Mónica Blanco has a nice article in the current issue of Historia Mathematica on Thomas Simpson and mathematical publishing in mid-18th-century London.
Thomas Simpson (1710—1761), now mostly remembered for Simpson’s rule for approximating definite integrals, wrote two books on calculus. The first, A New Treatise of Fluxions, was published in 1737, and the second, a new book rather than a second edition of the first, The Doctrine and Application of Fluxions, in 1750.
Blanco traces Simpson’s background, particularly the influences of Edmund Stone (1695?—1768) and his 1730 re-working of L’Hopital’s text, and Simpson’s friend Francis Blake (1707/8—1780). All three were Fellows of the Royal Society.
The core of Blanco’s paper is a detailed comparison of the structure and contents of Simpson’s two works, and an exploration of the reasons for the differences. However, possibly of wider interest, she also includes some general remarks on mathematical publishing and the reception of mathematical works.
Simpson’s first book appears to have been supported by subscription, although there is no list of subscribers attached to the volume, and was published by Thomas Gardner, a printer “with a dubious reputation” (68). By the time the second work appeared, Simpson was a known and successful author (he published several other mathematical works in between the two calculus books), and the project was taken on by the prominent bookseller John Nourse, whose mathematical list included the likes of Newton, Maclaurin, and Brook Taylor, putting Simpson in distinguished company. Long after Simpson’s death, Nourse brought out a second edition.
Blanco, M. Thomas Simpson: Weaving fluxions in 18th-century London. Historia Mathematica
41 (1) (2014), 38—81.