1generally speaking,
it is not deep; but there are usually several, all
inclined, and one always following the other. Therefore, if a tunnel is seventy
seven 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.
inclined, and one always following the other. Therefore, if a tunnel is seventy
seven 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.
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.
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.
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
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