It may be regarded as based on arithmetic, or as dealing in the first instance with formal results of the laws of arithmetical number; and in this sense Sir Isaac Newton gave the title Universal Arithmetic to a work on algebra.
The main work of Descartes, so far as algebra was concerned, was the establishment of a relation between arithmetical and geometrical measurement.
The nature of logarithms is explained by reference to the motion of points in a straight line, and the principle upon which they are based is that of the correspondence of a geometrical and an arithmetical series of numbers.
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.
Nothing shows more clearly the rude state of arithmetical knowledge at the beginning of the 17th century than the universal satisfaction with which Napier's invention was welcomed by all classes and regarded as a real aid to calculation.