Agricola, Georgius, De re metallica, 1912/1950

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="caption">
              <s>
                <pb pagenum="132"/>
              the first cord, and makes a note of this first side of the minor triangle
                <emph type="sup"/>
              17
                <emph.end type="sup"/>
              .
                <lb/>
              </s>
              <s>Afterward, starting again from that point where the third cord intersects the
                <lb/>
              second cord, he measures the straight space which lies between that point
                <lb/>
              and the opposite point on the first cord, and in that way forms the minor
                <lb/>
              triangle, and he notes this second side of the minor triangle in the same way as
                <lb/>
              before. </s>
              <s>Then, if it is necessary, from the angle formed by the first cord and
                <lb/>
              the second side of the minor triangle, he measures upward to the end of the
                <lb/>
              first cord and also makes a note of this third side of the minor triangle. </s>
              <s>The
                <lb/>
              third side of the minor triangle, if the shaft is vertical or inclined and is sunk
                <lb/>
              on the same vein in which the tunnel is driven, will necessarily be the same
                <lb/>
              length as the third cord above the point where it intersects the second cord;
                <lb/>
              and so, as often as the first side of the minor triangle is contained in the
                <lb/>
              length of the whole cord which descends obliquely, so many times the length
                <lb/>
              of the second side of the minor triangle indicates the distance between the
                <lb/>
              mouth of the tunnel and the point to which the shaft must be sunk; and
                <lb/>
              similarly, so many times the length of the third side of the minor triangle
                <lb/>
              gives the distance between the mouth of the shaft and the bottom of the
                <lb/>
              tunnel.</s>
            </p>
            <p type="main">
              <s>When there is a level bench on the mountain slope, the surveyor first
                <lb/>
              measures across this with a measuring-rod; then at the edges of this bench
                <lb/>
              he sets up forked posts, and applies the principle of the triangle to the two
                <lb/>
              sloping parts of the mountain; and to the fathoms which are the length of
                <lb/>
              that part of the tunnel determined by the triangles, he adds the number
                <lb/>
              of fathoms which are the width of the bench. </s>
              <s>But if sometimes the
                <lb/>
              mountain side stands up, so that a cord cannot run down from the shaft to
                <lb/>
              the mouth of the tunnel, or, on the other hand, cannot run up from the
                <lb/>
              mouth of the tunnel to the shaft, and, therefore, one cannot connect them in
                <lb/>
              a straight line, the surveyor, in order to fix an accurate triangle, measures the
                <lb/>
              mountain; and going downward he substitutes for the first part of the cord
                <lb/>
              a pole one fathom long, and for the second part a pole half a fathom
                <lb/>
              long. </s>
              <s>Going upward, on the contrary, for the first part of the cord he sub­
                <lb/>
              stitutes a pole half a fathom long, and for the next part, one a whole fathom
                <lb/>
              long; then where he requires to fix his triangle he adds a straight line to
                <lb/>
              these angles.</s>
            </p>
            <p type="main">
              <s>To make this system of measuring clear and more explicit, I will proceed
                <lb/>
              by describing each separate kind of triangle. </s>
              <s>When a shaft is vertical or
                <lb/>
              inclined, and is sunk in the same vein on which the tunnel is driven, there
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              is created, as I said, a triangle containing a right angle. </s>
              <s>Now if the minor
                <lb/>
              triangle has the two sides equal, which, in accordance with the numbering
                <lb/>
              used by surveyors, are the second and third sides, then the second and third
                <lb/>
              sides of the major triangle will be equal; and so also the intervening
                <lb/>
              distances will be equal which lie between the mouth of the tunnel and the
                <lb/>
              bottom of the shaft, and which lie between the mouth of the shaft and the
                <lb/>
              bottom of the tunnel. </s>
              <s>For example, if the first side of the minor triangle is
                <lb/>
              seven feet long and the second and likewise the third sides are five feet, and </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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