAYSPRESERVES
THESAMEFORCE, BUT NOT THESAMEQUANTITY OFMOTION...
AGAINST THECARTESIANS ANDSOMEOTHERS
I have often mentioned subaltern maxims or laws of nature already, and it would be good
to give an example. Our new philosophers commonly make use of that famous rule
advanced by Descartes that God always preserves the same quantity of motion in the
world. It seems highly plausible indeed, and in the past I held it to be indubitable. But
I have since come to recognise wherein lay its error. It is that Descartes and many other
able mathematicians thought that the quantity of motion (i.e. the speed times the size of
the mobile) was the same thing as the force, or at least expressed it perfectly, or geomet-
rically speaking, that the forces are in compound proportion of the speeds and the bodies.
Now it is obvious indeed that the same force should always be preserved in the universe.
So, when we attend to the phenomena with care, we see clearly that mechanical perpet-
ual motion does not occur, because then the force of a machine, which is continually
being slightly diminished by friction, and must consequently soon cease, would be
replaced and so would increase of itself without any new impulsion from outside. We
also note that the force of a body is diminished solely to the extent that it gives some of
it to neighbouring bodies or to its own parts in so far as these have independent motions.
Thus they thought that what can be said of force could also be said of quantity of
motion. But, to show the difference, I suppose that a body falling from a particular
height acquires the force needed to climb up again, if its direction of travel should take
it that way, unless there are hindrances. For example, a pendulum would rise right back
again to the height it had fallen from if the resistance of the air and other small obstacles
did not somehow diminish the force acquired.
I supposealso that as much force is needed to raise a body A of one pound a
height CD of four fathoms as to raise a body B of four pounds a height EF of one
fathom. All this is accepted by our new philosophers.
Hence, it is manifest that body (A), after falling from the height CD has acquired
as much force precisely as body (B) after falling from the height EF. For when body (B)
has arrived at F and has the force to climb back to E (by the first supposition), it has in
consequence the force to carry a body of four pounds, that is its own body, to the height
EF of one fathom, and similarly, when body (A) has reached D and has the force to
climb back to C, it has the force to carry a body of one pound, that is its own body, to