On the Acceleration of Falling Bodies

...differed regarding the cause of acceleration, by teaching that gravity alone
is the cause of the beginning of motion, and that only the medium, namely the air, is the
cause of acceleration, insofar as it recoils from the front, and from behind
it closes in and pushes the heavy object; whereas otherwise, if gravity alone were acting,
and remaining constant, as in a vacuum, the descent would be uniform,
and would persist in its same state: therefore the opportunity was taken and accepted,
and in this place granted, to add something regarding the physical cause.
For first, the fall indicated at the end of the previous letter is deduced
a little more extensively: namely, by declaring by what progression
it had been attempted, in the letters On motion impressed by a moved
mover original: "de Motu impresso à motore translato", to explain the cause why heavy objects are
accelerated according to the progression of odd numbers starting from
one; This refers to the law of falling bodies, where the distance traveled in successive units of time follows the ratio of odd numbers: 1, 3, 5, 7, etc. and how such a cause had been recognized when
in the first moment, only the attractive force of the Earth would impress
a single stroke: then in the second and remaining moments, both the same
attractive force, as well as the air following from behind and pressing, so that
in any given moment two strokes, as it were, were impressed:
and thus in the first moment, one degree of velocity would be acquired, by which
one space would be traversed: in each following moment, however, two more would
be added, and they would therefore be three, five, seven, etc.,
by which just as many spaces would consequently be traversed: from which
it would also be consistent that the velocities are as the spaces, which therefore
ought to be represented together by those areas of triangles:
which was noticed to be contradictory. Next, however, it is shown,
why, since a single cause is sufficient according to what was explained before
(it is assumed, moreover, that this cause is none other than
the attractive force of the Earth itself), it is shown, I say, that both causes
assigned by the Reverend Father original: "R. P." referring to Marin Mersenne seem to be rejected, insofar as the
medium, namely the air, contributes nothing to acceleration, but rather