# The Newtonian Sources of Analytical Mechanics

# The Newtonian Sources of Analytical Mechanics

This chapter looks at the immediate influence of the Principia in germinating analytical mechanics. The first French review of the treatise in the Journal des savants in 1688 is analyzed, showing how the French read Newton's work as brilliant mathematical mechanics, but as a flawed and unpersuasive natural philosophy. Key to this reading was the ability to isolate, and focus only upon, the first two books (its geometrical sections) while ignoring Book III (its empirical and physical sections). The French review emphasized this division of the book, and the chapter compares it with Edmund Halley's review in the Proceedings of the Royal Society of London, which reads all three books together as an innovative treatise in mathematical natural philosophy. In France, the chapter argues, Halley's understanding of the work as a physical critique of René Descartes vortical system of celestial mechanics was not at first operative, and the Principia influenced French science as a work of mathematical mechanics only. But because Newton was a mathematical traditionalist, preferring ancient geometry to the new analytic algebraic mathematics at the center of Leibniz's calculus, the influence of the Principia in making analytical mechanics was indirect and suggestive more than determinative.

*Keywords:*
Pierre Varignon, Edmund Halley, Journal des savants, physics and natural philosophy, Mathematical mechanics, geometry, synthesis versus analysis, René Descartes, vortical celestial mechanics/vortices