Thomas Hariot, the Mathematician, the Philosopher and the Scholar Part 6

Veritatis indagator ftudiofiffimus, Dei Trini-uniui cultor piiffimus, s.e.xagenarius, aut eo circiter, Mortalitati valedixit, Non vitae, Anno Christi M.DC.XXI. Iulii 2.

Shortly after there was erected to his memory in the chancel, at the expense, it is understood, of his n.o.ble friend the Earl of Northumberland, a fine marble monument, bearing the above neat and appropriate inscription.

St Christopher's, a very old church, with its records (still preserved) extending back in an almost unbroken series to 1488, pa.s.sed through many vicissitudes before itwas finally swallowed up by the leviathan of the world's commerce. The site of it is now occupied by the south-west cornerof the Bank of England on Princes Street, to the left of the entrance, nearly opposite the Mansion House. The church was restored and redecorated the year of Hariot's death, and again twelve years later, but was burnt in the great fire of 1666. Hariot's monument perished with it, but the inscription had been preserved by Stow. The church was rebuilt on the same foundation by Sir Christopher Wren in 1680.

About a century ago the church, with the whole parish of St Christopher (called then St Christopher-le-stocks because near the stocks standing at the east end of Cheapside), together with a large portion of two other parishes, St Margaret's and St Bartholomew's, was purchased by the Old Lady of Threadneedle Street for the site of the new Bank of England.

Thus one great bank of this modern metropolis covers a large part of three parishes of old London.

The whole area of the Bank, however, was not given up to mammon, though still here men most do congregate, and wors.h.i.+ppers most do wors.h.i.+p. One small consecrated spot, enough perhaps to leaven and memorize the whole site, was respected, and not built over. It was the churchyard of St Christopher. This ' G.o.d's acre' the architect and the governors have dedicated to Beauty, Art, and Nature. The little ' Garden of the Bank of England,' the loveliest spot in all London at this day, measuring about twenty-four by thirty-two yards, was just a hundred years ago the little churchyard of St Christopher, where still repose the bones of THOMAS HARIOT.

Virginia, which once comprehended the present United States from South to North, has been called the monument to Sir Walter Raleigh. So the Bank of England, built round the churchyard of St Christopher, may be called the monument to Thomas Hariot.

The present year, 1879, is just three centuries since Hariot went forth, a youth of twenty, from the University of Oxford. We have briefly told his story. England is all the richer for his life, and the world itself acknowledges the wealth of his science and the worth of his philosophy.

The Bank of England is built round his bones, but it cannot cover his memory.

Stay, traveller, tread lightly ; Near this spot lies what was mortal of that most celebrated man THOMAS HARRIOT.

He was the very learned Harriot of Sion on Thames ; by birth and education an Oxonian, Who cultivated all the sciences, and excelled in all, In Mathematics, Natural Philosophy, Theology.

A most studious investigator of truth, A most pious wors.h.i.+pper of the Triune G.o.d, At the age of sixty, or thereabouts, He bade farewell to mortality, not to life, July 2d A.D. 1621.

He lived, died, and was forgotten in the parish of St Christopher.

Henceforward, whenever Englishmen and Americans, merchants and scholars, rich and poor, men of genius and men of money, enter this little'

Garden,' let them read there in English what Henry Percy originally set up in Latin, the above inscription.

An impression has gone abroad, traceable chiefly to Aubrey and to Anthony a Wood, that Hariot was unsound in religious principles and matters of belief; that he was, in fact, not only a Deist himself, but that he exerted a baleful influence over Raleigh and his History as well as over the Earl of Northumberland. Not to misstate this utterly unfounded imputation, the very words of Wood, as first printed in his Athenae in 1691, and never since modified, are here given in full: ' But notwithstanding his great skill in mathematics, he had strange thoughts of the scripture, and always undervalued the old story of the creation of the world, and could never believe that trite position, _Ex nihilo nihil fit._ He made a _Philosophical Theology,_ wherein he cast off the OLD TESTAMENT, so that consequently the New would have no foundation. He wasaDeist, and his doctrine he did impart to the said Count [the Earl]

and to Sir Walt. Raleigh when he was compiling the _History of the World,_ and would controvert the matter with eminent divines of those times; who therefore having no good opinion of him, did look on the manner of his death as a judgment upon him for those matters, and for nullifying the scripture.'

It is needless to say that in all our investigations into the life, actions, and character of this eminent philosopher and Christian, from the time when, as a young man in 1585, he took delight in reading the Bible to the Indians of Virginia, down to the time that he made his remarkable will in 1621, not one word has been found in cor-roboration of these statements; but, on the contrary, many pa.s.sages have appeared to contradict and disprove them. Let any one notice the numerous citations of the various books of the Bible in Raleigh's History, and he will surely fail to discover any evidence of Raleigh's being a Deist, or that Hariot had taught him to undervalue the scripture.

It is not necessary here to say more in this connection than to quote the following pa.s.sage from one of the Latin letters in 1616 referred to above by Hariot to the eminent physician who had just received a high medical appointment at Court, describing himself and his terrible affliction [a cancer on the lip]. The pa.s.sage is given in English, but the original Latin may be seen in the British Museum (Add. 6789). It seems to have been written on purpose to refute such slanders. He writes :

Think of me as your sincere friend. Your interests are involved as well as mine. My recovery will be your triumph, but through the Almighty who is the Author of all good things.

As I have now and then said, I believe these three points. I believe in G.o.d Almighty; I believe that Medicine was ordained by him ; I trust the Physician as his minister. My faith is sure, my hope firm. I wait however with patience for everything in its own time according to His Providence. We must act earnestly, fight boldly, but in His name, and we shall conquer. Sic transit gloria mundi, omnia transibunt, nos ibimus, ibitis, ibunt. So pa.s.ses away the glory of this world, all things shall pa.s.s away, we shall pa.s.s away, you will pa.s.s away, they will pa.s.s away.

There is unfortunately no portrait known of Hariot, and we can form no idea of his personal appearance; but, fortunately, the drafts of the three Latin letters to his eminent friend at Court, alluded to above, fully describe his terrible disease and other bodily infirmities in 1615 and 1616, and give us some notion of himself and his personal habits.

His regular physician was Dr Turner, and his apothecary Mr May-orne, both employed also by Sir Walter.

Dr Alexander Read, in his ' Chirurgicall Lectures of Tumors and Vlcers Delivered in the Chirurgeans Hall, 1632-34. London. 1638,' 4, says in Treatise 2, Lecture 26, page 307:

Cancerous ulcers also feize upon this part [lips]. This grief haftened the end of that famous Mathematician, Mr. Hariot, with whom I was acquainted but a fhorttime before his death : whom at one time, together with Mr. Hughes, who wrote of the Globes, Mr. Warner, and Mr. Torperley, the n.o.ble Earl of Northumberland, the favourer of all good learning, and Mecaenas of learned men, maintained while he was in the Tower for their worth and various literature

A great deal of misconception has. .h.i.therto prevailed respecting Hariot's great printed work on Algebra. His reputation as a mathematician has been permitted to hinge chiefly upon it, very much to his disadvantage.

A brief bibliographical statement of facts will probably present the matter in a new light. But first let the book be described as it lies before us and has been described by many others since the days of Professor Wallis, nearly two hundred years ago. The t.i.tle is as follows : 'Artis a.n.a.lyticae / Praxis / Ad aequationes Algebraicas nouae, expeditae, & generali / methodo, resoluendas : / Tractatus/ E posthumis THOMae HARRIOTI Philosophi ac Mathematici ce- / leberrimi sche-diasmatis summae fide & diligentia / descriptus:/ Et/Illvstrissimo Domino/Dom.

HenricoPercio,/ Northvmbriae Comiti,/Qui haec prim, sub Patronatus & Munificentiae suae auspicjss / ad proprios vsus elucubrata, in communem Mathematicorum / vtilitatem, denu reuisenda, describenda, & publicanda / mandauit, meritissimi Honoris erg / Nuncupatus. / Londini / Apud Robertvm Barker, Typographum / Regium : Et Haered. Io. Billii. /Anno 1631. / _t.i.tle, reverse blank;_ Prefatio 4 pages; Text 180 pages, and Errata 1 page (Bbb) followed by a blank page, folio. A very handsomely printed book. In the British Museum, 529 m 8, is Charles the First's copy in old calf, gilt edges, with the royal arms on the sides. In the Preface the editors (Aylesbury and Prothero aided by Warner)say:

Artis a.n.a.lyticae, cuius caufa hic agitur, port eruditum illud Graecorum faeculum antiquitatae iamdiu & incultae iacentis, rcft.i.tutionem _Francifcus Viete,_ Gallus, vir clariflimus, & ob infignem in fcientijs Mathematicis peritiam, Gallicae gentis decus, primus fingulari confilio & intentato ante hac conamine aggreffus eft; atque ingenuam hanc animi fui intentionem per varios tractatus, quos in argumenti huius elaboratione eleganter & acute confcripfit, pofteris teftatem rcliquit. Dum ver ille veteris a.n.a.lytices reft.i.tutionem, quam fibi propofuit, feri molitus eft, non tam eam reft.i.tutam, quam proprijs inuentionibus actam & exornatam, tanquam nouam & fuam, n.o.bis tradidifle videtur. Quod generali conceptu enuntiatum paulo fufius explicandum eft; vt, oftenfo eo quod primum a _Vieta_ in inft.i.tuto fuo promouendo actum eft, quid poftea ab auth.o.r.e noftro doctifiimo _Thoma Harrioto,_ qui ilium certamine ifto a.n.a.lytico fequntus eft, praeft.i.tum fit, melius innotefcere possit. [Which done into English is substantially as follows]

Francis Vieta, a Frenchman, a most distinguished man, and on account of his remarkable skill in Mathematical Science the honour of the French nation, first of all with singular genius and with industry hitherto unattempted undertook the restoration of the a.n.a.lytic art, of which subject we are here treating, which after the learned age of the Greeks for a long time had become antiquated and remained uncultivated : and by various treatises which he eloquently and ingeniously wrote in the working out of this line of argument, left a record to posterity of this n.o.ble design of his mind. But while he seriously laboured at the restoration of the old a.n.a.lysis, which he had proposed to himself, he seems not so much to have transmitted to us a restoration of that science, as a new and original method, worked out and ill.u.s.trated by his own discoveries. This, having been enunciated in general terms, must be explained a little more at length ; so that having shown what was first effected by Vieta in promoting his design, it may be more clear, what was afterwards performed by our very learned author Thomas Harriot, who followed him in these a.n.a.lytical investigations.

And at the end of the volume, on page 180, is the following explanatory note :

AD MATHIMATICIS STUDIOSOS.

'Ex omnibus _Thoma Harrioti_ fcriptis Mathematicis,qud opus hoc a.n.a.lytic.u.m primum in public.u.m emiflum fit, haud inconfulto factum eft. Nam, quum reliqua eius opera, multiplici inuentorum nouitate excellentia, eodem omnino quo tractatus ifte (Logiftices fpeciofsae exemplis omnimodis totus compofitus) ftilo Logiftico, hactenus inufitato, confcripta fint, ea certe ratione fit, vt prodromus hic tractatus, vltra proprium ipfius inaeftimabilem vfum, reliquis _Harrioti_ fcriptis, de quorum editione iam ferio cogitatur, pro neceffario preparamento fiue introductorio opportune inferuire poffit. De qua quidem accefforia operis huius vtilitate rerum Mathematicarum ftudiofos paucis his praemonuiffe operaeprecium 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 a.n.a.lysis 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 a.n.a.lytics 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 a.n.a.lyses from the times of the Greeks.

Vieta's' Canon Mathematicus' was published at Paris in 1579, and was reissued in London with a new t.i.tle in 1589 as his ' Opera Mathematica.'

But this work does not contain the Algebra. That was first published in 1591 under the following t.i.tle :

'Francisci Vietae/InArtem a.n.a.lyticam/Isagoge/Seorfim excuffa ab Opere reft.i.tutae Mathematicae/a.n.a.lyfeos, seu, Algebraica noua. / 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 n.o.bleman of mathematical tastes, who had been studying in Paris, the following :-' De Nvmerosa Potestatvm / Ad Exegefum / Resolvtione. / Ex Opere reft.i.tutae Mathematicae a.n.a.lyfeos, / feu, Algebra noua / Francisci Vietae. / 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 antic.i.p.ated 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,reb.u.t.ting 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.

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 encyclopaedias 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 pa.s.sages :

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 lords.h.i.+p (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 lords.h.i.+p (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 a.n.a.lytics. 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 pa.s.sage 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.