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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/179.jpg" pagenum="161"/>
              is, fifteen firſt minutes of a degree, in one firſt minute of an hour;
                <lb/>
              that is, fifteen ſeconds of a degree, in one ſecond of an hour; and
                <lb/>
              becauſe one ſecond is the time of the ſhot, therefore in this time
                <lb/>
              the Weſtern horizon riſeth fifteen ſeconds of a degree, and ſo
                <lb/>
              much likewiſe the mark; and therefore fifteen ſeconds of that
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              cle, whoſe ſemidiameter is five hundred paces (for ſo much the
                <lb/>
              ſtance of the mark from the Piece was ſuppoſed.) Now let us
                <lb/>
              look in the table of Arches and Chords (ſee here is
                <emph type="italics"/>
              Copernicus
                <emph.end type="italics"/>
              his
                <lb/>
              book) what part is the chord of fifteen ſeconds of the
                <lb/>
              ter, that is, five hundred paces. </s>
              <s>Here you ſee the chord (or
                <lb/>
              tenſe) of a firſt minute to be leſs than thirty of thoſe parts, of
                <lb/>
              which the ſemidiameter is an hundred thouſand. </s>
              <s>Therefore the
                <lb/>
              chord of a ſecond minute ſhall be leſs then half of one of thoſe
                <lb/>
              parts, that is leſs than one of thoſe parts, of whichthe
                <lb/>
              ter is two hundred thouſand; and therefore the chord of fifteen
                <lb/>
              conds ſhall be leſs than fifteen of thoſe ſame two hundred thouſand
                <lb/>
              parts; but that which is leſs than
                <emph type="italics"/>
              (a)
                <emph.end type="italics"/>
              fifteen parts of two hun­</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg352"/>
                <lb/>
              dred thouſand, is alſo more than that which is four centeſmes of
                <lb/>
              five hundred; therefore the aſcent of the mark in the time of the
                <lb/>
              balls motion is leſſe than four centeſmes, that is, than one twenty
                <lb/>
              fifth part of a pace; it ſhall be therefore
                <emph type="italics"/>
              (b)
                <emph.end type="italics"/>
              about two inches:
                <lb/>
              And ſo much conſequently ſhall be the variation of each Weſtern
                <lb/>
              ſhot, the Earth being ſuppoſed to have a diurnal motion. </s>
              <s>Now if I
                <lb/>
              ſhall tell you, that this variation (I mean of falling two inches ſhort
                <lb/>
              of what they would do in caſe the Earth did not move) upon
                <lb/>
                <arrow.to.target n="marg353"/>
                <lb/>
              all doth happen in all ſhots, how will you convince me
                <emph type="italics"/>
              Simplicius,
                <emph.end type="italics"/>
                <lb/>
              ſhewing me by an experiment that it is not ſo? </s>
              <s>Do you not ſee
                <lb/>
              that it is impoſſible to confute me, unleſs you firſt find out a way
                <lb/>
              to ſhoot at a mark with ſo much exactneſſe, as never to miſſe an
                <lb/>
              hairs bredth? </s>
              <s>For whilſt the ranges of great ſhot conſiſt of
                <lb/>
              rent numbers of paces, as
                <emph type="italics"/>
              de facto
                <emph.end type="italics"/>
              they do, I will affirm that in
                <lb/>
              each of thoſe variations there is contained that of two inches
                <lb/>
              ſed by the motion of the Earth.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg352"/>
                <emph type="italics"/>
              (a)
                <emph.end type="italics"/>
              That is, in
                <lb/>
              plainer termes the
                <lb/>
              fraction 15/200000, is
                <lb/>
              more than the
                <lb/>
              ction 4/50000, for
                <lb/>
              viding the
                <lb/>
              nators by their
                <lb/>
              minators, and the
                <lb/>
              firſt produceth
                <lb/>
              13333 1/3 the other
                <lb/>
              but 12500.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg353"/>
                <emph type="italics"/>
              (b)
                <emph.end type="italics"/>
              It ſhall be
                <lb/>
              neer 2 2/5 inches,
                <lb/>
              counting the pace
                <lb/>
              to be Geometrical,
                <lb/>
              containing 5 foot.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>Pardon me,
                <emph type="italics"/>
              Salviatus,
                <emph.end type="italics"/>
              you are too liberal. </s>
              <s>For I would
                <lb/>
                <arrow.to.target n="marg354"/>
                <lb/>
              tell the
                <emph type="italics"/>
              Peripateticks,
                <emph.end type="italics"/>
              that though every ſhot ſhould hit the very
                <lb/>
              centre of the mark, that ſhould not in the leaſt diſprove the motion
                <lb/>
              of the Earth. </s>
              <s>For the Gunners are ſo conſtantly imployed in
                <lb/>
              velling the ſight and gun to the mark, as that they can hit the ſame,
                <lb/>
              notwithſtanding the motion of the Earth. </s>
              <s>And I ſay, that if the
                <lb/>
              Earth ſhould ſtand ſtill, the ſhots would not prove true; but the
                <lb/>
              Occidental would be too low, and the Oriental too high: now let
                <lb/>
                <emph type="italics"/>
              Simplicius
                <emph.end type="italics"/>
              diſprove me if he can.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg354"/>
                <emph type="italics"/>
              It is
                <lb/>
              ted with great
                <lb/>
              tilty, that the
                <lb/>
              Earths motion
                <lb/>
              poſed, Canon ſhot
                <lb/>
              ought not to vary
                <lb/>
              more than in reſt.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>This is a ſubtilty worthy of
                <emph type="italics"/>
              Sagredus:
                <emph.end type="italics"/>
              But whether
                <lb/>
              this variation be to be obſerved in the motion, or in the reſt of the
                <lb/>
              Earth, it muſt needs be very ſmall, it muſt needs be ſwallowed up </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>