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

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1motion of deſcent, diminiſhed in infinitum by the approach of
the
moveable to the firſt ſtate of reſt, which approximation is
augmentable
in infinitum. Now let us find the other diminution
of
velocity, which likewiſe may proceed to infinity, by the
minution
of the gravity of the moveable, and this ſhall be
ſented
by drawing other lines from the point A, which contein
angles
leſſe than the angle B A E, which would be this line A D,
the
which interſecting the parallels K L, H I, F G, in the points
M
, N, and O, repreſent unto us the degrees F O, H N, K M,
acquired
in the times A F, A H, A K, leſſe than the other
grees
F G, H I, K L, acquired in the ſame times; but theſe
latter
by a moveable more ponderous, and thoſe other by a
moveable
more light. And it is manifeſt, that by the retreat of
the
line E A towards A B, contracting the angle E A B (the
which
may be done in infinitum, like as the gravity may in
nitum
be diminiſhed) the velocity of the cadent moveable may
in
like manner be diminiſhed in infinitum, and ſo conſequently
the
cauſe that impeded the projection; and therefore my thinks
that
the union of theſe two reaſons againſt the projection,
niſhed
to infinity, cannot be any impediment to the ſaid
ction
.
And couching the whole argument in its ſhorteſt terms, we
will
ſay, that by contracting the angle E A B, the degrees of
locity
L K, I H, G F, are diminiſhed; and moreover by the
treat
of the parallels K L, H I, F G, towards the angle A, the
fame
degrees are again diminiſhed; and both theſe diminutions
extend
to infinity: Therefore the velocity of the motion of
ſcent
may very well diminiſh ſo much, (it admitting of a twoſold
diminution
in infinitum) as that it may not ſuffice to reſtore the
moveable
to the circumference of the wheel, and thereupon may
occaſion
the projection to be hindered and wholly obviated.

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