The brief period of thirty years from 1763 to 1793 marks an important phase in the history of science and technology, especially in the foundation of modern chemistry, and in the improvement of the steam-engine by the invention of the separate condenser, an improvement that led directly to the development of steam-power. The bases of the quantitative study of three great departments of physics, namely, heat, electricity and magnetism, were firmly established in these years; and there was much progress in geology and in biology. At the beginning of the period Newtonianism had not only permeated scientific thought but had also already passed beyond the boundaries of the world of science into general thought and literature through the writings of Henry Pemberton in England and of Voltaire and Mme du Châtelet in France. Sciences other than astronomy and mechanics were, however, not so well advanced; and chemistry still explained the material complexity of the world in terms of a small number of ultimate elementary components.

In mathematics and mechanics the researches of this period were characterised by generalisation and deduction. Joseph-Louis Lagrange (1736–1813) continued the work of the earlier half of the century on the calculus; he extended mathematical analysis and the theory of equations; and in 1788 he published his Mécanique analytique, a work second only to Newton's Principia in the history of mechanics. Adrien-Marie Legendre (1752–1833) made further studies on the calculus of variations and other branches of mathematics, as well as contributing to the study of mechanics.