And at the end of the volume, on page 180, is the following explanatory note :
AD MATHIMATICIS STUDIOSOS.
‘Ex omnibus Thoma Harrioti fcriptis Mathematicis,quòd opus hoc Analyticum primum in publicum emiflum fit, haud inconfulto factum eft. Nam, quùm reliqua eius opera, multiplici inuentorum nouitate excellentia, eodem omnino quo tractatus ifte (Logiftices fpeciofsæ exemplis omnimodis totus compofitus) ftilo Logiftico, hactenùs inufitato, confcripta fint, eâ certè ratione fit, vt prodromus hic tractatus, vltra proprium ipfius inæftimabilem vfum, reliquis Harrioti fcriptis, de quorum editione iam ferio cogitatur, pro neceffario preparamento fiue introductorio opportunè inferuire poffit. De quâ quidem accefforiâ operis huius vtilitate rerum Mathematicarum ftudiofos paucis his præmonuiffe operæprecium efle duximus.’ [Which being interpreted reads as follows in English]
TO STUDENTS OF MATHEMATICS.
It is not without good reason that, of all Thomas Harriot’s Mathematical writings, this on Analysis has been published first. For whereas all his remaining works, remarkable for their manifold novelties of discovery, are written precisely in the same, hitherto unusual, logical style as this treatise (which consists entirely of varied specimens of beautiful reasoning); this was certainly done that this preliminary treatise, besides its own inestimable utility, might suitably serve as a necessary preparation or introduction to the study of Harriot’s remaining works, the publication of which is now under serious consideration. Of this accessory use of this treatise we have thought it worth while to remind mathematical students in these brief remarks.
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.
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.