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.
Wallis ranked Oughtred’s Clavis and Hariot’s Praxis very high, and because both were first printed in 1631, treated them as productions or inventions of that year, whereas Hariot’s method, as we have seen, had been long practically before his disciples; and was, ten years after the author’s death, given to the world avowedly as an’ accessory’ only, or preliminary treatise, that it ‘might suitably serve as a necessary preparation or introduction to the study of Hariot’s remaining works, the publication of which is now under serious consideration.’ Unfortunately this excellent scheme fell through, probably in consequence of the death of the Earl of Northumberland, and perhaps partly because of the death of Nathaniel Torporley who had long been engaged in ‘penning the doctrine’ of Hariot’s mathematical papers. They both died in 1632, shortly after the publication of the Praxis. Wallis’s charge had a basis of truth, but it was narrow and petty. As an Algebraist he seems to have lost sight of the main point, that Descartes’ great work was on Geometry and not on Algebra, and that Hariot’s method, though first printed in 1631, was almost as old as Descartes himself. Montucla the French mathematician, near the close of the last century, in his History of Mathematics, summed up the controversy raised by Wallis including the minor one raised by Dr Zach in 1785, clearing Descartes of Wallis’s charges and relegating Hariot to the respectability of a second-rate mathematician. If Montucla’s verdict be based on mathematical reasoning as loose and slipshod as is his statement of the historical points of the case, to say nothing of his utter ignorance of Hariot’s biography and true position as an English man of science, one feels justified in rejecting it as worthless : as one also is compelled to do the vapid conclusions drawn from Montucla which have since found their way into many recent biographical dictionaries and into many pretentious articles in learned encyclopædias respecting Hariot and his works. The truth seems to be that Hariot was unlucky and fell into oblivion accidentally. He was a man of immense industry and great mental power, but perhaps careless of his scientific and literary reputation. As has been seen, he always had many irons in the fire, and was overtaken by death in the prime of life, leaving, as his will shows, many things unfinished, and none of his papers in a state ready for publication. He was surrounded by the best of friends, but time and opportunity, as so often happens in the affairs of busy men, worked against him, and he was well nigh consigned to forgetfulness.
However, after a half century’s slumber, when the great fire of London had destroyed his monument, and too late many scholars were minded to attempt the recovery and preservation of memorials of the past, John Collins the mathematician began soundings in the pool of oblivion for Hariot and his papers. He and his correspondents fished up a great deal of truth and history, but so mixed with error and conjecture that the results, though interesting, are misleading.
In the ‘Correspondence of Scientific Men of the Seventeenth Century, Edited by Professor S.J. Rigaud, 2 volumes, Oxford 1841,’ 8°, are found the following instructive and amusing passages :
As for Geysius, he published an Algebra and Stereometria divers years before the first edition of the Clavis [of Oughtred, 1631] was extant in Mr. Harriot’s method, out of which Alsted took what he published of algebra in his Encylopasdia printed in 1630, the year before the Clavis was first extant (see Christmannus and Raymarus). Mr. Harriot’s method is now more used than Oughtred’s, and himself in the esteem of Dr. Wallis not beneath Des Cartes. Dr. Hakewill, in his Apology, tells you Harriot was the first that squared the area of a spherical triangle; and I can tell you, by the perusal of some papers of Torporley’s it appears that Harriot could make the sign of any arch at demand, and the converse, and apply a table of sines to solve all equations, and treated largely of figurate arithmetic. His papers fell into the hands of Sir Thomas Aylesbury, father to the Lord Chancellor’s lady, where I hope they still are, unless they had the hard fate to be lent out, before the fire, and be burned, as some have said.
Collins to Wallis, no date, circa 1670, vol. ii, page 478.
As to Harriot, he was so learned, saith Dr. Pell, that had he published all he knew in algebra, he would have left little of the chief mysteries of that art unhandled. His papers fell into the hands of Sir Thomas Aylesbury, who was father to the late Lord Chancellor’s [Clarendon] Lady,by which means they fell into the Lord Chancellor’s hands, to whom application was made by the members of the Royal Society to obtain them: his lordship (then in the height of his dignity and employments) gave order for a search to be made, and in result the answer was, they could not be found. I am afraid the search was but perfunctory, and that, if his lordship (now at leisure) were solicited for them, he might write to his son the Lord Cornbury to make a diligent search for them. One Mr. Protheroe, in Wales, was executor to Mr. Harriot, and from him the Lord Vaughan, the Earl of Carbery’s son, received more than a quire of Mr. Harriot’s Analytics. The Lord Brounker has about two sheets of Harriot de Motu et Collisione Corporum, and more of his I know not of: there is nothing of Harriot’s extant but that piece which Mons. Garibal hath.
Collint to Vernon, not dated but circa 1671, vol. i, page 153.
Upon this passage Professor Rigaud makes the following note, written at Oxford in 1841:
Harriot’s will is not to be found, but Camden says that he left his property to Viscount Lisle and Sir Thomas Aylesbury. Lord Lisle’s share of the papers appear to have been given up to his father-in-law, Henry earl of Northumberland, who had been Harriot’s munificent patron, and they descended with the family property to the E. of Egremont, by whom a large portion has been given to the British Museum, and the remainder are still preserved at Petworth. Sir Thomas Aylesbury’s share became the property of his son-in-law Lord Chancellor Clarendon, to whom the Royal Society applied, but, as it appears, without obtaining them. (See Birch, Hist. Royal Society, vol. ii, pp. 120, 116, 309.)—Vol. i, page 153.
Here seems to be the germ of Professor Wallis’s charge of plagiarism against Descartes, written to Collins twelve years before it appeared in thefirst editionof his History of Algebra in English in 1685. It subsequently took a wider range, and was strenuously defended by Wallis when opposed:
That which I most valued in his [Des Cartes] method, and which pleased me best, was the way of bringing over the whole equations to one side, making it equal to nothing, and thereby forming his compound equations by the multiplication of simples, from thence also determining the number of roots, real or imaginary, in each. This artifice, on which all the rest of his doctrine is grounded, was that which most made me to set a value on him, presuming it had been properly his own; but afterwards I perceived that he had it from Hariot, whose Algebra was published after his death in the year 1631, six years before Des Cartes’ Geometry in French in the year 1637 : and yet Des Cartes makes no mention at all of Harriot, whom he follows in designing his species by small letters, and the power: of them by the number of dimensions, without the characters of j, c, qq, &c.
Walla to Collins, Oxford, 12 April 1673, vol, ii, page 573.
And had I but known of any precedent, (as since in Harriot I find one, and I think but one √—dddddd,) I should not have scrupled to follow it; but I was then too young an algebraist to innovate without example. Since that time I have been more venturous, and I find now that others do not scruple to use it as well as I. [Just what Descartes did. He ‘innovated’ prior to 1637, when he took Hariot’s well recognized notation in algebra to work out his problems in geometry for which Hariot himself would have thanked him.]
Wallis to Collins, May 6, 1673, vol. ii, page 578.
One Torporley, long since, left a manuscript treatise in Latin in Sion College, wherein is a much more copious table of figurate numbers, which I have caused to be transcribed, with what he says de combinationibus, to send to Mr. Strode.