Agricola, Georgius
,
De re metallica
,
1912/1950
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the first cord, and makes a note of this first side of the minor triangle
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17
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.
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<
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>Afterward, starting again from that point where the third cord intersects the
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second cord, he measures the straight space which lies between that point
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and the opposite point on the first cord, and in that way forms the minor
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triangle, and he notes this second side of the minor triangle in the same way as
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before. </
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<
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>Then, if it is necessary, from the angle formed by the first cord and
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the second side of the minor triangle, he measures upward to the end of the
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first cord and also makes a note of this third side of the minor triangle. </
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<
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>The
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third side of the minor triangle, if the shaft is vertical or inclined and is sunk
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on the same vein in which the tunnel is driven, will necessarily be the same
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length as the third cord above the point where it intersects the second cord;
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and so, as often as the first side of the minor triangle is contained in the
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length of the whole cord which descends obliquely, so many times the length
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of the second side of the minor triangle indicates the distance between the
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mouth of the tunnel and the point to which the shaft must be sunk; and
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similarly, so many times the length of the third side of the minor triangle
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gives the distance between the mouth of the shaft and the bottom of the
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tunnel.</
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<
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>When there is a level bench on the mountain slope, the surveyor first
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measures across this with a measuring-rod; then at the edges of this bench
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he sets up forked posts, and applies the principle of the triangle to the two
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sloping parts of the mountain; and to the fathoms which are the length of
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that part of the tunnel determined by the triangles, he adds the number
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of fathoms which are the width of the bench. </
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<
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>But if sometimes the
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mountain side stands up, so that a cord cannot run down from the shaft to
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the mouth of the tunnel, or, on the other hand, cannot run up from the
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mouth of the tunnel to the shaft, and, therefore, one cannot connect them in
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a straight line, the surveyor, in order to fix an accurate triangle, measures the
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mountain; and going downward he substitutes for the first part of the cord
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a pole one fathom long, and for the second part a pole half a fathom
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long. </
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<
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>Going upward, on the contrary, for the first part of the cord he subĀ
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stitutes a pole half a fathom long, and for the next part, one a whole fathom
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long; then where he requires to fix his triangle he adds a straight line to
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these angles.</
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>To make this system of measuring clear and more explicit, I will proceed
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by describing each separate kind of triangle. </
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<
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>When a shaft is vertical or
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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. </
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<
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>Now if the minor
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triangle has the two sides equal, which, in accordance with the numbering
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used by surveyors, are the second and third sides, then the second and third
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sides of the major triangle will be equal; and so also the intervening
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distances will be equal which lie between the mouth of the tunnel and the
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bottom of the shaft, and which lie between the mouth of the shaft and the
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bottom of the tunnel. </
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<
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>For example, if the first side of the minor triangle is
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seven feet long and the second and likewise the third sides are five feet, and </
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