Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667
page |< < of 701 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/190.jpg" pagenum="172"/>
                <arrow.to.target n="marg365"/>
                <lb/>
              them. </s>
              <s>From the things premiſed I gather that the project ſwiftly
                <lb/>
              ſwinged round by the projicient, in its ſeparating from it, doth
                <lb/>
              tain an
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              of continuing its motion by the right line, which
                <lb/>
              toucheth the circle deſcribed by the motion of the projicient in
                <lb/>
              the point of ſeparation, by which motion the project goeth
                <lb/>
              tinually receding from the centre of the circle deſcribed by the
                <lb/>
              motion of the projicient.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg365"/>
                <emph type="italics"/>
              The project
                <lb/>
              veth by the
                <lb/>
              gent of the circle of
                <lb/>
              the motion
                <lb/>
              dent in the point of
                <lb/>
              ſeparation.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>You know then by this time the reaſon why grave
                <lb/>
              dies ſticking to the rim of a wheele, ſwiftly moved, are extruded
                <lb/>
              and thrown beyond the circumference to yet a farther diſtance
                <lb/>
              from the centre.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I think I underſtand this very well; but this new
                <lb/>
              ledg rather increaſeth than leſſeneth my incredulity that the Earth
                <lb/>
              can turn round with ſo great velocity, without extruding up into
                <lb/>
              the sky, ſtones, animals,
                <emph type="italics"/>
              &c.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>In the ſame manner that you have underſtood all this,
                <lb/>
              you ſhall, nay you do underſtand the reſt: and with recollecting
                <lb/>
              your ſelf, you may remember the ſame without the help of
                <lb/>
              thers: but that we may loſe no time, I will help your memory
                <lb/>
              therein. </s>
              <s>You do already know of your ſelf, that the circular
                <lb/>
              tion of the projicient impreſſeth on the project an
                <emph type="italics"/>
              impetus
                <emph.end type="italics"/>
              of
                <lb/>
              ving (when they come to ſeparate) by the right Tangent, the
                <lb/>
              circle of the motion in the point of ſeparation, and continuing
                <lb/>
              long by the ſame the motion ever goeth receding farther and
                <lb/>
              ther from the projicient: and you have ſaid, that the project
                <lb/>
              would continue to move along by that right line, if there were not
                <lb/>
              by its proper weight an inclination of deſcent added unto it; from
                <lb/>
              which the incurvation of the line of motion is derived. </s>
              <s>It ſeems
                <lb/>
              moreover that you knew of your ſelf, that this incurvation
                <lb/>
              ways bended towards the centre of the Earth, for thither do all
                <lb/>
              grave bodies tend. </s>
              <s>Now I proceed a little farther, and ask you,
                <lb/>
              ther the moveable after its ſeparation, in continuing the right
                <lb/>
              tion goeth always equally receding from the centre, or if you will,
                <lb/>
              from the circumference of that circle, of which the precedent
                <lb/>
              tion was a part; which is as much as to ſay, Whether a moveable,
                <lb/>
              that forſaking the point of a Tangent, and moving along by the
                <lb/>
              ſaid Tangent, doth equally recede from the point of contact, and
                <lb/>
              from the circumference of the circle?</s>
            </p>
            <p type="main">
              <s>SIMP. No, Sir: for the Tangent near to the point of contact,
                <lb/>
              recedeth very little from the circumference, wherewith it keepeth
                <lb/>
              a very narrow angle, but in its going farther and farther
                <lb/>
              off, the diſtance always encreaſeth with a greater proportion; ſo
                <lb/>
              that in a circle that ſhould have
                <emph type="italics"/>
              v. </s>
              <s>g.
                <emph.end type="italics"/>
              ten yards of diameter, a point
                <lb/>
              of the Tangent that was diſtant from the contact but two palms,
                <lb/>
              would be three or four times as far diſtant from the circumference </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>