papers in the British Museum that he was well acquainted with Pappus and other geometrical works which had then been recently published abroad. There is a remarkable note of Sir Charles Cavendish at p. 84, who says, "Dr. Jungius prefers the analitics of the ancients before Vieta's by letters, which he saies is more subject to errors or mistakes, though more facile and quick of dispatch, but I conceive not yet whye." This serves to show that the τοπος αναλυομενος of the Alexandrian school still held its sway in the minds of foreign mathematicians, notwithstanding the writings of Vieta and Descartes; but we find no traces in this country of its influence over the new analysis before the time of Robert Simson, that is, nearly a century afterwards.

The science of the seventeenth century possessed one feature which is now obsolete, and which probably contributed, in a great measure, to preserve and foster a taste for analytics. We allude to the practice of publicly proposing problems for solution—a kind of challenge from individuals to the science of all Europe—and thus exciting an emulation which, perhaps, would otherwise not have been felt. The superiority of the new analysis over the ancient geometry was soon acknowledged, and although some questions were required to be solved geometrically, yet mathematicians soon evinced their dislike to a system of attaining by a long and tedious method that which was often capable of speedy and easy resolution by another analysis. Specimens of these challenges are preserved among Pell's papers in the