1ninety-five fathoms deep, the last will
reach the bottom of the tunnel when
it is sunk a further depth of five fathoms.
it is sunk a further depth of five fathoms.
A TRIANGLE HAVING ALL ITS ANGLES ACUTE AND ITS THREE SIDES EQUAL.
If a triangle is made which has all its angles acute, but only two sides
equal, namely, the first and third, then the second and third sides are not
equal; therefore the distances to be dug cannot be equal. For example, if
the first side of the minor triangle is six feet long, and the second is four feet,
and the third is six feet, 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 the distance between the mouth of the tunnel and the bottom of
the last shaft will be sixty-six fathoms and four feet. But the distance from the
mouth of the first shaft to the bottom of the tunnel is one hundred fathoms.
So if the tunnel is sixty fathoms long, the remaining distance to be driven
into the mountain is six fathoms and four feet. If the shaft is ninety-seven
fathoms deep, the last one will reach the bottom of the tunnel when a further
depth of three fathoms has been sunk.
equal, namely, the first and third, then the second and third sides are not
equal; therefore the distances to be dug cannot be equal. For example, if
the first side of the minor triangle is six feet long, and the second is four feet,
and the third is six feet, 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 the distance between the mouth of the tunnel and the bottom of
the last shaft will be sixty-six fathoms and four feet. But the distance from the
mouth of the first shaft to the bottom of the tunnel is one hundred fathoms.
So if the tunnel is sixty fathoms long, the remaining distance to be driven
into the mountain is six fathoms and four feet. If the shaft is ninety-seven
fathoms deep, the last one will reach the bottom of the tunnel when a further
depth of three fathoms has been sunk.
TRIANGLE HAVING ALL ITS ANGLES ACUTE AND TWO SIDES EQUAL, A, B, UNEQUAL SIDE
C.
If a minor triangle is produced which has all its angles acute, but its
three sides unequal, then again the distances to be dug cannot be equal.
For example, if the first side of the minor triangle is seven feet long, the
second side is four feet, and the third side is six feet, and the cord measure
ment for the side of the major triangle is one hundred and one times seven
feet or one hundred and seventeen fathoms and four feet, the distance
between the mouth of the tunnel and the bottom of the last shaft will be
four hundred feet or sixty-six fathoms, and the depth between the mouth of
the first shaft and the bottom of the tunnel will be one hundred fathoms.
Therefore, if a tunnel is fifty fathoms long, it will reach the middle of the
bottom of the newest shaft when it has been driven sixteen fathoms and four
feet further. But if the shafts are then ninety-two fathoms deep, the last
three sides unequal, then again the distances to be dug cannot be equal.
For example, if the first side of the minor triangle is seven feet long, the
second side is four feet, and the third side is six feet, and the cord measure
ment for the side of the major triangle is one hundred and one times seven
feet or one hundred and seventeen fathoms and four feet, the distance
between the mouth of the tunnel and the bottom of the last shaft will be
four hundred feet or sixty-six fathoms, and the depth between the mouth of
the first shaft and the bottom of the tunnel will be one hundred fathoms.
Therefore, if a tunnel is fifty fathoms long, it will reach the middle of the
bottom of the newest shaft when it has been driven sixteen fathoms and four
feet further. But if the shafts are then ninety-two fathoms deep, the last