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knowledge of the differential calculus spread rapidly throughout Europe. The

1 The full title was L 'analyse des infiniment petits pour l'intelligence des lignes courbes. There is an enormous literature concerning the early history of the calculus (see, for example, Boyer

2 (1959), Kline (1972) and the works cited therein).

Varignon also brought the calculus to bear on theories that utilized alternatives to Kepler's second law, e.g. those of Boulliau and Ward.

new calculus tempted mathematicians to try and provide analytical solutions to more and more challenging problems in mechanics and, as we shall see, the difficulties these problems generated led to fundamental improvements in the mathematical procedures themselves.

The calculus, as it was developed on the mainland of Europe, followed the notation introduced by Leibniz, whereas in England, Newton's symbols were used. Newton regarded variable quantities as being generated by motion, and he designated the rate at which a quantity changed (called a fluxion) by using so-called 'pricked letters', which consisted of placing a dot over the symbol representing the variable (which he called a fluent, i.e. something that flows). Thus, if x and y are fluents, their fluxions are denoted by x and y. Fluxions of fluxions were written x etc. Leibniz, on the other hand, used the symbols dx and dy to represent infinitesimal changes in the quantities x and y, and the ratio dy/dx to represent the rate at which y varied as x varied. This has the

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