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

Table of figures

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        <body>
          <chap>
            <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
                <lb/>
              the moveable to the firſt ſtate of reſt, which approximation is
                <lb/>
              augmentable
                <emph type="italics"/>
              in infinitum.
                <emph.end type="italics"/>
              Now let us find the other diminution
                <lb/>
              of velocity, which likewiſe may proceed to infinity, by the
                <lb/>
              minution of the gravity of the moveable, and this ſhall be
                <lb/>
              ſented by drawing other lines from the point A, which contein
                <lb/>
              angles leſſe than the angle B A E, which would be this line A D,
                <lb/>
              the which interſecting the parallels K L, H I, F G, in the points
                <lb/>
              M, N, and O, repreſent unto us the degrees F O, H N, K M,
                <lb/>
              acquired in the times A F, A H, A K, leſſe than the other
                <lb/>
              grees F G, H I, K L, acquired in the ſame times; but theſe
                <lb/>
              latter by a moveable more ponderous, and thoſe other by a
                <lb/>
              moveable more
                <emph type="italics"/>
              light.
                <emph.end type="italics"/>
              And it is manifeſt, that by the retreat of
                <lb/>
              the line E A towards A B, contracting the angle E A B (the
                <lb/>
              which may be done
                <emph type="italics"/>
              in infinitum,
                <emph.end type="italics"/>
              like as the gravity may
                <emph type="italics"/>
              in
                <lb/>
              nitum
                <emph.end type="italics"/>
              be diminiſhed) the velocity of the cadent moveable may
                <lb/>
              in like manner be diminiſhed
                <emph type="italics"/>
              in infinitum,
                <emph.end type="italics"/>
              and ſo conſequently
                <lb/>
              the cauſe that impeded the projection; and therefore my thinks
                <lb/>
              that the union of theſe two reaſons againſt the projection,
                <lb/>
              niſhed to infinity, cannot be any impediment to the ſaid
                <lb/>
              ction. </s>
              <s>And couching the whole argument in its ſhorteſt terms, we
                <lb/>
              will ſay, that by contracting the angle E A B, the degrees of
                <lb/>
              locity L K, I H, G F, are diminiſhed; and moreover by the
                <lb/>
              treat of the parallels K L, H I, F G, towards the angle A, the
                <lb/>
              fame degrees are again diminiſhed; and both theſe diminutions
                <lb/>
              extend to infinity: Therefore the velocity of the motion of
                <lb/>
              ſcent may very well diminiſh ſo much, (it admitting of a twoſold
                <lb/>
              diminution
                <emph type="italics"/>
              in infinitum
                <emph.end type="italics"/>
              ) as that it may not ſuffice to reſtore the
                <lb/>
              moveable to the circumference of the wheel, and thereupon may
                <lb/>
              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
                <lb/>
              ſary that the ſpaces by which the project is to deſcend for the
                <lb/>
              reuniting it ſelf to the Wheel, be made ſo ſhort and cloſe
                <lb/>
              ther, that though the deſcent of the moveable be retarded, yea
                <lb/>
              more, diminiſhed
                <emph type="italics"/>
              in infinitum,
                <emph.end type="italics"/>
              yet it ſufficeth to reconduct it thither:
                <lb/>
              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
                <lb/>
              infinity, as that it may ſuperate the double infinity that is made in
                <lb/>
              the diminution of the velocity of the deſcending moveable. </s>
              <s>But
                <lb/>
              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
                <emph type="italics"/>
              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,
                <emph.end type="italics"/>
              as well
                <lb/>
              by the diminution of the gravity of the moveable, as by the
                <lb/>
              proxination to the firſt term of the motion, that is, to the ſtate </s>
            </p>
          </chap>
        </body>
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    </archimedes>