n, suppose d to e; then the distance
between the centres of the sun and of the satellite's orbit would be
always greater than the distance between the centres of the sun and
of Jupiter nearly in the subduplicate of that proportion: as by some
computations I have found. And if the satellite did gravitate towards
the sun with a force, lesser in the proportion of e to d, the distance
of the centre of the satellite's orb from the sun would be less than the
distance of the centre of Jupiter from the sun in the subduplicate of
the same proportion. Therefore, if at equal distances from the sun, the
accelerative gravity of any satellite towards the sun were greater
or less than the accelerative gravity of Jupiter towards the sun by
one-one-thousandth part of the whole gravity, the distance of the centre
of the satellite's orbit from the sun would be greater or less than the
distance of Jupiter from the sun by one one-two-thousandth part of the
whole distance--that is, by a fifth part of the distance of the utmost
satellite from the centre of Jupiter; an eccentricity of the orbit which
would be very sensible. But the orbits of the satellites are concentric
to Jupiter, and therefore the accelerative gravities of Jupiter and of
all its satellites towards the sun, at equal distances from the sun, are
as their several quantities of matter; and the weights of the moon and
of the earth towards the sun are either none, or accurately proportional
to the masses of matter which they contain.

"COR. 5.--The power of gravity is of a different nature from the
power of magnetism; for the magnetic attraction is not as the matter
attracted. Some bodies are attracted more by the magnet; others less;
most bodies not at all. The power of magnetism in one and the same body
may be increased and diminished; and is sometimes far stronger, for the
quantity of matter, than the power of gravity; and in receding from
the magnet decreases not in the duplicate, but almost in the triplicate
proportion of the distance, as nearly as I could judge from some rude
observations.

"PROPOSITION VII., THEOREM VII.

"That there is a power of gravity tending to all bodies, proportional to
the several quantities of matter which they contain.

"That all the planets mutually gravitate one towards another we have
proved before; as well as that the force of gravity towards every one of
them considered apart, is reciprocally as the square of the distance of
pla