Meantime, on the Continent, very largely through the brilliant solutions of some of the higher problems, accomplished by the Bernouillis, the Calculus of Leibnitz was universally accepted, and improved by many mathematicians.
An extraordinary development of the science now took place, and continued throughout the century.

To the Binomial theorem, previously discovered by Newton, Taylor now added, in his "Method of Increments," the celebrated theorem that bears his name.

This was in 1715.

The Calculus of Partial Differences was introduced by Euler in 1734.

It was extended by D'Alembert, and was followed by that of Variations, by Euler and Lagrange, and by the method of Derivative Functions, by Lagrange, in 1772.
But it was not only in Italy, in Germany, in England, in France, that this great movement in mathematics was witnessed; Scotland had added a new gem to the intellectual diadem with which her brow is encircled, by the grand invention of Logarithms, by Napier of Merchiston.