This study is aiming at finding a “Missing Link” in history of mechanics at the beginning of the 18th century. In a traditional view, many historians have claimed that Newton established the foundation of mechanics. But Truesdell, who was a former editor of Leonhardi Euleri Opera Omnia, proposed an alternative and excellent view. He argued that classical mechanics started with Euler’s formation of the equation of motion. However, from this point of view, the gap between Newton’s mechanics and Euler’s seems considerably large. This is an attempt to fill the gap by reexamining Johann Bernoulli’s mature research on mechanics.

While Johann Bernoulli is a well-known and highly appreciated mathematician, his research on mechanics have been studied little. It is partly because his mechanics has been regarded as an inconsistent aggregation of Newtonian, Leibnizian and Cartesian physics. The study is to show that there were two research traditions on mechanics (i.e. Continental and Newtonian) at the beginning of the 18th century and Johann Bernoulli contributed to merge these two traditions.

The author focused on Johann Bernoulli’s research on mechanics after his “Discours sur les loix de la communication du mouvement” (1724) and discovered that he gave two different solutions to one problem and obtained the same result: (1) the solution using the conservation of living forces and (2) the solution using Newton’s second law of motion. The former solution belongs to continental research tradition and the latter to Newtonian tradition.

In an article issued in 1735, the relation between two solutions became clearer. He treated the conservation of living forces as a heuristics and Newton’s second law of motion as a fundamental law of mechanics. As a result, compatibility of the two laws (i.e., the conservation of living forces and Newton’s second law of motion) was established. Such an understanding of these laws is quite different from the traditional view that the former was derived from the latter.

In traditional history of science, it has been believed analytical mechanics emerged as a result of applying calculus to Newton’s Principia. But in reality, the formation process of analytical mechanics was quite different from the traditional view. It was formed by embedding Newton’s Principia to Continental tradition of mechanics. Johann succeeded both Continental tradition and Newton’s, and merged them in one.