... The function M (a, b) is a homogeneous infinitely multivalued function of its arguments. The properties of the function M (a, b) were specified by C. F. Gauss. However, the results of his research, published in posthumous editions, represent only separate notes, not connected by unity of presentation, and it is difficult to judge from them the form of a complete presentation of the subject. The latter has prompted numerous comments to reconstruct a coherent statement of the properties of the arithmetic-geometric mean, and a number of studies to improve or modify certain details of such a reconstruction. The properties of the function M (a, b) follow directly from the properties of the algorithm defining it. Meanwhile, the proposed statements of the properties of the arithmetic-geometric mean go beyond the defining algorithm and involve considerations that are superfluous to the task at hand.

The spatial position of the borehole is usually determined by measuring its inclination 8k and azimuth fk at a number of points Mk, the distance Sk from the wellhead is known (k - 1, 2 . .). Such determination is reduced either to the calculation of the coordinates of the well axis, or to its graphical construction according to the measurement data ...