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

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<s>
motion of deſcent, diminiſhed
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in infinitum
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by the approach of
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the moveable to the firſt ſtate of reſt, which approximation is
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augmentable
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in infinitum.
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Now let us find the other diminution
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of velocity, which likewiſe may proceed to infinity, by the
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minution of the gravity of the moveable, and this ſhall be
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ſented by drawing other lines from the point A, which contein
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angles leſſe than the angle B A E, which would be this line A D,
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the which interſecting the parallels K L, H I, F G, in the points
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M, N, and O, repreſent unto us the degrees F O, H N, K M,
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acquired in the times A F, A H, A K, leſſe than the other
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grees F G, H I, K L, acquired in the ſame times; but theſe
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latter by a moveable more ponderous, and thoſe other by a
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moveable more
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light.
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And it is manifeſt, that by the retreat of
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the line E A towards A B, contracting the angle E A B (the
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which may be done
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in infinitum,
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like as the gravity may
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in
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nitum
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be diminiſhed) the velocity of the cadent moveable may
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in like manner be diminiſhed
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in infinitum,
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and ſo conſequently
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the cauſe that impeded the projection; and therefore my thinks
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that the union of theſe two reaſons againſt the projection,
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niſhed to infinity, cannot be any impediment to the ſaid
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ction. </s>
<s>And couching the whole argument in its ſhorteſt terms, we
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will ſay, that by contracting the angle E A B, the degrees of
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locity L K, I H, G F, are diminiſhed; and moreover by the
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treat of the parallels K L, H I, F G, towards the angle A, the
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fame degrees are again diminiſhed; and both theſe diminutions
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extend to infinity: Therefore the velocity of the motion of
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ſcent may very well diminiſh ſo much, (it admitting of a twoſold
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diminution
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in infinitum
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) as that it may not ſuffice to reſtore the
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moveable to the circumference of the wheel, and thereupon may
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occaſion the projection to be hindered and wholly obviated.</s>
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<s>Again on the contrary, to impede the projection, it is
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ſary that the ſpaces by which the project is to deſcend for the
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reuniting it ſelf to the Wheel, be made ſo ſhort and cloſe
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ther, that though the deſcent of the moveable be retarded, yea
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more, diminiſhed
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in infinitum,
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yet it ſufficeth to reconduct it thither:
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and therefore it would be requiſite, that you find out a
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on of the ſaid ſpaces, not only produced to infinity, but to ſuch an
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infinity, as that it may ſuperate the double infinity that is made in
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the diminution of the velocity of the deſcending moveable. </s>
<s>But
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how can a magnitude be diminiſhed more than another, which
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hath a twofold diminution
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in infinitum
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? </s>
<s>Now let
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Simplicius
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ſerve how hard it is to philoſophate well in nature, without
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metry.
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The degrees of velocity diminiſhed
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in infinitum,
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as well
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by the diminution of the gravity of the moveable, as by the
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proxination to the firſt term of the motion, that is, to the ſtate </s>
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</chap>
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</text>
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