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

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