quantities, and again, quantitates inassignabiles, which spring from quantitates assignabiles by the law of continuity. In this last presentation Leibniz approached nearest to Newton.
In England the principles of fluxions were boldly attacked by Bishop Berkeley, the eminent metaphysician, who argued with great acuteness, contending, among other things, that the fundamental idea of supposing a finite ratio to exist between terms absolutely evanescent—"the ghosts of departed quantities," as he called them—was absurd and unintelligible. The reply made by Jurin failed to remove all the objections. Berkeley was the first to point out what was again shown later by Lazare Carnot, that correct answers were reached by a "compensation of errors." Berkeley's attack was not devoid of good results, for it was the immediate cause of the work on fluxions by Maclaurin. In France Michel Rolle rejected the differential calculus and had a controversy with Varignon on the subject.
Among the most vigorous promoters of the calculus on the Continent were the Bernoullis. They and Euler made Basel in Switzerland famous as the cradle of great mathematicians. The family of Bernoullis furnished in course of a century eight members who distinguished themselves in mathematics. We subjoin the following genealogical table:—
| Nicolaus Bernoulli, the Father | ||||
| Jacob, 1654–1705 | Nicolaus | Johann, 1667–1748 | ||
| | | | | |||
| Nicolaus, | 1687–1759 | Nicolaus, 1695–1726 | ||
| Daniel, 1700–1782 | ||||
| Johann, 1710–1790 | ||||
| Daniel | Johann, 1744–1807 | Jacob, 1758–1789 | ||
Most celebrated were the two brothers Jacob (James) and Johann (John), and Daniel, the son of John. James and
