# A Glimpse at the Eighteenth Century: From John Bernoulli to Lagrange

## Abstract

This essay tries to answer the following question: “What happened to Mechanics between Newton and Lagrange?”, hence during what is commonly called the century of the enlightenment or *Age of Reason*. This period where knowledge and learning are the main incentive for intellectuals—of which philosophers and scientists are most representative—, witnessed an evolution that went from the mechanics of point particles (or massive objects seen as such) with Newton to the first elements of continuum mechanics in the hands of Euler and Lagrange. The most famous contributors between these scientists are Jacques (Jacob) Bernoulli, John (Johann) Bernoulli, Daniel Bernoulli, Pierre Varignon, Jean Le Rond d’Alembert, Pierre de Maupertuis, and Leonhard Euler. We peruse the works and the contributions to the formulation and consolidation of various principles by these “mechanicians” on the basis of primary sources—sometimes with original English translations—and accounting for comments by Lagrange and more recent historians–mechanicians such as Jouguet and Truesdell. This period is marked by a great emphasis placed on the notion of living forces, the exploitation of the principle of virtual work, and the expansion of the calculus of variations, which all characterize the “continental” development of the principles of mechanics as opposed to the Newtonian vision. This essay is a prerequisite to the examination in other essays of all what was to be expanded in the thermo-mechanics of continua during the nineteenth century.

### Keywords

Mechanics Living forces Bernoulli Virtual work D’Alembert principle Euler Lagrange equations Calculus of variations### References

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