From this it appears that Hariot’s system of Analytics or Algebra was based on that of his friend and correspondent Francois Vieta, as Vieta’s was avowedly based on that of the ancients. There appears to have been no attempt whatever on the part of the Englishman to appropriate the honors of the Frenchman, as many foreign writers have charged. Full credit was given by Hariot and his friends to the distinguished French mathematician. But Hariot’s modifications, improvements, and simplifications were so distinct and marked that from the first, and long before publication, they were called among his students and correspondents ‘Hariot’s Method,’ meaning thereby only Hariot’s peculiarities, without reference to the great merits of Vieta’s restoration, modification, adaptation, and improvement of the old analyses from the times of the Greeks. Vieta’s’ Canon Mathematicus’ was published at Paris in 1579, and was reissued in London with a new title in 1589 as his ‘Opera Mathematica.’ But this work does not contain the Algebra. That was first published in 1591 under the following title : ‘Francisci Vietæ/InArtem Analyticam/Isagoge/Seorfim excuffa ab Opere reftitutæ Mathematicæ/Analyfeos, seu, Algebraicâ nouâ. / Tvronis,/ Apud Iametivm Mettayer Typographium Regium. / Anno 1591.’ / folio. A Supplement appeared in 1593. Seven years later there came out under the auspices of Ghetaldi, a young Italian nobleman of mathematical tastes, who had been studying in Paris, the following:—‘De Nvmerosa Potestatvm / Ad Exegefum / Resolvtione. / Ex Opere reftitutæ Mathematicæ Analyfeos, / feu, Algebrà nouà / Francisci Vietæ. / Parisiis, / Excudebat David le Clerc. / 1600.’ / folio. On the last page of this book is an interesting letter from Marino Ghetaldi to his preceptor Michele Coignetto, dated at Paris the I5th of February 1600. These three thin folio volumes of great rarity are models of typographic beauty. They manifestly served as the model for printing Hariot’s Algebra in 1631. The set here described (the three bound in one volume), Prince Henry’s own copies, bearing his arms and the Prince of Wales’ feathers, is preserved in the British Museum, press-marked 530, m. 10. Thus Vieta’s method appears to have been given to the world in three instalments between 1591 and 1600, while the author himself died in 1603. It was probably in reference to one or both of these works that Lower gently reproached Hariot for having allowed himself to be anticipated in the public announcement of his discoveries in Algebra by Vieta. It has already been seen, on page 101 above, what Torperley, the friend of Vieta, wrote of his two masters in 1602, and also, on page 121, what Lower wrote to Hariot in 1610.