As you know, one could add to Roger Cotes, Abraham de Moivre, FRS, a french
emigrated to Britain. Among other articles:
A Method of extracting the Rest of an infinite equation
Phil. Trans. 1698
which has many interests beside the history of complex numbers.
A study of this article was made, if memory serves, by Anton von Braunmuehl
among others.
By the way, Roger Cotes's Harmonia Mensurarum is a good example of an
interesting mathematical text, original in content, in latin, posthumous,
edited by a not very competent contemporary, difficult to interpret in
detail. It is not necessary to have a whiggish view of the history of
mathematics to be intrigued by the document and his author but it seems
far-fetched to ascribe to Cotes a result as clear, precise and general as
expressed in Euler's formula.
In fact, Euler's formula was one of the thing he was searching for, having
started the project of exposing this harmony between measures (circular and
logarithmic, angles and ratios) which is the origin of the title.
I take this occasion to express my gratitude to Etienne Delacroix de La
Valette who introduced me to Cotes and de Moivre works ten years ago.
Olivier Gerard