do really descend; for a
pendulum oscillating seconds in the latitude of Paris will be 3 Paris
feet, and 8 lines 1/2 in length, as Mr. Huygens has observed. And the
space which a heavy body describes by falling in one second of time
is to half the length of the pendulum in the duplicate ratio of the
circumference of a circle to its diameter (as Mr. Huygens has also
shown), and is therefore 15 Paris feet, 1 inch, 1 line 4/9. And
therefore the force by which the moon is retained in its orbit is
that very same force which we commonly call gravity; for, were gravity
another force different from that, then bodies descending to the earth
with the joint impulse of both forces would fall with a double velocity,
and in the space of one second of time would describe 30 1/6 Paris feet;
altogether against experience."(1)

All this is beautifully clear, and its validity has never in recent
generations been called in question; yet it should be explained that the
argument does not amount to an actually indisputable demonstration.
It is at least possible that the coincidence between the observed and
computed motion of the moon may be a mere coincidence and nothing more.
This probability, however, is so remote that Newton is fully justified
in disregarding it, and, as has been said, all subsequent generations
have accepted the computation as demonstrative.

Let us produce now Newton's further computations as to the other
planetary bodies, passing on to his final conclusion that gravity is a
universal force.

"PROPOSITION V., THEOREM V.

"That the circumjovial planets gravitate towards Jupiter; the
circumsaturnal towards Saturn; the circumsolar towards the sun; and by
the forces of their gravity are drawn off from rectilinear motions, and
retained in curvilinear orbits.

"For the revolutions of the circumjovial planets about Jupiter, of the
circumsaturnal about Saturn, and of Mercury and Venus and the other
circumsolar planets about the sun, are appearances of the same sort with
the revolution of the moon about the earth; and therefore, by Rule ii.,
must be owing to the same sort of causes; especially since it has been
demonstrated that the forces upon which those revolutions depend tend
to the centres of Jupiter, of Saturn, and of the sun; and that those
forces, in receding from Jupiter, from Saturn, and from the sun,
decrease in the same proportion, and according to the same law, as the
force of gravity does in recedin