Fiedler, Die Elemente der neueren Geometrie and der Algebra der bindren Formen (Leipzig, 1862); A.
Elliott, Algebra of Quantics, Art.
During this period logarithms were invented, trigonometry and algebra developed, analytical geometry invented, dynamics put upon a sound basis, and the period closed with the magnificent invention of (or at least the perfecting of) the differential calculus by Newton and Leibnitz and the discovery of gravitation.
Passing over the invention of logarithms by John Napier, and their development by Henry Briggs and others, the next author of moment was an Englishman, Thomas Harriot, whose algebra (Artis analyticae praxis) was published posthumously by Walter Warner in 1631.
Heath, Diophantos of Alexandria: A Study in the History of Greek Algebra (Cambridge, 1885).
The doctrine of geometrical continuity and the application of algebra to geometry, developed in the 16th and 17th centuries mainly by Kepler and Descartes, led to the discovery of many properties which gave to the notion of infinity, as a localized space conception, a predominant importance.
Young, The Algebra of Invariants (Cambridge, 1903).
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.
Some writers have attempted unification by treating algebra as concerned with functions, and Comte accordingly defined algebra as the calculus of functions, arithmetic being regarded as the calculus of values.
But when I took up algebra I had a harder time still.