Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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1turn round, ſtaying there above, and moving along with the
urnal converſion.
Now I tell him, that that ſame ball falling from
the concave unto the centre, will acquire a degree of velocity
much more than double the velocity of the diurnal motion of the
Lunar concave; and this I will make out by ſolid and not

tinent ſuppoſitions.
You muſt know therefore that the grave
body falling and acquiring all the way new velocity according
to the proportion already mentioned, hath in any whatſoever
place of the line of its motion ſuch a degree of velocity, that if it
ſhould continue to move therewith, uniformly without farther
encreaſing it; in another time like to that of its deſcent, it would
paſſe a ſpace double to that paſſed in the line of the precedent
motion of deſcent.
And thus for example, if that ball in coming
from the concave of the Moon to its centre hath ſpent three hours,
22 min. prim. and 4 ſeconds, I ſay, that being arrived at the
tre, it ſhall find it ſelf conſtituted in ſuch a degree of velocity, that
if with that, without farther encreaſing it, it ſhould continue to
move uniformly, it would in other 3 hours, 22 min. prim. and
4 ſeconds, paſſe double that ſpace, namely as much as the whole
diameter of the Lunar Orb; and becauſe from the Moons
cave to the centre are 196000 miles, which the ball paſſeth in 3
hours 22 prim. min. and 4 ſeconds, therefore (according to what
hath been ſaid) the ball continuing to move with the velocity
which it is found to have in its arrival at the centre, it would
paſſe in other 3 hours 22 min.
prim. and 4 ſeconds, a ſpace
ble to that, namely 392000 miles; but the ſame continuing in
the concave of the Moon, which is in circuit 1232000 miles, and
moving therewith in a diurnal motion, it would make in the ſame
time, that is in 3 hours 22 min.
prim. and 4 ſeconds, 172880
miles, which are fewer by many than the half of the 392000
miles.
You ſee then that the motion in the concave is not as the
modern Author ſaith, that is, of a velocity impoſſible for the
ing ball to partake of, &c.
The falling
able if it move with
a degree of
ty acquired in a
like time with an
uniform motion, it
ſhall paß a ſpace
double to that
ſed with the
leratedmotion.
SAGR. The diſcourſe would paſs for current, and would give
me full ſatisfaction, if that particular was but ſalved, of the
ving of the moveable by a double ſpace to that paſſed in falling
in another time equal to that of the deſcent, in caſe it doth continue
to move uniformly with the greateſt degree of velocity acquired
in deſcending.
A propoſition which you alſo once before
ſed as true, but never demonſtrated.
SALV. This is one of the demonſtrations of Our Friend, and
you ſhall ſee it in due time; but for the preſent, I will with ſome
conjectures (not teach you any thing that is new, but) remember you
of a certain contrary opinion, and ſhew you, that it may haply ſo be.
A bullet of lead hanging in a long and fine thread faſtened to the