Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/034.jpg" pagenum="18"/>
              in as much more time as it was in coming by the inclining plane, it
                <lb/>
              would paſs double the ſpace of the plane inclined: namely (for
                <lb/>
              example) if the ball had paſt the plane D A in an hour,
                <lb/>
              tinuing to move uniformly with that degree of velocity which it
                <lb/>
              is found to have in its arriving at the term A, it ſhall paſs in an
                <lb/>
              hour a ſpace double the length D A; and becauſe (as we have
                <lb/>
              ſaid) the degrees of velocity acquired in the points B and A, by
                <lb/>
              the moveables that depart from any point taken in the
                <lb/>
              lar C B, and that deſcend, the one by the inclined plane, the
                <lb/>
              ther by the ſaid perpendicular, are always equal: therefore the
                <lb/>
              cadent by the perpendicular may depart from a term ſo near to B,
                <lb/>
              that the degree of velocity acquired in B, would not ſuffice (ſtill
                <lb/>
              maintaining the ſame) to conduct the moveable by a ſpace
                <lb/>
              ble the length of the plane inclined in a year, nor in ten, no nor
                <lb/>
              in a hundred. </s>
              <s>We may therefore conclude, that if it be true,
                <lb/>
              that according to the ordinary courſe of nature a moveable, all
                <lb/>
              external and accidental impediments removed, moves upon an
                <lb/>
              clining plane with greater and greater tardity, according as the
                <lb/>
              inclination ſhall be leſs; ſo that in the end the tardity comes to be
                <lb/>
              infinite, which is, when the inclination concludeth in, and joyneth
                <lb/>
              to the horizontal plane; and if it be true likewiſe, that the
                <lb/>
              gree of velocity acquired in ſome point of the inclined plane, is
                <lb/>
              equal to that degree of velocity which is found to be in the
                <lb/>
              able that deſcends by the perpendicular, in the point cut by a
                <lb/>
              parallel to the Horizon, which paſſeth by that point of the
                <lb/>
              ning plane; it muſt of neceſſity be granted, that the cadent
                <lb/>
              parting from reſt, paſſeth thorow all the infinite degrees of
                <lb/>
              dity, and that conſequently, to acquire a determinate degree of
                <lb/>
              velocity, it is neceſſary that it move firſt by right lines,
                <lb/>
              ing by a ſhort or long ſpace, according as the velocity to be
                <lb/>
              red, ought to be either leſs or greater, and according as the plane
                <lb/>
              on which it deſcendeth is more or leſs inclined; ſo that a plane
                <lb/>
              may be given with ſo ſmall inclination, that to acquire in it the
                <lb/>
              aſſigned degree of velocity, it muſt firſt move in a very great ſpace,
                <lb/>
              and take a very long time; whereupon in the horizontal plane, any
                <lb/>
              how little ſoever velocity, would never be naturally acquired,
                <lb/>
              ſince that the moveable in this caſe will never move: but the </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg48"/>
                <lb/>
              motion by the horizontal line, which is neither declined or
                <lb/>
              ned, is a circular motion about the centre: therefore the
                <lb/>
              lar motion is never acquired naturally, without the right motion
                <lb/>
              precede it; but being once acquired, it will continue perpetually
                <lb/>
              with uniform velocity. </s>
              <s>I could with other diſcourſes evince and
                <lb/>
              demonſtrate the ſame truth, but I will not by ſo great a
                <lb/>
              fion interrupt our principal argument: but rather will return to
                <lb/>
              it upon ſome other occaſion; eſpecially ſince we now aſſumed the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum