Academia Algebra, Germanice;
Ansa Artis mirabilis, Latine;

Miracula Arithmetica and other small tracts, Germanice.

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. One Anderson, a weaver, who hath solved these problems; The sides of a trapezium and its area given, to situate the figure which amounts to an equation of the eighth power; divers problems about the Tactions of spheres; and this problem found in the Mathematical Exercises of Anderson the Scot, A cube is the greatest solid of a square base that can be inscribed in a sphere, let a solidity less than that be proposed, and let it be required to find a parallelepiped of a square base equal thereto, that may be inscribed in the same sphere; the Exercises find two of a greater or lesser base, and lesser or greater length. This problem the weaver hath improved, and applied to the gauging of casks part cut below the heads, by producing the planes of the parallelepipedons, so that their sides shall cut off, (viz. each parallelepiped twelve,) second segments in the whole equal, which he distinguishes in all cases, as well when the base is a rectangle as a square. Mr. Dary, the tobacco cutter, a knowing man in algebra, hath performed this problem: Let any two plane figures, (as an ellipse and trapezium1,) howsoever posited in a parallel position, have a right

1 The word is not expressed, but a figure is roughly drawn in this place, which seems to have this meaning.

line extended between them in the nature of an axis, about which let a plane move round, which will cut both figures, and where on their verge or extremity they are so cut, let right lines be joined and they will be clothed with a surface; he can compute or cube the solid of given bases contained under that surface, and hence finds Mr. Oughtred's rules in the Circles of Proportion about tapering timber insufficient. I might name Wadley, a lighterman, and may acquiesce in these men's judgments, or at least in Dr. Pell's, who hath said it is unworthy the present age to continue it, as rendering easy matters obscure. 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.

As to the third objection, about the defect of argument, and fourth, about the improvement of the general method, they cannot properly concern the author, nor is he to be blamed for not publishing what probably he knew not, which yet, in good part, was then extant in Gerrard and Vieta de Recognitione et Emendatione Equationum; but those works of Vieta came out piecemeal, most of them at his own dispose, and thence became almost unknown and unprocurable.

The aim of those objections was not to disparage the author, but to incline you to supply the defect of him, that his book, together with yours, might be of the more durable esteem, and not be undervalued, (as that author now is by Mr. Hooke and Dr. Croone,) as wanting the most material parts of algebra.

I agree with you, the author is not to be rejected ; he was, without doubt, a very learned divine and mathematician, and one that did much good in his

generation.

I know no man that would willingly be without his book, and certainly it had been a great detriment to learning to have wanted it.

About the resolution of adfected equations in numbers, neither Dr. Pell, nor Albert Girard, if alive, will think it fully done unless as soon as one root is known the equation be depressed and all the rest found; on which account Albert Girard in his Invention Nouvelle en l'Algebre, printed at Amsterdam in 1629, finds fault with Stevin, Vieta, and all his predecessors, for not giving so many answers as the index of the highest power denotes. Wherewith Dr. Wallis agrees, saying he doth first find, by the doctrine of limits, whether an equation be possible, and in what bounds an answer is to be found, and then supposing a root doth by positions frame a table that shall give the first and second figure of the root, afterwards finds the rest without hesitation by the general method, and expresseth the impossible roots just as Albert Girard doth.

These impossible roots, saith Dr. Pell, ought as well to be given in number as the negative and affirmative roots, their use being to shew how much the data must be mended to make the roots possible, and give points or bounds in delineations, shewing how much a curve must pass beneath or beyond a given right line, by aid whereof the roots are found.

Now I am come to your latter letter, and will tell you the truth. I never learned Greek, nor more of Latin than an ordinary schoolboy, and do not so well understand it as to be able to espy a fault, (and because I find defects in others, you may think I have high conceits of myself,') nor am I at all conceited

This parenthesis has been nizing well with the rest of the added in an interlineation, which

will account for its not harmo

VOL. II.

sentence.

I i

of any thing I have done, nor would be sorry if they were all burned, being toys done in ignorance and haste; that which was of most use, to wit, an Introduction to Merchants' Accounts, lately reprinted, underwent the fate. In my very Paper of Interest, the precept for equations of payments will discover the time, when one sum at simple interest shall amount to any other proposed, but I deny that there can be any such thing as an equation of payments, or a purchase of an inheritance at simple interest.

I doubt not but your mechanic inventions would be very acceptable, and worth the owning. I have been troubled with smoking chimneys, but never read what Lucar in his Gunnery, or Des Cartes in his second volume of Letters, p. 504, saith as to the remedy.

CCXCIX.

COLLINS TO WALLIS.

Reverend Sir,

I received yours of the 5th instant, in answer to mine of the 2nd preceding, since the writing whereof Mr. Pitts, having conference with Mr. Thompson, a bookseller, who lived in Paul's church-yard, and now in Little Britain, was by him informed that he was importuned, since the fire, to treat with Mrs. Lichfield for the impression, who offered it for 367., and the said Mr. Thompson would not give more than 327. for it, the rather because it is printed upon worse paper than the former impression; he having one of them here did also shew it. I prevailed with them to meet, being near together, and Mr. Pitts

declared his unwillingness to interpose without the consent of Mr. Thompson, who offered and desired him to take what part or share thereof he would. I cannot prevail with them to bid more for it; they say it is not a book so much inquired for here as in the universities, and they both doubt it will not sell without a comment; and Mr. Thompson says he was long possessed of Mr. Clarke's comment, who would freely have imparted it to any one to print, and presumes he may have it again if he request it, and affirms it is very large, and will make above twenty sheets. And this they agree upon, if they may have liberty to print that comment here by itself, and to sell it apart or bound up with the book, as they see convenient, and that the book be not reprinted so long as they have an hundred books left, they will then give 327., and no more, for the impression. This is not different from what Mr. Thompson saith himself formerly designed, and doth think the widow will be inclinable to, forasmuch as her daughter was lately with him about it. Now as to the book itself, Dr. Croone and Mr. Colwall can attest that the late Mr. Foster of Gresham College seldom heard it mentioned, but took occasion to utter his dislike of it, and Dr. Croone hath formerly said as much to Mr. Thompson. By reason whereof, in anno 1649, I asked Mr. Foster what authors he would advise unto; he replied, that the Algebra of Schubelius, (out of which Mr. Bunning hath taken some of his notes,) Stifelius, Clavius, Dibuadius, Stevin, did fully handle the surds and Euclid's irrational lines; that Harriot, Herigone, Des Cartes, and Ghetaldus sufficiently [handle] the specious and exegetic part, not mentioning Vieta or Mr. Oughtred, whose works might then be scarce, and not so large as now, Vieta not being then in one volume.