hases
which it shows and the proportion of its apparent diameters; for from
its appearing full near conjunction with the sun and gibbous in its
quadratures,[4] it is certain that it travels round the sun. And since
its diameter appears about five times greater when in opposition to the
sun than when in conjunction therewith, and its distance from the earth
is reciprocally as its apparent diameter, that distance will be about
five times less when in opposition to than when in conjunction with the
sun; but in both cases its distance from the sun will be nearly about
the same with the distance which is inferred from its gibbous appearance
in the quadratures. And as it encompasses the sun at almost equal
distances, but in respect of the earth is very unequally distant, so by
radii drawn to the sun it describes areas nearly uniform; but by radii
drawn to the earth it is sometimes swift, sometimes stationary, and
sometimes retrograde.

That Jupiter in a higher orbit than Mars is likewise revolved about the
sun with a motion nearly equable as well in distance as in the areas
described, I infer from Mr. Flamsted's observations of the eclipses of
the innermost satellite; and the same thing may be concluded of Saturn
from his satellite by the observations of Mr. Huyghens and Mr. Halley.

If Jupiter was viewed from the sun it would never appear retrograde or
stationary, as it is seen sometimes from the earth, but always to go
forward with a motion nearly uniform. And from the very great inequality
of its apparent geocentric motion we infer--as it has been previously
shown that we may infer--that the force by which Jupiter is turned out
of a rectilinear course and made to revolve in an orbit is not directed
to the centre of the earth. And the same argument holds good in Mars and
in Saturn. Another centre of these forces is, therefore, to be looked
for, about which the areas described by radii intervening may be
equable; and that this is the sun, we have proved already in Mars and
Saturn nearly, but accurately enough in Jupiter.

The distances of the planets from the sun come out the same whether,
with Tycho, we place the earth in the centre of the system, or the sun
with Copernicus; and we have already proved that, these distances are
true in Jupiter. Kepler and Bullialdus have with great care determined
the distances of the planets from the sun, and hence it is that their
tables agree best with the heavens. And in all the planet