Basic formulas of spherical and plane tetragonometry
Abstract
The formulas of spherical tetragonometry are considered, which are also applicable to plane tetragonometry. For practical purposes of crystal chemical analysis, the graphical techniques used are quite sufficient, despite the inaccuracy associated with them. But over time, as the material expands, the need for replacement of roughly obtained numbers with more accurate, which in many cases will reduce the increasingly complex labor of finding in the tables the substance defined as the symbol of the complex. A closer acquaintance with the upcoming problem shows that here it is not just necessary to solve spherical trigons at three given angles, which is precisely what is exhausted by spherical trigonometry, but that here it is possible to calculate spherical elements, in an indefinite number obtained by constructing from given four points, and find for each such element a corresponding formula expressing it even with an arbitrary change in the position of the four main points.
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