I30 BOOK V. 



by carelessness into a slight error, this at the end wUl produce great errors. 

 Now these triangles are of many shapes, since shafts differ among themselves 

 and are not all sunk by one and the same method into the depths of the 

 earth, nor do the slopes of all mountains come down to the valley or plain in 

 the same manner. For if a shaft is vertical, there is a triangle with a right 

 angle, which the Greeks call ofidoydiviof and this, according to the 

 inequaUties of the mountain slope, has either two equal sides or three unequal 

 sides. The Greeks call the former Tpiywvov laoaKiXiQ the latter oKaXrivov for 

 a right angle triangle cannot have three equal sides. If a shaft is incHned 

 and sunk in the same vein in which the tunnel is driven, a triangle is likewise 

 made with a right angle, and this again, according to the various inequaUties 

 of the mountain slope, has either two equal or three unequal sides. But if 

 a shaft is inclined and is sunk in one vein, and a tunnel is driven in 

 another vein, then a triangle comes into existence which has either an obtuse 

 angle or all acute angles. The former the Greeks call ufijiXvyiliviov, the latter 

 otKywviov. That triangle which has an obtuse angle cannot have three 

 equal sides, but in accordance with the different mountain slopes has either 

 two equal sides or three unequal sides. That triangle which has all acute 

 angles in accordance with the different mountain slopes has either three equal 

 sides, which the Greeks call Tjui-ywvov laowXtvpov or two equal sides or three 

 unequal sides. 



The surveyor, as I said, employs his art when the owners of the mines 

 desire to know how many fathoms of the intervening ground require to be 

 dug ; when a tunnel is being driven toward a shaft and does not yet reach 

 it ; or when the shaft has not yet been sunk to the depth of the bottom of the 

 tunnel which is under it ; or when neither the tunnel reaches to that point, 

 nor has the shaft been sunk to it. It is of importance that miners should 

 know how many fathoms remain from the tunnel to the shaft, or from the 

 shaft to the tunnel, in order to calculate the expenditure ; and in order that 

 the owners of a metal-bearing mine may hasten the sinking of a shaft and 

 the excavation of the metal, before the tunnel reaches that point and the 

 tunnel owners excavate part of the metal by any right of their own ; and on 

 the other hand, it is important that the owners of a tunnel may similarly 

 hasten their driving before a shaft can be sunk to the depth of a tunnel, so 

 that they may excavate the metal to which they will have a right. 



The surveyor, first of all, if the beams of the shaft-house do not give him 

 the opportunity, sets a pair of forked posts by the sides of the shaft in such 

 a manner that a pole may be laid across them. Next, from the pole he lets 

 down into the shaft a cord with a weight attached to it. Then he stretches a 

 second cord, attached to the upper end of the first cord, right down along the 

 slope of the mountain to the bottom of the mouth of the tunnel, and fixes it to 

 the ground. Next, from the same pole not far from the first cord, he lets 

 down a third cord, similarly weighted, so that it may intersect the second 

 cord, which descends obliquely. Then, starting from that point where the 

 third cord cuts the second cord which descends obliquely to the mouth of the 

 tunnel, he measures the second cord upward to where it reaches the end of 



