The early application of the calculus to the inverse square force problem
The author concentrates on the translation of Newton's propositions in the Principia on inverse square central forces into the language of the differential calculus. He studies the proofs of Jacob Hermann, Pierre Varignon and Johann Bernoulli in detail. His conclusion is that although these proofs lack rigor, the mathematicians involved knew very well what they were doing. The problem was visualized geometrically and solved analytically using rules for differentials that satisfied clear algebraic identities. That is why the lack of rigor was not experienced as a frustrating problem.
scientific article; zbMATH DE number 5790091