I'm doing research on the history of the Lagrange inversion theorem. The earliest predecessor I've found is the one referenced by De Morgan; viz. Jo. H. Lambert's construction in Observationes Variae in Mathesin Puram, Acta Helvetica, Vol. 3, 1758, pp. 128-168.


If anyone knows of an earlier construction I'd greatly appreciate hearing about it.


Thanks in advance.


Cheers, Scott



History of the Lagrange Inversion Theorem
If you count *any* inversion of a power series as a predecessor of Lagrange
inversion, then I believe the earliest examples are Newton's inversion of the
log series to obtain the exponential series, and inversion of the inverse sine 
series to obtain the sine series. The exponential series is in his *De methodis*
(1671), p.61, and the sine series is in his *De analysi* (1669), p. 233, 237.


Also, de Moivre, *Philosophical Transactions* 20 (1698), pp. 190-193, gave a 
more general formula in a paper entitled "A method of extracting the root of an
infinite equation."


