The paper discusses Newton’s attempts to a unitary view of mathematics, i.e. his attempts to integrate the new methods of infinitesimal calculus — his method of fluxions — into the framework of finite Cartesian algebra and classical geometry. This topic is discussed by several examples from Newton’s papers and the “Principia". Newton’s approach is compared to Descartes’ methods, and the examples are discussed very clearly to show how Newton tries to approach and/or demonstrate his results obtained by the method of fluxions by more classical methods. Also, the reasons of Newton’s unsuccessful attempt to compose a treatise that would describe all his results obtained by the “new" methods integrated into the classical mathematics of ancient Greece.

Reviewer:

Franka Miriam Brückler (Zagreb)