The sum of the angles differed from 180° by less than two thirds of a second; he is known to have mentioned in conversation that this constituted an approximate verification of the axiom of parallels (which he regarded as an empirical matter because his studies of hyperbolic trigonometry had led him to recognize the possibility of logical alternatives). However, he never doubted Euclidean geometry in his geodetic work. On the contrary, he continually used 180° angle sums as a powerful check for observational errors, which helped him to achieve standards of precision.
The sum of the angles differed from 180° by less than two thirds of a second; he is known to have mentioned in conversation that this constituted an approximate verification of the axiom of parallels (which he regarded as an empirical matter because his studies of hyperbolic trigonometry had led him to recognize the possibility of logical alternatives). However, he never doubted Euclidean geometry in his geodetic work. On the contrary, he continually used 180° angle sums as a powerful check for observational errors, which helped him to achieve standards of precision.
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