At this time the notation was in an imperfect state.
The publication of the Geometry of Descartes, which contains the application of algebra to the definition and investigation of curve lines (1637), constitutes an epoch in the history of the mathematical sciences.

Two years previously, Cavalieri's work on Indivisibles had appeared.

This method was improved by Torricelli and others.

The way was now open, for the development of the Infinitesimal Calculus, the method of Fluxions of Newton, and the Differential and Integral Calculus of Leibnitz.

Though in his possession many years previously, Newton published nothing on Fluxions until 1704; the imperfect notation he employed retarded very much the application of his method.