eighteenth-century British mathematics does not enjoy a good reputation. The eighteenth century, a ‘period of indecision’ as many historians would say, is said to have witnessed ‘the crisis’ or the ‘decline’ of mathematics in the country of Newton, Wallis and Barrow. However, even a glance at the following list of names should be sufficient to refute the prevailing image of eighteenth-century British mathematics. To the imported Abraham de Moivre one can add the native Brook Taylor, James Stirling, Edmond Halley, Roger Cotes, Thomas Bayes, Colin Maclaurin, Thomas Simpson, Matthew Stewart, John Landen and Edward Waring. Through their work they contributed to several branches of mathematics: algebra, pure geometry, physical astronomy, pure and applied calculus and probability.

I devote this work to a theory that all these natural philosophers knew very well: the calculus of fluxions. This was the British equivalent of the more famous continental differential and integral calculus. It is usually agreed that the calculus of fluxions was clumsy in notation and awkward in methodology: the preference given to Newton's dots and to geometrical methods engendered a period which was eventually labelled as the ‘Dot-Age’. Furthermore, the calculus of fluxions is usually indicated as the principal cause of the decadence of British mathematics: the ‘Dot-Age’ was the price paid for a chauvinistic attachment to Newton's theory.