Those Wikipedia and Wikiversity pages (History of Lorentz transformations and History of Topics in Special Relativity) have lots of information on the mathematical history of the Lorentz transformations preserving:
Starting as early as 1800 by Gauss and many others, quadratic forms equivalent to ...
I found that a prediction of a solar eclipse was made Nicholas Culpeper for the April 8, 1652 eclipse in England. At first I was confused by the date, thinking the prediction was wrong, then realized it is the Julian Date which corresponds to the Georgian date in April.
Black Monday: the Great Solar Eclipse of 1652
Best I could determine after a searching for a couple of hours, this function was first introduced in the following publication, a scan of which is made available by the Bibliothèque nationale de France:
P. Langevin, "Magnétisme et théorie des électrons," Annales de chimie et de physique, 8:5 (1905), 70-127.
On page 117 one finds:
Le moment ...