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

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            <p type="main">
              <s>
                <pb xlink:href="040/01/196.jpg" pagenum="178"/>
              motion of deſcent, diminiſhed
                <emph type="italics"/>
              in infinitum
                <emph.end type="italics"/>
              by the approach of
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              the moveable to the firſt ſtate of reſt, which approximation is
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              augmentable
                <emph type="italics"/>
              in infinitum.
                <emph.end type="italics"/>
              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
                <emph type="italics"/>
              light.
                <emph.end type="italics"/>
              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
                <emph.end type="italics"/>
              be diminiſhed) the velocity of the cadent moveable may
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              in like manner be diminiſhed
                <emph type="italics"/>
              in infinitum,
                <emph.end type="italics"/>
              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
                <emph type="italics"/>
              in infinitum
                <emph.end type="italics"/>
              ) 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>
            </p>
            <p type="main">
              <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
                <emph type="italics"/>
              in infinitum,
                <emph.end type="italics"/>
              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
                <emph type="italics"/>
              in infinitum
                <emph.end type="italics"/>
              ? </s>
              <s>Now let
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              Simplicius
                <emph.end type="italics"/>
                <lb/>
              ſerve how hard it is to philoſophate well in nature, without
                <emph type="italics"/>
                <lb/>
              metry.
                <emph.end type="italics"/>
              The degrees of velocity diminiſhed
                <emph type="italics"/>
              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>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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