There remain the stringers in which gold alone is sometimes found, in the vicinity of rivers and streams, or in swamps. If upon the soil being removed, many of these are found, composed of earth somewhat baked and burnt, as may sometimes be seen in clay pits, there is some hope that gold may be obtained from them, especially if several join together. But the very point of junction must be pierced, and the length and width searched for ore, and in these places very deep shafts cannot be sunk.
I have completed one part of this book, and now come to the other, in which I will deal with the art of surveying. Miners measure the solid mass of the mountains in order that the owners may lay out their plans, and that their workmen may not encroach on other people's possessions. The surveyor either measures the interval not yet wholly dug through, which lies between the mouth of a tunnel and a shaft to be sunk to that depth, or between the mouth of a shaft and the tunnel to be driven to that spot which lies under the shaft, or between both, if the tunnel is neither so long as to reach to the shaft, nor the shaft so deep as to reach to the tunnel; and thus on both sides work is still to be done. Or in some cases, within the tunnels and drifts, are to be fixed the boundaries of the meers, just as the _Bergmeister_ has determined the boundaries of the same meers above ground.[16]
Each method of surveying depends on the measuring of triangles. A small triangle should be laid out, and from it calculations must be made regarding a larger one. Most particular care must be taken that we do not deviate at all from a correct measuring; for if, at the beginning, we are drawn by carelessness into a slight error, this at the end will 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 [Greek: orthogônion] and this, according to the inequalities of the mountain slope, has either two equal sides or three unequal sides. The Greeks call the former [Greek: trigônon isoskeles] the latter [Greek: skalênon] for a right angle triangle cannot have three equal sides. If a shaft is inclined 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 inequalities 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 [Greek: amblygônion], the latter [Greek: oxygônion]. 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 [Greek: trigônon isopleuron] or two equal sides or three unequal sides.