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Figure 6 - Leonhard Euler, (1707-1783)

The mathematical analytical traditions established by Newton and Leibniz flourished during the 18th century as more mathematicians learned calculus and elaborated upon its initial formulation. The application of mathematical analysis to problems of motion was known as rational mechanics, or mixed mathematics (and was later termed classical mechanics). This work primarily revolved around celestial mechanics, although other applications were also developed, such as the Swiss mathematician Daniel Bernoulli’s treatment of fluid dynamics, which he introduced in his 1738 work Hydrodynamica.

Rational mechanics dealt primarily with the development of elaborate mathematical treatments of observed motions, using Newtonian principles as a basis, and emphasized improving the tractability of complex calculations and developing of legitimate means of analytical approximation. A representative contemporary textbook was published by Johann Baptiste Horvath. By the end of the century analytical treatments were rigorous enough to verify the stability of the solar system solely on the basis of Newton’s laws without reference to divine intervention—even as deterministic treatments of systems as simple as the three body problem in gravitation remained intractable.

British work, carried on by mathematicians such as Brook Taylor and Colin Maclaurin, fell behind Continental developments as the century progressed. Meanwhile, work flourished at scientific academies on the Continent, led by such mathematicians as Daniel Bernoulli, Leonhard Euler, Joseph-Louis Lagrange, Pierre-Simon Laplace, and Adrien-Marie Legendre. At the end of the century, the members of the French Academy of Sciences had attained clear dominance in the field [10, http://en.wikipedia.org/wiki/History_of_physics].

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