Agricola, Georgius
,
De re metallica
,
1912/1950
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depth there must be deducted half a fathom, two palms, one and a half digits
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and the fifth part of half a digit. </
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<
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>But if the tunnel has been driven to a
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point where it is under the shaft, then to reach the roof of the tunnel the
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shaft must still be sunk a depth of eleven fathoms, two and a half feet, one
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palm, two digits, and four-fifths of half a digit.</
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>If a minor triangle is produced of the kind having three unequal sides,
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then the sides of the greater triangle cannot be equal; that is, if the first
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side of the minor triangle is eight feet long, the second six feet long, and the
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third five feet long, and the cord along the side of the greater triangle, not
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to go too far from the example just given, is one hundred and one times
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eight feet, that is, one hundred and thirty-four fathoms and four feet, the
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distance which lies between the mouth of the tunnel and the bottom of the
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shaft will occupy one hundred times six feet in length, that is, one hundred
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fathoms. </
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<
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>The distance between the mouth of the shaft and the bottom of the
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tunnel is one hundred times five feet, that is, eighty-three fathoms and two feet.
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</
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<
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>And so, if the tunnel is eighty-five fathoms long, the remainder to be driven
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into the mountain is fifteen fathoms long, and here, too, a correction in
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measurement must be taken from the depth of the shaft and added to the
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length of the tunnel; what this is precisely, I will pursue no further, since
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everyone having a small knowledge of arithmetic can work it out. </
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<
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>If the
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shaft is sixty-seven fathoms deep, in order that it may reach the bottom of
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the tunnel, the further distance required to be sunk amounts to sixteen
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fathoms and two feet.</
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>A TRIANGLE HAVING A RIGHT ANGLE AND THREE UNEQUAL SIDES.</
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<
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>The surveyor employs this same method in measuring the mountain,
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whether the shaft and tunnel are on one and the same vein, whether the vein
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is vertical or inclined, or whether the shaft is on the principal vein and the tunnel
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on a transverse vein descending vertically to the depths of the earth; in the
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latter case the excavation is to be made where the transverse vein cuts the
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vertical vein. </
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<
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>If the principal vein descends on an incline and the cross-vein
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descends vertically, then a minor triangle is created having one obtuse angle or
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all three angles acute. </
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<
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>If the minor triangle has one angle obtuse and the two
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sides which are the second and third are equal, then the second and third
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sides of the major triangle will be equal, so that if the first side of the minor
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triangle is nine feet, the second, and likewise the third, will be five feet. </
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<
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>Then
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the first side of the major triangle will be one hundred and one times nine
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feet, or one hundred and fifty-one and one-half fathoms, and each of the
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other sides of the major triangle will be one hundred times five feet, that is,
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eighty-three fathoms and two feet. </
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<
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>But when the first shaft is inclined, </
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