That there continued to be a group of students and teachers who desired a fuller exposition than is given by Oughtred is evident from the appearance, over fifty years after the first publication of the Clavis, of a booklet by Gilbert Clark, entitled Oughtredus Explicatus, London, 1682. A review of this appeared in the Acta Eruditorum (Leipzig, 1684), on p. 168, wherein Oughtred is named “clarissimus Angliae mathematicus.” John Collins wrote Wallis in 1666-67 that Clark, “who lives with Sir Justinian Isham, within seven miles of Northampton, . . . . intimates he wrote a comment on the Clavis, which lay long in the hands of a printer, by whom he was abused, meaning Leybourne.”[64]
We shall have occasion below to refer to Oughtred’s inability to secure a copy of a noted Italian mathematical work published a few years before. In those days the condition of the book trade in England must have been somewhat extraordinary. Dr. J. W. L. Glaisher throws some light upon this subject.[65] He found in the Calendar of State Papers, Domestic Series, 1637, a petition to Archbishop Laud in which it is set forth that when Hooganhuysen, a Dutchman, “heretofore complained of in the High Commission for importing books printed beyond the seas,” had been bound “not to bring in any more,” one Vlacq (the computer and publisher of logarithmic tables) “kept up the same agency and sold books in his stead. . . . . Vlacq is now preparing to go beyond the seas to avoid answering his late bringing over nine bales of books contrary to the decree of the Star Chamber.” Judgment was passed that, “Considering the ill-consequence and scandal that would arise by strangers importing and venting in this kingdom books printed beyond the seas,” certain importations be prohibited, and seized if brought over.
This want of easy intercommunication of results of scientific research in Oughtred’s time is revealed in the following letter, written by Oughtred to Robert Keylway, in 1645:
I speak this the rather, and am induced to a better confidence of your performance, by reason of a geometric-analytical art or practice found out by one Cavalieri, an Italian, of which about three years since I received information by a letter from Paris, wherein was praelibated only a small taste thereof, yet so that I divine great enlargement of the bounds of the mathematical empire will ensue. I was then very desirous to see the author’s own book while my spirits were more free and lightsome, but I could not get it in France. Since, being more stept into years, daunted and broken with the sufferings of these disastrous times, I must content myself to keep home, and not put out to any foreign discoveries.[66]
It was in 1655, when Oughtred was about eighty years old, that John Wallis, the great forerunner of Newton in Great Britain, began to publish his great researches on the arithmetic of infinites. Oughtred rejoiced over the achievements of his former pupil. In 1655, Oughtred wrote John Wallis as follows:
I have with unspeakable delight, so far as my necessary businesses, the infirmness of my health, and the greatness of my age (approaching now to an end) would permit, perused your most learned papers, of several choice arguments, which you sent me: wherein I do first with thankfulness acknowledge to God, the Father of lights, the great light he hath given you; and next I congratulate you, even with admiration, the clearness and perspicacity of your understanding and genius, who have not only gone, but also opened a way into these profoundest mysteries of art, unknown and not thought of by the ancients. With which your mysterious inventions I am the more affected, because full twenty years ago, the learned patron of learning, Sir Charles Cavendish, shewed me a paper written, wherein were some few excellent new theorems, wrought by the way, as I suppose, of Cavalieri, which I wrought over again more agreeably to my way. The paper, wherein I wrought it, I shewed to many, whereof some took copies, but my own I cannot find. I mention it for this, because I saw therein a light breaking out for the discovery of wonders to be revealed to mankind, in this last age of the world: which light I did salute as afar off, and now at a nearer distance embrace in your prosperous beginnings. Sir, that you are pleased to mention my name in your never dying papers, that is your noble favour to me, who can add nothing to your glory, but only my applause. . . . .[67]
The last sentence has reference to Wallis’ appreciative and eulogistic reference to Oughtred in the preface. It is of interest to secure the opinion of later English writers who knew Oughtred only through his books. John Locke wrote in his journal under the date, June 24, 1681, “the best algebra yet extant is Outred’s.”[68] John Collins, who is known in the history of mathematics chiefly through his very extensive correspondence with nearly all mathematicians of his day, was inclined to be more critical. He wrote Wallis about 1667:
It was not my intent to disparage the author, though I know many that did lightly esteem him when living, some whereof are at rest, as Mr. Foster and Mr. Gibson. . . . . You grant the author is brief, and therefore obscure, and I say it is but a collection, which, if himself knew, he had done well to have quoted his authors, whereto the reader might have repaired. You do not like those words of Vieta in his theorems, ex adjunctione plano solidi, plus quadrato quadrati, etc., and think Mr. Oughtred the first that abridged those expressions by symbols; but I dissent, and tell you ’twas done before by Cataldus, Geysius, and Camillus Gloriosus,[69] who in his first decade of exercises, (not the first tract,) printed at Naples in 1627, which was four years before the first edition of the Clavis, proposeth this equation just as I here give it you, viz. 1ccc+16qcc+41qqc-2304cc-18364qc-133000qq-54505c+3728q+8064 N aequatur 4608, finds N or a root of it to be 24, and composeth the whole out of it for proof, just in Mr. Oughtred’s symbols and method. Cataldus on Vieta came out fifteen years before, and I cannot quote that, as not having it by me.
. . . . And as for Mr. Oughtred’s method of symbols, this I say to it; it may be proper for you as a commentator to follow it, but divers I know, men of inferior rank that have good skill in algebra, that neither use nor approve it. . . . . Is not A⁵ sooner wrote than Aqc? Let A be 2, the cube of 2 is 8, which squared is 64: one of the questions between Maghet Grisio and Gloriosus is whether 64=Acc or Aqc. The Cartesian method tells you it is A⁶, and decides the doubt. . . . .[70]
There is some ground for the criticisms passed by Collins. To be sure, the first edition of the Clavis is dated 1631—six years before Descartes suggested the exponential notation which came to be adopted as the symbolism in our modern algebra. But the second edition of the Clavis, 1647, appeared ten years after Descartes’ innovation. Had Oughtred seen fit to adopt the new exponential notation in 1647, the step would have been epoch-making in the teaching of algebra in England. We have seen no indication that Oughtred was familiar with Descartes’ Géométrie of 1637.
The year preceding Oughtred’s death Mr. John Twysden expressed himself as follows in the preface to his Miscellanies: