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

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1
Projects
nue
their motion
by
the right line
that
followeth the
direction
of the
motion
, made
gether
with the
projicient
, whil'ſt
they
were conjoin'd
therewith
.
SIMP. So it is, in my opinion.
SAGR. Conſider well what you ſay: for I believe that it will
not
be perpendicular.
It would indeed be perpendicular, if the
Earth
ſtood ſtill, for ſo the ball would have no other motion but
that
proceeding from the fire.
But in caſe the Earth turns round,

the
ball that is in the piece, hath likewiſe a diurnal motion, ſo
that
there being added to the ſame the impulſe of the fire, it
veth
from the breech of the piece to the muzzle with two motions,
from
the compoſition whereof it cometh to paſſe that the motion
made
by the centre of the balls gravity is an inclining line.
And
for
your clearer underſtanding the ſame, let the piece A C [in
Fig
. 2.] be erected, and in it the ball B; it is manifeſt, that the
piece
ſtanding immoveable, and fire being given to it, the ball
will
make its way out by the mouth A, and with its centre,
ſing
thorow the the piece, ſhall have deſcribed the perpendicular
line
B A, and it ſhall purſue that rectitude when it is out of the
piece
, moving toward the Zenith.
But in caſe the Earth ſhould
move
round, and conſequently carry the piece along with it, in
the
time that the ball driven out of the piece ſhall move along
the
cylinder, the piece being carried by the Earth, ſhall paſſe
to
the ſituation D E, and the ball B, in going off, would be at
the
corniſh D, and the motion of the bals centre, would have
been
according to the line B D, no longer perpendicular, but
clining
towards the Eaſt; and the ball (as hath been concluded)
being
to continue its motion through the air, according to the
direction
of the motion made in the piece, the ſaid motion ſhall
continue
on according to the inclination of the line B D, and ſo
ſhall
no longer be perpendicular, but inclined towards the Eaſt,
to
which part the piece doth alſo move; whereupon the ball may
follow
the motion of the Eerth, and of the piece.
Now Simplicius,
you
ſee it demonſtrated, that the Range which you took to be
perpendicular
, is not ſo.

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