**Pierre Varignon** was a French mathematician who worked on graphical statics and mechanics.

- Although this seems to be said by Varignon with the suggestion that he was rather hard done by, indeed the technical knowledge he received did prove very valuable to him later in his life.
- In Caen he became friends with a fellow student Charles Castel, Abbé de Saint-Pierre, who arranged for Varignon to receive an income of 300 livres.
- The two shared lodgings and it appears that at this time Varignon continued his studies at the University of Caen.
- Of course as a Jesuit he belonged to an Order that valued scholarship and teaching so Varignon was able to devote the rest of his life to teaching.
- In 1686, together with his friend Charles Castel, Abbé de Saint-Pierre, Varignon went to Paris and immediately made contact with mathematicians and scientists there.
- In 1687 Varignon published Projet d'une nouvelle méchanique which studied composition of forces using Leibniz's differential calculus in the study of mechanics.
- Varignon's chief contributions were to graphical statics and mechanics.
- Although Varignon made no major mathematical contributions, he developed analytic dynamics by adapting Leibniz's calculus to the inertial mechanics of Newton's Principia being one of the first French scholars to recognise the power and importance of the calculus.
- Varignon put aside these philosophical worries and began to rework large sections of the Principia into the Leibniz's approach to the differential and integral calculus.
- Experimental evidence had been found to support the law but in 1695 Varignon tried to deduce it.
- Varignon's proof rests on the idea that the small quantity of liquid that escapes at each moment gets all of its motion from the pressure exercised by the "weight of the columns of liquid with base equal to the opening".
- For Varignon, to have derived Torricelli's law jointly from the axiom according to which "causes are always proportional to their effects", from the principles of mechanics and from the general laws of motion was to have proved it "by reason alone".
- Varignon studied the problem of the motion of projectiles in resisting media in eleven long memoirs which he presented to the Academy of Sciences between 1707 and 1711.
- In 1724 Varignon's Nouvelle mécanique was published which gave the best approach to geometrical statics until the work of Poinsot over 75 years later.
- Varignon's work was to have a major influence on Euler in his study on particle dynamics.
- Varignon played a major role in defending the calculus from attacks.
- Varignon argued before the Academy of Sciences that Rolle's arguments which suggested that the calculus led to errors was wrong.
- In 1731, nine years after Varignon's death, his notes for teaching mathematics in schools was published as Élémens de mathématiques ...
- The book contains what is today known as Varignon's parallelogram theorem: The figure formed when the mid-points of the sides of a quadrilateral are joined in order is a parallelogram.
- Varignon was elected to the French Academy of Sciences in 1688, the Berlin Academy of Science in 1713 and the Royal Society of London in 1718.

Born 1654, Caen, France. Died 23 December 1722, Paris, France.

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Geometry, Physics

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive