generally speaking, it is not deep; but there are usually several, all inclined, and one always following the other. Therefore, if a tunnel is seventyseven fathoms long, it will reach to the middle of the bottom of a shaft when six fathoms and two feet further have been sunk. But if all such inclined shafts are seventy-six fathoms deep, in order that the last one may reach the bottom of the tunnel, a depth of seven fathoms and two feet remains to be sunk.
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Triangle having an obtuse angle and two equal sides.
If a minor triangle is made which has an obtuse angle and three unequal sides, then again the sides of the large triangle cannot be equal. For example, if the first side of the minor triangle is six feet long, the second three feet, and the third four feet, and the cord along the side of the greater triangle one hundred and one times six feet, that is, one hundred and one fathoms, the distance between the mouth of the tunnel and the bottom of the last shaft will be a length one hundred times three feet, or fifty fathoms; but the depth that lies between the mouth of the first shaft and the bottom of the tunnel is one hundred times four feet, or sixty-six fathoms and four feet. Therefore, if a tunnel is forty-four fathoms long, the remaining distance to be driven is six fathoms. If the shafts are fifty-eight fathoms deep, the newest will touch the bottom of the tunnel when eight fathoms and four feet have been sunk.
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Triangle having an obtuse angle and three unequal sides..
If a minor triangle is produced which has all its angles acute and its three sides equal, then necessarily the second and third sides of the minor triangle will be equal, and likewise the sides of the major triangle frequently referred to will be equal. Thus if each side of the minor triangle is six feet long, and the cord measurement for the side of the major triangle is one hundred and one times six feet, that is, one hundred and one fathoms, then both the distances to be dug will be one hundred fathoms. And thus if the tunnel is ninety fathoms long, it will reach the middle of the bottom of the last shaft when ten fathoms further have been driven. If the shafts are
