The main work of Descartes, so far as algebra was concerned, was the establishment of a relation between arithmetical and geometrical measurement.
Arithmetical Introduction to Algebra.
Order of Arithmetical Operations.
Even when the formal evolution of the science was fairly complete, it was taken for granted that its symbols of quantity invariably stood for numbers, and that its symbols of operation were restricted to their ordinary arithmetical meanings.
When algebra had advanced to the point where exponents were introduced, nothing would be more natural than that their utility as a means of performing multiplications and divisions should be remarked; but it is one of the surprises in the history of science that logarithms were invented as an arithmetical improvement years before their connexion with exponents was known.