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