Pierre Varignon

In existographies, Pierre Varignon (1654-1722) was mathematical physicist, noted for []

In 1700, Varignon, in his “General Way of Determining Forces”, supposedly, derived the following expression: [1]

∫ F dx = ½v ²

The mass ‘m’ here not shown, because he was treating a unit mass, wherein m = 1.

This, presumably, is one of the first formulations of kinetic energy, showing the ½-factor.

In 1717, in letter from Johann Bernoulli to Varignon, the term ‘energy’, in a semi-modern, presumably kinetic energy or gravitational energy, sense of the things, employed:

“The history of the birth of energetics is very curious. The word ‘energy’, in the sense of work was employed by Bernoulli in a letter to Varignon (1717), and by Couplet in 1726. Young used it in 1807, but its adoption exclusively in physics took place, thanks to Rankine and William Thomson between 1850 and 1870. At the same time a number of natural philosophers, from Huygens (1680) to Leibnitz (1896) and Lazare Carnot (1803) until Helmholtz (1847) made use of the expression ‘live force’ to designate work, or, more briefly, of the word force.”
— Jules Amar (1920), The Human Motor (pg. 42) [2]

In 1887, Georg Helm, in his The Doctrine of Energy, was citing Varignon, along with Bernoulli and Young, shown below, as terminology initiators of “energy” in the sense of kinetic energy:

2.9: Terminology (pg. 36)
Inclusion of the energy law in the contemporary 36.
Thomson 37.
Synonyms for force 37.
Bernoulli, Varignon, Young 38.
Thomson's 38.
Rankine Herschel's attack and Rankine Ver-defense 39.
Value of the terminology of popular dissemination 40.


1. (a) Varignon, Pierre. (1700). “General way of determining the Forces, the Speeds, the Spaces and the Times, only one of these four things being given in all sources of rectilinear movements vary at discretion” (“Maniere Generale de De Determiner les Forces, les Vitesses, les Espaces et les Temps, une seule de ces quatre choses etant donnee dans toutes sourtes de mouvemens rectilignues varez a discretion”), Memoires de ‘Academie des sciences de ‘Instittue de France (pg. 27). Paris.
(b) Hankins, Thomas L. (1965). “Eighteenth-Century Attempts to Resolve the Vis Viva Controversy” (abs) (pg. 287), Isis, 56(3):281-97.
2. Amar, Jules. (1920). The Human Motor: the Scientific Foundations of Labor and Industry (pg. 42). Publisher.

External links
Pierre Varignon – Wikipedia.
Pierre Varignon – MacTutor.

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