Greetings historians of physics! Newton's Principia is written almost entirely using geometrical proofs and diagrams, barely using any calculus at all. It is thought that Newton was reluctant to use his calculus in this work, fearing that it would undermine its credibility and reception, since the calculus was heavily criticised at the time as being based on philosophically unsound vanishing departed infinitesimal quantities. Further to this, we think of Newton as one of the founding fathers of modern science, yet the Principia is by no means a modern book. The Laws are stated in words, and there is not a single equation in the entire work. There is no analytical formulation presented at all. Newton laid out the physics of mechanics, but not the analytical approach. Many people are surprised by this, equating in their mind the equation F = ma as being Newton's work. The principle is, but not the mathematical statement. Currently, I am trying to determine who first put forward the analytical formulation of Newton's Mechanics. I have a feeling it was Euler in his Mechanica of 1736. I am actually sure it was him, but reading the work so far, I have not come across the section (it's a dense book, and in Latin). [Perhaps I had better just keep on reading!] Does anybody know the exact history of this matter? Was there anybody preceding Euler in this area?