# Pierre Varignon, bridge between maths and physics

VSo you know Varignon’s theorem? The four midpoints of the sides of any quadrilateral always form a parallelogram. Did we really have to wait for the beginning of the XVIII^{e} century to demonstrate such an elementary result, which we sometimes encounter today in college mathematics textbooks? Simple result, and not very interesting, it must be admitted. It’s a kind of curse: we often attribute to mathematicians results that in no way illustrate their work. Arnold’s theorem even asserts that no theorem with a proper name is due to this person (and this theorem applies to itself).

Pierre Varignon is a mathematician born in 1654 and died in 1722. A symposium, organized from January 17 to 19, on the occasion of the tercentenary of his death, allowed us to take a look at this fascinating period in the history of science. It is neither Isaac Newton (1642-1727) nor Gottfried Wilhelm Leibniz (1646-1716), whose works have been extensively studied, but a secondary character who nevertheless played an important role in mathematics. French.

Varignon was both a teacher and a researcher, also serving as an intermediary between the great thinkers of his time. The controversy raged: Newton and Leibniz both claimed the differential calculus, which they presented in very different ways. Varignon will play the role of “translator” between the two variants of the same language. His posthumous work *Clarifications on the analysis of infinitely small*published in 1725, will allow the introduction of this new differential calculus in France, at the origin of a true scientific revolution.

## Premises of vector calculus

In mechanics, we owe him clear statements on the composition of forces, only glimpsed before by Leonardo da Vinci and Galileo. His book *New Mechanics or Statics, whose project was given in 1687*, contains admirable plates. It shows weights suspended from cables in all sorts of configurations and describes the conditions of equilibrium. With a little imagination, we can guess the premises of the calculation of vectors, so important today, both in mathematics and in physics.

Varignon is perhaps the first professional teacher-researcher in France. He was the first professor of mathematics at the Mazarin College, in 1688, in the palace which would house the Institut de France much later. He will teach there until his death with great interest. His book *elements of mathematics*published in 1731, takes up his teaching and contains in particular Varignon’s theorem.

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