Gauss claimed to have discovered the method of least squares in 1795, not
1794.
Legendre's independent discovery of least squares cannot be dated precisely,
but it appears to have occurred late in the preparation of his 1805 work
_Nouvelles me/thodes pour la de/termination des orbites des come\tes_.
Source: Stephen Stigler _The History of Statistics: The Measurement of
Uncertainty before 1900_ Cambridge MA, Belknap Press of Harvard University
Press, 1986.
Stigler has this to say about the resulting priority dispute:
Begin quote
Gauss deeply affronted Legendre by referring to the method of least squares
as "our principle"... and by claiming the he, Guass, had beenusing the method
since 1795. The ensuing priotity displute, and another one involving the law
of quadratic reciprocity of numbe thoery, exacerbated the reatlionship
between the two men. The heat of the displute never reached that of the
Newton - Leibniz controversy, but it reached dramatic levels nonetheless.
Legendre appended a semianonymous attack on Guass to the 1820 verison of his
_Nouvelle me/thodes pour la de/termination des orbites des come\tes_, and
Gauss solicited reluctant testimony from friends that he had told them of the
method before 1805....There is no indication that [Gauss] saw its great
general potential before he learned of Legendre's work.. legendre's 1805
appendix, on the other hand, although it fell far showrt of Gauss's work in
development, was a dramatic and clear proclamation of a general method by a
man who had no doubt about its importance.
James A. Landau