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.
Again on the contrary, to impede the projection, it is
ſary that the ſpaces by which the project is to deſcend for the
reuniting it ſelf to the Wheel, be made ſo ſhort and cloſe
ther, that though the deſcent of the moveable be retarded, yea
more, diminiſhed in infinitum, yet it ſufficeth to reconduct it thither:
and therefore it would be requiſite, that you find out a
on of the ſaid ſpaces, not only produced to infinity, but to ſuch an
infinity, as that it may ſuperate the double infinity that is made in
the diminution of the velocity of the deſcending moveable.
But
how can a magnitude be diminiſhed more than another, which
hath a twofold diminution in infinitum? Now let Simplicius
ſerve how hard it is to philoſophate well in nature, without
metry. The degrees of velocity diminiſhed in infinitum, as well
by the diminution of the gravity of the moveable, as by the
proxination to the firſt term of the motion, that is, to the ſtate