It remains that I should adde something touching the beginning, and use of these Sciences. . . . . I shall only, to their honours, name some of our own Nation yet living, who have happily laboured upon both stages. That succeeding ages may understand that in this of ours, there yet remained some who were neither ignorant of these Arts, as if they had held them vain, nor condemn them as superfluous. Amongst them all let Mr. William Oughtred, of Aeton, be named in the first place, a Person of venerable grey haires, and exemplary piety, who indeed exceeds all praise we can bestow upon him. Who by an easie method, and admirable Key, hath unlocked the hidden things of geometry. Who by an accurate Trigonometry and furniture of Instruments, hath inriched, as well geometry, as Astronomy. Let D. John Wallis, and D. Seth Ward, succeed in the next place, both famous Persons, and Doctors in Divinity, the one of geometry, the other of astronomy, Savilian Professors in the University of Oxford.[71]
The astronomer Edmund Halley, in his preface to the 1694 English edition of the Clavis, speaks of this book as one of “so established a reputation, that it were needless to say anything thereof,” though “the concise Brevity of the author is such, as in many places to need Explication, to render it Intelligible to the less knowing Mathematical matters.”
In closing this part of our monograph, we quote the testimony of Robert Boyle, the experimental physicist, as given May 8, 1647, in a letter to Mr. Hartlib:
The Englishing of, and additions to Oughtred’s Clavis mathematica does much content me, I having formerly spent much study on the original of that algebra, which I have long since esteemed a much more instructive way of logic, than that of Aristotle.[72]
WAS DESCARTES INDEBTED TO OUGHTRED?
This question first arose in the seventeenth century, when John Wallis, of Oxford, in his Algebra (the English edition of 1685, and more particularly the Latin edition of 1693), raised the issue of Descartes’ indebtedness to the English scientists, Thomas Harriot and William Oughtred. In discussing matters of priority between Harriot and Descartes, relating to the theory of equations, Wallis is generally held to have shown marked partiality to Harriot. Less attention has been given by historians of mathematics to Descartes’ indebtedness to Oughtred. Yet this question is of importance in tracing Oughtred’s influence upon his time.
On January 8, 1688-89, Samuel Morland addressed a letter of inquiry to John Wallis, containing a passage which we translate from the Latin:
Some time ago I read in the elegant and truly precious book that you have written on Algebra, about Descartes, this philosopher so extolled above all for having arrived at a very perfect system by his own powers, without the aid of others, this Descartes, I say, who has received in geometry very great light from our Oughtred and our Harriot, and has followed their track though he carefully suppressed their names. I stated this in a conversation with a professor in Utrecht (where I reside at present). He requested me to indicate to him the page-numbers in the two authors which justified this accusation. I admitted that I could not do so. The Géométrie of Descartes is not sufficiently familiar to me, although with Oughtred I am fairly familiar. I pray you therefore that you will assume this burden. Give me at least those references to passages of the two authors from the comparison of which the plagiarism by Descartes is the most striking.[73]
Following Morland’s letter in the De algebra tractatus, is printed Wallis’ reply, dated March 12, 1688 (“Stilo Angliae”), which is, in part, as follows:
I nowhere give him the name of a plagiarist; I would not appear so impolite. However this I say, the major part of his algebra (if not all) is found before him in other authors (notably in our Harriot) whom he does not designate by name. That algebra may be applied to geometry, and that it is in fact so applied, is nothing new. Passing the ancients in silence, we state that this has been done by Vieta, Ghetaldi, Oughtred and others, before Descartes. They have resolved by algebra and specious arithmetic [literal arithmetic] many geometrical problems. . . . . But the question is not as to application of algebra to geometry (a thing quite old), but of the Cartesian algebra considered by itself.