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We are interested in the case of Friedrich Christoph Mayer, who in the 1720s, while at the Imperial Academy of Sciences in St. Petersburg (in Latin Academiae scientiarum imperialis Petropolitanae), developed a system of the aurora borealis, as well as a mathematical method for calculating the height of the aurora from the geometrical characteristics of the auroral arc. Mayer, encountering a major contradiction in his system which placed the aurora at the height of the clouds, whereas his mathematical method led to an altitude a hundred times higher, never a