136 BOOK V. 



ninety-five fathoms deep, the last will reach the bottom of the tunnel when 

 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. 



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 



