Agricola, Georgius, De re metallica, 1912/1950

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="130"/>
              by carelessness into a slight error, this at the end will produce great errors.
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              </s>
              <s>Now these triangles are of many shapes, since shafts differ among themselves
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              and are not all sunk by one and the same method into the depths of the
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              earth, nor do the slopes of all mountains come down to the valley or plain in
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              the same manner. </s>
              <s>For if a shaft is vertical, there is a triangle with a right
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              angle, which the Greeks call
                <foreign lang="grc">ὀρθογώνιον</foreign>
              and this, according to the
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              inequalities of the mountain slope, has either two equal sides or three unequal
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              sides. </s>
              <s>The Greeks call the former
                <foreign lang="grc">τρίγωνον ἰσοσκελές</foreign>
              the latter
                <foreign lang="grc">σκαληνόν</foreign>
              for
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              a right angle triangle cannot have three equal sides. </s>
              <s>If a shaft is inclined
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              and sunk in the same vein in which the tunnel is driven, a triangle is likewise
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              made with a right angle, and this again, according to the various inequalities
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              of the mountain slope, has either two equal or three unequal sides. </s>
              <s>But if
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              a shaft is inclined and is sunk in one vein, and a tunnel is driven in
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              another vein, then a triangle comes into existence which has either an obtuse
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              angle or all acute angles. </s>
              <s>The former the Greeks call
                <foreign lang="grc">ἀμβλυγώνιον,</foreign>
              the latter
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                <foreign lang="grc">ὀχυγώνιον.</foreign>
              That triangle which has an obtuse angle cannot have three
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              equal sides, but in accordance with the different mountain slopes has either
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              two equal sides or three unequal sides. </s>
              <s>That triangle which has all acute
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              angles in accordance with the different mountain slopes has either three equal
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              sides, which the Greeks call
                <foreign lang="grc">τρίγωνον ἰσόπλευρον</foreign>
              or two equal sides or three
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              unequal sides.</s>
            </p>
            <p type="main">
              <s>The surveyor, as I said, employs his art when the owners of the mines
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              desire to know how many fathoms of the intervening ground require to be
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              dug; when a tunnel is being driven toward a shaft and does not yet reach
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              it; or when the shaft has not yet been sunk to the depth of the bottom of the
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              tunnel which is under it; or when neither the tunnel reaches to that point,
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              nor has the shaft been sunk to it. </s>
              <s>It is of importance that miners should
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              know how many fathoms remain from the tunnel to the shaft, or from the
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              shaft to the tunnel, in order to calculate the expenditure; and in order that
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              the owners of a metal-bearing mine may hasten the sinking of a shaft and
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              the excavation of the metal, before the tunnel reaches that point and the
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              tunnel owners excavate part of the metal by any right of their own; and on
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              the other hand, it is important that the owners of a tunnel may similarly
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              hasten their driving before a shaft can be sunk to the depth of a tunnel, so
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              that they may excavate the metal to which they will have a right.</s>
            </p>
            <p type="main">
              <s>The surveyor, first of all, if the beams of the shaft-house do not give him
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              the opportunity, sets a pair of forked posts by the sides of the shaft in such
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              a manner that a pole may be laid across them. </s>
              <s>Next, from the pole he lets
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              down into the shaft a cord with a weight attached to it. </s>
              <s>Then he stretches a
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              second cord, attached to the upper end of the first cord, right down along the
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              slope of the mountain to the bottom of the mouth of the tunnel, and fixes it to
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              the ground. </s>
              <s>Next, from the same pole not far from the first cord, he lets
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              down a third cord, similarly weighted, so that it may intersect the second
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              cord, which descends obliquely. </s>
              <s>Then, starting from that point where the
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              third cord cuts the second cord which descends obliquely to the mouth of the
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              tunnel, he measures the second cord upward to where it reaches the end of </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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