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

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1compoſition of the two motions do go alwayes receding with
greater and greater proportion from the circumference of that
cle, which the centre of the ſtones gravity would have deſigned,
if it had alwayes ſtaid upon the Tower; it followeth of neceſſity
that this receſſion at the firſt be but little, yea very ſinall, yea,
more, as ſmall as can be imagined, ſeeing that the deſcending
grave body departing from reſt, that is, from the privation of
motion, towards the bottom and entring into the right motion
downwards, it muſt needs paſſe through all the degrees of
ty, that are betwixt reſt, and any aſſigned velocity; the which
degrees are infinite; as already hath been at large diſcourſed and
proved.
It being ſuppoſed therefore, that the progreſſe of the
ration being after this manner, and it being moreover true, that
the deſcending grave body goeth to terminate in the centre of the
Earth, it is neceſſary that the line of its mixt motion be ſuch, that

it go continually receding with greater and greater proportion
from the top of the Tower, or to ſpeak more properly, from
the circumference of the circle deſcribed by the top of the Tower,
by means of the Earths converſion; but that ſuch receſſions be
leſſer and leſſer in infinitum; by how much the moveable finds it
ſelf to be leſſe and leſſe removed from the firſt term where it
reſted.
Moreover it is neceſſary, that this line of the
ed motion do go to terminate in the centre of the Earth.
Now
having preſuppoſed theſe two things, I come to deſcribe about
the centre A [in Fig. 1. of this ſecond Dialogue;] with the ſemi­
diameter A B, the circle B I, repreſenting to me the Terreſtrial
Globe, and prolonging the ſemidiameter A B to C, I have
ſcribed the height of the Tower B C; the which being carried
about by the Earth along the circumference B I, deſcribeth with
its top the arch C D: Dividing, in the next place, the line C A
in the middle at E; upon the centre E, at the diſtance E C, I
ſcribe the ſemicircle C I A: In which, I now affirm, that it is very
probable that a ſtone falling from the top of the Tower C, doth
move, with a motion mixt of the circular, which is in common,
and of its peculiar right motion.
If therefore in the circumference
C D, certain equal parts C F, F G, G H, H L, be marked, and
from the points F, G, H, L, right lines be drawn towards the
centre A, the parts of them intercepted between the two
cumferences C D and B I, ſhall repreſent unto us the ſame
Tower C B, tranſported by the Terreſtrial Globe towards D I;
in which lines the points where they come to be interſected by the
arch of the ſemicircle C I, are the places by whichfrom time to
time the falling ſtone doth paſſe; which points go continually
with greater and greater proportion receding from the top of the