Agricola, Georgius, De re metallica, 1912/1950

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="137"/>
              shaft will reach the bottom of the tunnel when it has been sunk a further
                <lb/>
              eight fathoms.</s>
            </p>
            <figure number="66"/>
            <p type="caption">
              <s>A TRIANGLE HAVING ALL ITS ANGLES ACUTE AND ITS THREE SIDES UNEQUAL.</s>
            </p>
            <p type="main">
              <s>This is the method of the surveyor in measuring the mountain, if the
                <lb/>
              principal vein descends inclined into the depths of the earth or the transverse
                <lb/>
              vein is vertical. </s>
              <s>But if they are both inclined, the surveyor uses the same
                <lb/>
              method, or he measures the slope of the mountain separately from the slope
                <lb/>
              of the shaft. </s>
              <s>Next, if a transverse vein in which a tunnel is driven does not
                <lb/>
              cut the principal vein in that spot where the shaft is sunk, then it is necessary
                <lb/>
              for the starting point of the survey to be in the other shaft in which the
                <lb/>
              transverse vein cuts the principal vein. </s>
              <s>But if there be no shaft on that spot
                <lb/>
              where the outcrop of the transverse vein cuts the outcrop of the principal
                <lb/>
              vein, then the surface of the ground which lies between the shafts must
                <lb/>
              be measured, or that between the shaft and the place where the outcrop of
                <lb/>
              the one vein intersects the outcrop of the other.</s>
            </p>
            <p type="main">
              <s>Some surveyors, although they use three cords, nevertheless ascertain
                <lb/>
              only the length of a tunnel by that method of measuring, and determine
                <lb/>
              the depth of a shaft by another method; that is, by the method by
                <lb/>
              which cords are re-stretched on a level part of the mountain or in
                <lb/>
              a valley, or in flat fields, and are measured again. </s>
              <s>Some, however, do
                <lb/>
              not employ this method in surveying the depth of a shaft and the
                <lb/>
              length of a tunnel, but use only two cords, a graduated hemicycle
                <emph type="sup"/>
              18
                <emph.end type="sup"/>
              and a
                <lb/>
              rod half a fathom long. </s>
              <s>They suspend in the shaft one cord, fastened
                <lb/>
              from the upper pole and weighted, just as the others do. </s>
              <s>Fastened to the
                <lb/>
              upper end of this cord, they stretch another right down the slope of the mountain
                <lb/>
              to the bottom of the mouth of the tunnel and fix it to the ground. </s>
              <s>Then to
                <lb/>
              the upper part of this second cord they apply on its lower side the broad part
                <lb/>
              of a hemicycle. </s>
              <s>This consists of half a circle, the outer margin of which is
                <lb/>
              covered with wax, and within this are six semi-circular lines. </s>
              <s>From the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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