One is forced, therefore, to the conclusion that by 1600, if not some time before, Hariot had completed his method in Algebra, and distributed his well known problems to his admiring scholars. It has also been seen how, from 1603 to the day of his death, he was occupied in many other absorbing matters connected with Raleigh and Percy. Yet he may have felt, as Lower expressed it, that when he surveyed his storehouse of inventions this one of Algebra might seem in ‘comparison of manie others smal or of no value.’ The matter is introduced here mainly because certain foreign writers,rebutting Wallis’s patriotic claims in behalf of Hariot, have not only accused Hariot of appropriating Vieta’s rights, but they even describe the distinguished English mathematician as working on the ‘Cartesian Method.’ While the truth appears to be that Hariot’s method in Algebra, though not published for more than thirty years after its invention, must date from a time when Descartes was scarcely four years old. On the other hand, on looking into Descartes’ great and original work on geometry, first published in 1637, six years after Hariot’s Algebra first saw the light in print, one is not disposed to accuse the great philosopher of plagiarism because in working out his problems of great novelty in reference to geometrical curves he employed any systems of notation and calculation in algebra (Hariot’s among the others) that happened to be before the world. The point or essence of Descartes’ work was geometry and not algebra. Therefore, in climbing to his loft, he was perfectly justified in using the ladder which Hariot had left, as it was then in general use, and was only an incidental aid in his independent calculations, especially as the fame of his great mathematical brother was well established, and he had been already sixteen years in St Christopher’s. Vieta therefore had manifestly no just reason to complain, and Descartes stands acquitted. The history of Hariot’s _Praxis_ has attracted a great deal of attention for more than two centuries and has long been obscured by many misconceptions and erroneous statements. In the first place it has been always said from the days of Collins that it was edited by Walter Warner, and Wood adds that Warner was to have his pension continued by Algernon Percy, for that scientific labor. There is evidence that Warner, though employed on the work by Sir Thomas Aylesbury, was not the sole editor. See Aylesbury’s Letter to the Earl on page 189. The book led to a great deal of international or patriotic controversy, and with great injustice to Hariot was treated by the English advocates as his masterpiece in science. Wallis in 1685 in his History of Algebra, after much correspondence with Collins and others on the subject between 1667 and 1676, became Hariot’s English champion. The controversy respecting the Methods of Hariot and of Descartes became as warm as that respecting the discoveries of Leibnitz and of Newton.