Agricola, Georgius, De re metallica, 1912/1950

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="136"/>
              ninety-five fathoms deep, the last will reach the bottom of the tunnel when
                <lb/>
              it is sunk a further depth of five fathoms.</s>
            </p>
            <figure number="64"/>
            <p type="caption">
              <s>A TRIANGLE HAVING ALL ITS ANGLES ACUTE AND ITS THREE SIDES EQUAL.</s>
            </p>
            <p type="main">
              <s>If a triangle is made which has all its angles acute, but only two sides
                <lb/>
              equal, namely, the first and third, then the second and third sides are not
                <lb/>
              equal; therefore the distances to be dug cannot be equal. </s>
              <s>For example, if
                <lb/>
              the first side of the minor triangle is six feet long, and the second is four feet,
                <lb/>
              and the third is six feet, and the cord measurement for the side of the major
                <lb/>
              triangle is one hundred and one times six feet, that is, one hundred and one
                <lb/>
              fathoms, then the distance between the mouth of the tunnel and the bottom of
                <lb/>
              the last shaft will be sixty-six fathoms and four feet. </s>
              <s>But the distance from the
                <lb/>
              mouth of the first shaft to the bottom of the tunnel is one hundred fathoms.
                <lb/>
              </s>
              <s>So if the tunnel is sixty fathoms long, the remaining distance to be driven
                <lb/>
              into the mountain is six fathoms and four feet. </s>
              <s>If the shaft is ninety-seven
                <lb/>
              fathoms deep, the last one will reach the bottom of the tunnel when a further
                <lb/>
              depth of three fathoms has been sunk.</s>
            </p>
            <figure number="65"/>
            <p type="caption">
              <s>TRIANGLE HAVING ALL ITS ANGLES ACUTE AND TWO SIDES EQUAL, A, B, UNEQUAL SIDE C.</s>
            </p>
            <p type="main">
              <s>If a minor triangle is produced which has all its angles acute, but its
                <lb/>
              three sides unequal, then again the distances to be dug cannot be equal.
                <lb/>
              </s>
              <s>For example, if the first side of the minor triangle is seven feet long, the
                <lb/>
              second side is four feet, and the third side is six feet, and the cord measure­
                <lb/>
              ment for the side of the major triangle is one hundred and one times seven
                <lb/>
              feet or one hundred and seventeen fathoms and four feet, the distance
                <lb/>
              between the mouth of the tunnel and the bottom of the last shaft will be
                <lb/>
              four hundred feet or sixty-six fathoms, and the depth between the mouth of
                <lb/>
              the first shaft and the bottom of the tunnel will be one hundred fathoms.
                <lb/>
              </s>
              <s>Therefore, if a tunnel is fifty fathoms long, it will reach the middle of the
                <lb/>
              bottom of the newest shaft when it has been driven sixteen fathoms and four
                <lb/>
              feet further. </s>
              <s>But if the shafts are then ninety-two fathoms deep, the last </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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