Basic formulas of spherical and plane tetragonometry
Abstract
The formulas of spherical tetragonometry are considered, which are also applicable to plane tetragonometry. For the practical purposes of crystal-chemical analysis, the graphical techniques used are quite sufficient, despite the inaccuracies associated with them. But over time, as the body of material expands, the need for replacement of roughly obtained firures with more precise ones will be felt more and more, in many cases this will reduce the increasingly complex labor of searching tables for a substance identified by its symbol of the complex. A closer examination of the problem at hand shows that it is not just a matter of solving spherical triangles from three given angles, which is precisely what spherical trigonometry covers, but rather that here we have the opportunity to calculate spherical elements, obtained in an indefinite number by constructing from four given points, and to find for each such element the corresponding formula, expressing it even when the positions of the four fundamental points are arbitrarily varied.
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