The method of Gauss in 1799 (Q5926345)

In 1799, Gauss, proceeding from a meridian arc measurement separated into four parts, derived the parameters of the earth's ellipsoid of revolution without explaining his approach. The author unsuccessfully attempted to reconstruct the calculations and concluded that Gauss could have applied the method of least squares, but only if he made arithmetical errors. He also repeats \textit{S. M. Stigler}'s [The history of statistics (1986; Zbl 0656.62005)] wrong statement claiming that, prior to Legendre's publication of 1805, Gauss hardly informed anyone of his invention of the method. The reviewer has refuted Stigler (who also dared to defame Euler [see \textit{O. Sheynin} (O. Cheinine), ``On the history of the principle of least squares'', Arch. Hist. Exact Sci. 46, 39-54 (1993) and ``The discovery of the principle of least squares'', Hist. Sci. II. Ser. 8, 249-264 (1999)]). The second paper also discusses all the cases in which Gauss could have applied the method of least squares before 1805.