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In modern times the belief that the ultimate explanation of all things was to be found in Newtonian mechanics was an adumbration of the truth that all science, as it grows towards perfection, becomes mathematical in its ideas.
In N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
Lagrange's Analytical Mechanics
The title page of Joseph Lagrange’s Mécanique analitique published in 1788. This was Lagrange’s definitive work. It summarized all the accomplishments in the field of mechanics from the time of Isaac Newton forward. In his discussions, Lagrange employed applications of the calculus of variations and differential equations, transforming mechanics into a branch of mathematical analysis. Admired for its clarity and structure, this book has been described as a great mathematical classic and a “scientific poem”.
A discussion from Langrange’s Mechanics, pages 58-59, on the resolution of three forces acting at a distance on a fixed point.