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

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SALV. This is a doubt worthy of Sagredus; and to explain it ſo as
that
we may more cleerly apprehend it, for that you ſay that you
your
ſelf have but a confuſed Idea of it, we will diſtinguiſh of the
ſame
by reducing it into figure; which may alſo perhaps afford us
ſome
caſe in reſolving the ſame.
Let us therefore [in Fig. 4.] draw
a
perpendicular line towards the centre, and let it be AC, and to it
at
right angles let there be drawn the Horizontal line A B, upon
which
the motion of the projection ought to be made; now the
ject
would continue to move along the ſame with an even motion, if
ſo
be its gravity did not incline it downwards.
Let us ſuppoſe from
the
point A a right line to be drawn, that may make any angle at
pleaſure
with the line A B; which let be A E, and upon AB let us
mark
ſome equal ſpaces AF, FH, HK, and from them let us let fall
the
perpendiculars FG, HI, K L, as far as AE.
And becauſe, as al
ready
hath been ſaid, the deſcending grave body departing from reſt,
goeth
from time to time acquiring a greater degree of velocity,
according
as the ſaid time doth ſucceſſively encreaſe; we may
ceive
the ſpaces AF, FH, HK, to repreſent unto us equal times; and
the
perpendiculars FG, HI, KL, degrees of velocity acquired in the
ſaid
times; ſo that the degree of velocity acquired in the whole time
A
K, is as the line K L, in reſpect to the degree H I, acquired in the
time
AH, and the degree FG in the time AF; the which degrees KL,
HI
, FG, are (as is manifeſt) the ſame in proportion, as the times K A,
HA
, F A, and if other perpendiculars were drawn from the points
marked
at pleaſure in the line F A, one might ſucceſſively find
grees
leſſe and leſſe in infinitum, proceeding towards the point A,
repreſenting
the firſt inſtant of time, and the firſt ſtate of reſt.
And
this
retreat towards A, repreſenteth the firſt propenſion to the

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