Here is the e-mail from Julio Gonzalez Cabillon about Implicit
function theorem. Stephen Maurer just spoke of it
It was sent on 17 March 99
Best wishes
Arnaud Pascal from the south-east of France
>Date: Wed, 17 Mar 1999 18:10:01 -0300
>To: HISTORIA MATEMATICA <historia-matematica@chasque.apc.org>
>From: Julio Gonzalez Cabillon <jgc@adinet.com.uy>
>Subject: Re: [HM] Jacobian, implicit (and inverse) function theorems
>Dear Israel,
>
>The term JACOBIAN was coined by James Joseph Sylvester (1814-1897), who used
>it as early as 1853:
>
> "In Arts. 65, 66, I consider the relation of the Bezoutiant
> to the differential determinant, so called by Jacobi, but
> which for greater brevity I call the Jacobian."
>
>Cf. The Philosophical Transactions of the Royal Society of London, vol
>CXLIII, part III, pp 407-548, London 1853. Also in Sylvester's _Collected
>Mathematical Papers_, vol 1, Cambridge (At the University Press), 1904.
>
>An extensive and original study of the topic was first carried out by
>Carl Gustav Jacob Jacobi (1804-1851) in "De determinantibus functionalibus",
>_Journal fuer die reine und angewandte Mathematik_ (Crelle's Journal),
>vol 22, pp 319-352, 1841. Needless to say, you will not find there math
>terms and symbols as we use them today; anyhow the intellectual seeds and
>mathematical flowers to the point are all there (and no weeds whatsoever!).
>
>Regards,
>Julio Gonzalez Cabillon