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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/167.jpg" pagenum="149"/>
              the ground, as well in the one ſhot as in the other: for thus you
                <lb/>
              may ſee exactly how much one ſhaft flew farther than the other.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg337"/>
              * Baleſtrone da
                <lb/>
              zoni.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>In my thoughts this experiment is very proper: and I
                <lb/>
              do not doubt but that the flight, that is, the ſpace between the
                <lb/>
              ſhaft and the place where the chariot was at the ſhafts fall, will be
                <lb/>
              leſs by much when one ſhooteth towards the chariots courſe, than
                <lb/>
              when one ſhooteth the contrary way. </s>
              <s>For an example, let the
                <lb/>
              flight of it ſelf be three hundred yards, and the courſe of the
                <lb/>
              riot in the time whilſt the ſhaft ſtayeth in the air, an hundred
                <lb/>
              yards, therefore ſhooting towards the courſe, of the three hundred
                <lb/>
              yards of the flight, the chariot will have gone one hundred; ſo
                <lb/>
              then at the ſhafts coming to the ground, the ſpace between it and
                <lb/>
              the chariot, ſhall be but two hundred yards onely; but on the
                <lb/>
              contrary, in the other ſhoot, the chariot running contrary to the
                <lb/>
              ſhaft, when the ſhaft ſhall have paſſed its three hundred yards, and
                <lb/>
              the chariot its other hundred the contrary way, the diſtance
                <lb/>
              poſing ſhall be found to be four hundred yards.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Is there any way to ſhoot ſo that theſe flights may be
                <lb/>
              equal?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>I know no other way, unleſs by making the chariot to
                <lb/>
              ſtand ſtill.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>This we know; but I mean when the chariot runneth
                <lb/>
              in full carreer.</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>In that caſe you are to draw the Bow higher in
                <lb/>
              ing forwards, and to ſlack it in ſhooting the contrary way.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Then you ſee that there is one way more. </s>
              <s>But how
                <lb/>
              much is the bow to be drawn, and how much ſlackened?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>In our caſe, where we have ſuppoſed that the bow
                <lb/>
              ried three hundred yards, it would be requiſite to draw it ſo, as
                <lb/>
              that it might carry four hundred, and in the other to ſlacken it ſo,
                <lb/>
              as that it might carry no more than two hundred. </s>
              <s>For ſo each
                <lb/>
              of the flights would be but three hundred in relation to the chariot,
                <lb/>
              the which, with its courſe of an hundred yards which it ſubſtracts
                <lb/>
              from the ſhoot of four hundred, and addeth to that of two
                <lb/>
              dred, would reduce them both to three hundred.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>But what effect hath the greater or leſs intenſneſs of the
                <lb/>
              bow upon the ſhaft?</s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>The ſtiffer bow carrieth it with greater velocity, and the
                <lb/>
              weaker with leſs; and the ſame ſhaft flieth ſo much farther at one
                <lb/>
              time than another, with how much greater velocity it goeth out of
                <lb/>
              the tiller at one time, than another.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>So that to make the ſhaft ſhot either way, to flie at
                <lb/>
              qual diſtance from the running chariot, it is requiſite, that if in the
                <lb/>
              firſt ſhoot of the precedent example, it goeth out of the tiller with
                <lb/>
                <emph type="italics"/>
              v. </s>
              <s>g.
                <emph.end type="italics"/>
              four degrees of velocity, that then in the other ſhoot it </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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