Agricola, Georgius, De re metallica, 1912/1950

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="caption">
              <s>
                <pb pagenum="134"/>
              depth there must be deducted half a fathom, two palms, one and a half digits
                <lb/>
              and the fifth part of half a digit. </s>
              <s>But if the tunnel has been driven to a
                <lb/>
              point where it is under the shaft, then to reach the roof of the tunnel the
                <lb/>
              shaft must still be sunk a depth of eleven fathoms, two and a half feet, one
                <lb/>
              palm, two digits, and four-fifths of half a digit.</s>
            </p>
            <p type="main">
              <s>If a minor triangle is produced of the kind having three unequal sides,
                <lb/>
              then the sides of the greater triangle cannot be equal; that is, if the first
                <lb/>
              side of the minor triangle is eight feet long, the second six feet long, and the
                <lb/>
              third five feet long, and the cord along the side of the greater triangle, not
                <lb/>
              to go too far from the example just given, is one hundred and one times
                <lb/>
              eight feet, that is, one hundred and thirty-four fathoms and four feet, the
                <lb/>
              distance which lies between the mouth of the tunnel and the bottom of the
                <lb/>
              shaft will occupy one hundred times six feet in length, that is, one hundred
                <lb/>
              fathoms. </s>
              <s>The distance between the mouth of the shaft and the bottom of the
                <lb/>
              tunnel is one hundred times five feet, that is, eighty-three fathoms and two feet.
                <lb/>
              </s>
              <s>And so, if the tunnel is eighty-five fathoms long, the remainder to be driven
                <lb/>
              into the mountain is fifteen fathoms long, and here, too, a correction in
                <lb/>
              measurement must be taken from the depth of the shaft and added to the
                <lb/>
              length of the tunnel; what this is precisely, I will pursue no further, since
                <lb/>
              everyone having a small knowledge of arithmetic can work it out. </s>
              <s>If the
                <lb/>
              shaft is sixty-seven fathoms deep, in order that it may reach the bottom of
                <lb/>
              the tunnel, the further distance required to be sunk amounts to sixteen
                <lb/>
              fathoms and two feet.</s>
            </p>
            <figure number="61"/>
            <p type="caption">
              <s>A TRIANGLE HAVING A RIGHT ANGLE AND THREE UNEQUAL SIDES.</s>
            </p>
            <p type="main">
              <s>The surveyor employs this same method in measuring the mountain,
                <lb/>
              whether the shaft and tunnel are on one and the same vein, whether the vein
                <lb/>
              is vertical or inclined, or whether the shaft is on the principal vein and the tunnel
                <lb/>
              on a transverse vein descending vertically to the depths of the earth; in the
                <lb/>
              latter case the excavation is to be made where the transverse vein cuts the
                <lb/>
              vertical vein. </s>
              <s>If the principal vein descends on an incline and the cross-vein
                <lb/>
              descends vertically, then a minor triangle is created having one obtuse angle or
                <lb/>
              all three angles acute. </s>
              <s>If the minor triangle has one angle obtuse and the two
                <lb/>
              sides which are the second and third are equal, then the second and third
                <lb/>
              sides of the major triangle will be equal, so that if the first side of the minor
                <lb/>
              triangle is nine feet, the second, and likewise the third, will be five feet. </s>
              <s>Then
                <lb/>
              the first side of the major triangle will be one hundred and one times nine
                <lb/>
              feet, or one hundred and fifty-one and one-half fathoms, and each of the
                <lb/>
              other sides of the major triangle will be one hundred times five feet, that is,
                <lb/>
              eighty-three fathoms and two feet. </s>
              <s>But when the first shaft is inclined, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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