teps
of his progress somewhat in detail, and state his theories and their
demonstration in his own words. Proposition IV., theorem 4, of his
Principia is as follows:

"That the moon gravitates towards the earth and by the force of gravity
is continually drawn off from a rectilinear motion and retained in its
orbit.

"The mean distance of the moon from the earth, in the syzygies
in semi-diameters of the earth, is, according to Ptolemy and most
astronomers, 59; according to Vendelin and Huygens, 60; to Copernicus,
60 1/3; to Street, 60 2/3; and to Tycho, 56 1/2. But Tycho, and all that
follow his tables of refractions, making the refractions of the sun and
moon (altogether against the nature of light) to exceed the refractions
of the fixed stars, and that by four or five minutes NEAR THE HORIZON,
did thereby increase the moon's HORIZONTAL parallax by a like number of
minutes, that is, by a twelfth or fifteenth part of the whole
parallax. Correct this error and the distance will become about 60 1/2
semi-diameters of the earth, near to what others have assigned. Let us
assume the mean distance of 60 diameters in the syzygies; and suppose
one revolution of the moon, in respect to the fixed stars, to be
completed in 27d. 7h. 43', as astronomers have determined; and the
circumference of the earth to amount to 123,249,600 Paris feet, as
the French have found by mensuration. And now, if we imagine the moon,
deprived of all motion, to be let go, so as to descend towards the earth
with the impulse of all that force by which (by Cor. Prop. iii.) it is
retained in its orb, it will in the space of one minute of time describe
in its fall 15 1/12 Paris feet. For the versed sine of that arc which
the moon, in the space of one minute of time, would by its mean motion
describe at the distance of sixty semi-diameters of the earth, is nearly
15 1/12 Paris feet, or more accurately 15 feet, 1 inch, 1 line 4/9.
Wherefore, since that force, in approaching the earth, increases in the
reciprocal-duplicate proportion of the distance, and upon that account,
at the surface of the earth, is 60 x 60 times greater than at the moon,
a body in our regions, falling with that force, ought in the space of
one minute of time to describe 60 x 60 x 15 1/12 Paris feet; and in the
space of one second of time, to describe 15 1/12 of those feet, or more
accurately, 15 feet, 1 inch, 1 line 4/9. And with this very force we
actually find that bodies here upon earth