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Gauss tried to establish priority for the discovery of the least squares principle by claiming that he had been using it in his calculations since 1795 (when he was only 18!). This greatly irritated Legendre and led to some bitterness between the two men (see Plackett (1972), Stigler (1981)). The historical development of the least squares method is described in Hald (1998), Section 6.9 and Chapter 18.

Newton Principia, Book III, Propositions 40 and 41. The complexity of Newton's procedure meant that few astronomers actually used it in practice, but its utility was demonstrated by the great Russian scientist, Aleksei Nikolaevich Krylov, the author of a Russian translation of the Principia (1915) (see Kriloff (1925)).

Boskovic had proposed a method for determining cometary orbits in 1746 and he presented an improved version to the Academy in 1771. Laplace described Boskovic's approach as 'faulty, illusory, and erroneous' (Gillispie (1997), p. 97).

observation, and r is given in terms of p by

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