BOOK V.

135

generally speaking, it is not deep; but there are usually several, allinclined, 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 whensix fathoms and two feet further have been sunk. But if all such inclinedshafts are seventy-six fathoms deep, in order that the last one may reachthe bottom of the tunnel, a depth of seven fathoms and two feet remains tobe sunk.

Triangle having an obtuse angle and two equal sides.

If a minor triangle is made which has an obtuse angle and three unequalsides, then again the sides of the large triangle cannot be equal. Forexample, if the first side of the minor triangle is six feet long, the secondthree feet, and the third four feet, and the cord along the side of the greatertriangle one hundred and one times six feet, that is, one hundred and onefathoms, the distance between the mouth of the tunnel and the bottom ofthe 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 ofthe 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 tobe driven is six fathoms. If the shafts are fifty-eight fathoms deep, thenewest will touch the bottom of the tunnel when eight fathoms and fourfeet 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 itsthree sides equal, then necessarily the second and third sides of the minortriangle will be equal, and likewise the sides of the major triangle frequentlyreferred to will be equal. Thus if each side of the minor triangle is six feetlong, and the cord measurement for the side of the major triangle is onehundred and one times six feet, that is, one hundred and one fathoms, thenboth the distances to be dug will be one hundred fathoms. And thus if thetunnel is ninety fathoms long, it will reach the middle of the bottom of thelast shaft when ten fathoms further have been driven. If the shafts are