Agricola, Georgius, De re metallica, 1912/1950

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="133"/>
              the length shown by the cord for the side of the major triangle is 101 times
                <lb/>
              seven feet, that is 117 fathoms and five feet, then the intervening space, of
                <lb/>
              course, whether the whole of it has been already driven through or has yet
                <lb/>
              to be driven, will be one hundred times five feet, which makes eighty-three
                <lb/>
              fathoms and two feet. </s>
              <s>Anyone with this example of proportions will be
                <lb/>
              able to construct the major and minor triangles in the same way as I have
                <lb/>
              done, if there be the necessary upright posts and cross-beams. </s>
              <s>When a shaft is
                <lb/>
              vertical the triangle is absolutely upright; when it is inclined and is sunk on
                <lb/>
              the same vein in which the tunnel is driven, it is inclined toward one side. </s>
            </p>
            <figure number="60"/>
            <p type="caption">
              <s>A TRIANGLE HAVING A RIGHT ANGLE AND TWO EQUAL SIDES.
                <lb/>
              Therefore, if a tunnel has been driven into the mountain for sixty fathoms,
                <lb/>
              there remains a space of ground to be penetrated twenty-three fathoms and
                <lb/>
              two feet long; for five feet of the second side of the major triangle, which
                <lb/>
              lies above the mouth of the shaft and corresponds with the first side of the
                <lb/>
              minor triangle, must not be added. </s>
              <s>Therefore, if the shaft has been sunk
                <lb/>
              in the middle of the head meer, a tunnel sixty fathoms long will reach
                <lb/>
              to the boundary of the meer only when the tunnel has been extended a
                <lb/>
              further two fathoms and two feet; but if the shaft is located in the middle of
                <lb/>
              an ordinary meer, then the boundary will be reached when the tunnel has been
                <lb/>
              driven a further length of nine fathoms and two feet. </s>
              <s>Since a tunnel, for
                <lb/>
              every one hundred fathoms of length, rises in grade one fathom, or at all
                <lb/>
              events, ought to rise as it proceeds toward the shaft, one more fathom must
                <lb/>
              always be taken from the depth allowed to the shaft, and one added to the
                <lb/>
              length allowed to the tunnel. </s>
              <s>Proportionately, because a tunnel fifty
                <lb/>
              fathoms long is raised half a fathom, this amount must be taken from the
                <lb/>
              depth of the shaft and added to the length of the tunnel. </s>
              <s>In the same way
                <lb/>
              if a tunnel is one hundred or fifty fathoms shorter or longer, the same propor­
                <lb/>
              tion also must be taken from the depth of the one and added to the length
                <lb/>
              of the other. </s>
              <s>For this reason, in the case mentioned above, half a fathom
                <lb/>
              and a little more must be added to the distance to be driven through, so
                <lb/>
              that there remain twenty-three fathoms, five feet, two palms, one and a half
                <lb/>
              digits and a fifth of a digit; that is, if even the minutest proportions are
                <lb/>
              carried out; and surveyors do not neglect these without good cause.
                <lb/>
              </s>
              <s>Similarly, if the shaft is seventy fathoms deep, in order that it may reach to
                <lb/>
              the bottom of the tunnel, it still must be sunk a further depth of thirteen
                <lb/>
              fathoms and two feet, or rather twelve fathoms and a half, one foot, two
                <lb/>
              digits, and four-fifths of half a digit. </s>
              <s>And in this instance five feet must be
                <lb/>
              deducted from the reckoning, because these five feet complete the third side
                <lb/>
              of the minor triangle, which is above the mouth of the shaft, and from its </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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