uantity of matter in
gold was to the quantity of matter in the wood as the action of the
motive force (or vis motrix) upon all the gold to the action of the same
upon all the wood--that is, as the weight of the one to the weight
of the other: and the like happened in the other bodies. By these
experiments, in bodies of the same weight, I could manifestly have
discovered a difference of matter less than the thousandth part of the
whole, had any such been. But, without all doubt, the nature of gravity
towards the planets is the same as towards the earth. For, should we
imagine our terrestrial bodies removed to the orb of the moon, and
there, together with the moon, deprived of all motion, to be let go, so
as to fall together towards the earth, it is certain, from what we have
demonstrated before, that, in equal times, they would describe equal
spaces with the moon, and of consequence are to the moon, in quantity
and matter, as their weights to its weight.

"Moreover, since the satellites of Jupiter perform their revolutions in
times which observe the sesquiplicate proportion of their distances from
Jupiter's centre, their accelerative gravities towards Jupiter will
be reciprocally as the square of their distances from Jupiter's
centre--that is, equal, at equal distances. And, therefore, these
satellites, if supposed to fall TOWARDS JUPITER from equal heights,
would describe equal spaces in equal times, in like manner as heavy
bodies do on our earth. And, by the same argument, if the circumsolar
planets were supposed to be let fall at equal distances from the sun,
they would, in their descent towards the sun, describe equal spaces in
equal times. But forces which equally accelerate unequal bodies must be
as those bodies--that is to say, the weights of the planets (TOWARDS THE
SUN) must be as their quantities of matter. Further, that the weights
of Jupiter and his satellites towards the sun are proportional to the
several quantities of their matter, appears from the exceedingly
regular motions of the satellites. For if some of these bodies were more
strongly attracted to the sun in proportion to their quantity of matter
than others, the motions of the satellites would be disturbed by
that inequality of attraction. If at equal distances from the sun any
satellite, in proportion to the quantity of its matter, did gravitate
towards the sun with a force greater than Jupiter in proportion to his,
according to any given proportio