Philosophiae Naturalis Principia Mathematica: Its mathematical structure

We analyze the mathematical formulations used by Newton in his Philosophiae Naturalis Principia. Mathematica. Apparently, Newton intentionally omitted in all his book the use of the fluxional analysis that he developed. However, he could not avoid its use, at least in its conceptual frame, in some of the demonstrations he provided. The result is that his mathematical discourse in this book drifts from traditional geometry to fluxional theory (Calculus), being the central part a geometrical formulation of movement, or ''flowing geometry'', which lies in between the two former approaches.