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

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From the things premiſed I gather that the project ſwiftly
ſwinged round by the projicient, in its ſeparating from it, doth
tain an impetus of continuing its motion by the right line, which
toucheth the circle deſcribed by the motion of the projicient in
the point of ſeparation, by which motion the project goeth
tinually receding from the centre of the circle deſcribed by the
motion of the projicient.
The project
veth by the
gent of the circle of
the motion
dent in the point of
SALV. You know then by this time the reaſon why grave
dies ſticking to the rim of a wheele, ſwiftly moved, are extruded
and thrown beyond the circumference to yet a farther diſtance
from the centre.
SIMP. I think I underſtand this very well; but this new
ledg rather increaſeth than leſſeneth my incredulity that the Earth
can turn round with ſo great velocity, without extruding up into
the sky, ſtones, animals, &c.
SALV. In the ſame manner that you have underſtood all this,
you ſhall, nay you do underſtand the reſt: and with recollecting
your ſelf, you may remember the ſame without the help of
thers: but that we may loſe no time, I will help your memory
You do already know of your ſelf, that the circular
tion of the projicient impreſſeth on the project an impetus of
ving (when they come to ſeparate) by the right Tangent, the
circle of the motion in the point of ſeparation, and continuing
long by the ſame the motion ever goeth receding farther and
ther from the projicient: and you have ſaid, that the project
would continue to move along by that right line, if there were not
by its proper weight an inclination of deſcent added unto it; from
which the incurvation of the line of motion is derived.
It ſeems
moreover that you knew of your ſelf, that this incurvation
ways bended towards the centre of the Earth, for thither do all
grave bodies tend.
Now I proceed a little farther, and ask you,
ther the moveable after its ſeparation, in continuing the right
tion goeth always equally receding from the centre, or if you will,
from the circumference of that circle, of which the precedent
tion was a part; which is as much as to ſay, Whether a moveable,
that forſaking the point of a Tangent, and moving along by the
ſaid Tangent, doth equally recede from the point of contact, and
from the circumference of the circle?
SIMP. No, Sir: for the Tangent near to the point of contact,
recedeth very little from the circumference, wherewith it keepeth
a very narrow angle, but in its going farther and farther
off, the diſtance always encreaſeth with a greater proportion; ſo
that in a circle that ſhould have v. g. ten yards of diameter, a point
of the Tangent that was diſtant from the contact but two palms,
would be three or four times as far diſtant from the circumference

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