GAUSS, Carl Friedrich. Vermischte Nachrichten.
Weimar: Verlage des Industrie-Comptoirs, 1799. First edition.

An interesting letter by Gauss in regard to the famous priority dispute between him and Legendre on the method of least squares. Stephen Stigler, Statistics on the Table, Chapter 17: “The method of least squares is the automobile of modern statistical analysis: despite its limitations, occasional accidents, and incidental pollution, this method and its numerous variations, extensions, and related conveyances carry the bulk of statistical analysis, and are known and valued by nearly all. But there has been some dispute, historically, as to who is the Henry Ford of statistics. Adrien Marie Legendre published the method in 1805, an American Robert Adrain, published the method in late 1808, and Carl Friedrich Gauss published the method in 1809. Legendre appears to have discovered the method in early 1805, and Robert Adrain may have ‘discovered’ it in Legendre’s 1805 book ..., but in 1809 Gauss had the temerity to claim that he had been using the method since 1795, and one of the most famous priority disputes in the history of science was off and running. ... Four principle pieces of evidence that Gauss was the method’s earliest discoverer have been presented, either by Gauss or in his behalf by his often reverential followers: (1) Gauss’s word in 1806 and later that he had used the method since 1795 ... (2) A cryptic entry in Gauss’s mathematical diary, dated June 1798... (3) Gauss’s claim that he had told other astronomers, notably Olbers, Lindenau, and von Zach, about the method prior to 1805. (4) A letter of Gauss’s that was published in 1799 in ‘Allgemeine Geographische Ephemeriden’ which alludes to ‘meine Methode’ [the offered volume]”. The following translation of the complete letter (with footnotes by von Zach, the editor) are quoted from Plackett: The Discovery of the Method of Least Squares, Biometrika, Vol. 59, 1972, pp. 239-251:

“Allow me to point out a printer’s error in the July issue of the A.G.E. Pages XXXV of the introduction in the account of the arc between the Panthéon and Évaux, must read 76145.74 instead of 76545.74. The sum is correct and the error cannot be in any other place.* I disovered this error when I applied my method, a specimen of which I have given you,† to determine the ellipse simply from these four measured arcs, and found the ellipticity to be 1/150; after correction of that error I found 1/187, and 2565006 units of length in the whole quadrant (namely without consideration of the Degree in Peru). The difference between 1/150 and 1/187 is certainly not important in this case, because the end-points lie too close together. Brunswick, 24 Aug. 1799. C. F. Gauss.

* This printers error is confirmed, and may also be recognized by the decimal degree figure set beside it, 2^D.66868 – v.Z.

† Here at another time – v.Z.”

Unfortunately von Zach appears never to have published the details of Gauss’s method as promised in his foot note. (See Stigler: Statistics on the Table, pp.320-331 for a detailed discussion of this letter).

In: 'Allgemeine Geographische Ephemeriden', Vol. 4, p. 378. The whole volume offered: (4), XL, 575, (1:blank) pp. and 5 plates (not accompanying the Gauss letter). 8vo. Contemporary boards. Title page with old library stamp. Some very light sporring throughout - in all a very nice copy. Some copies of this journal volume have a frontispiece with a portrait of Laplace, this copy does not have a frontispiece but does not have any signs of removal either. Rare.