COMMENTARY ON ROBERT RECORDE
ROBERT RECORDE, born in Wales in 1510, taught mathematics at Oxford and Cambridge, got his M.D. degree at the latter university in 1545, became physician to Edward VI and Queen Mary, served for a time as "Comptroller of Mines and Monies" in Ireland and died in the King's Bench Prison, Southwark, where he was confined for debt--some historians hint at a darker offense-in 1558. Recorde published a number of mathematical works, chiefly in the then not uncommon form of dialogue between master and scholar. The most popular and influential of these treatises were The Ground of Artes (1540), and The Whetstone of Witte (1557), "containying extraction of Rootes: The Cossike practise, with the rule of Equation: and the woorkes of Surde Numbers."
England lagged behind Italy and France in the publication of mathematical books. 1 By the close of the fifteenth century Italy alone had printed more than 200 treatises on mathematics, whilst it was not until 1522 that the first book dealing exclusively with arithmetic 2-the "erudite but dull" De Arte Supputandi of Cuthbert Tonstall-appeared in Great Britain. The Ground of Artes (the selections below were taken from its edition of 1646) was an immensely successful commercial arithmetic, It went through at least eighteen editions in the sixteenth century and a dozen more in the seventeenth. Its influence, and that of The Whetstone of Witte, is at least partly explained by the economic development--manufacture and commerce--of England in the reign of Elizabeth. "Never (says D. E. Smith) was there a better opportunity for a commercial arithmetic, and never was the opportunity more successfully met."
Recorde's book discusses operations with arabic numerals as well as computation with counters, proportion, the "golden rule" of three, fractions and "allegation" and "contains the usual commercial topics which European countries north of the Alps had derived from Italy," It is hard to understand how anyone could learn from a dialogue delivered in the "formal" language of this primer. On second thought, it is perhaps just as remarkable that any of us profited from the average arithmetic texts visited on pupils as recently as twenty-five years ago. Recorde, whose work was "entail'd upon the People, ratified and sign'd by the approbation of Time," 3 was at least modest in his claims for it. He wrote in his preface: "And if any man obiect, that other books haue bene written of Arithmetike alreadie so sufficiently, that I needed not now to put penne to the booke, except I will codemne other mens writings: to them I answere. That as I codemne no mans diligence, so I know that no man can satisfie euery man, and therefore like as many do esteeme greatly other bookes, so I doubt not but some will like this my booke aboue any other English Arithmetike hitherto written, & namely such as shal lacke instructers, for whose sake I haue plain-Iy set forth the exaples, as no book (that I haue seene) hath hitherto: which thing shall be great case to the rude readers."
1 For the Source of these data see David Eugene Smith, Rare Arithmetica, Boston, 1908; also, the same author's standard History of Mathematics, Boslon and New York, 1923.
2 The first printed English book conlaining a reference to arithmetic is an anonymous translation from the French, The Mirrow of the World or Thymage of the same, issued in 1480 from the Caxton press. Chapter 10 of this book begins: "And after of Arsmetrike and whereof it proceedeth." See Smith, Rare Arithmetica.
3 A comment by Thomas Willsford in his 1662 edition of The Ground of Artes.
4 From the 1594 edition; see Smith, Rare Arithmetica, p.216
Someone who had begun to read geometry with Euclid, when he had learned the first proposition, asked Euclid, "But what shall I get by learning these things?" whereupon Euclid called his slave and said "Give him three-pence since he must make gain out of what he learns." --Stobabus
There still remain three studies suitable for free man. Arithmetic is one them. --Plato
By ROBERT RECORDE
TO THE LOVING READERS
THE PREFACE OF MR. ROBERT RECORD
SORE oft times have I lamented with my self the unfortunate condition of England, seeing so many great Clerks to arise in sundry other parts of the world, and so few to appear in this our Nation: whereas for pregnancy of naturall wit (I think) few Nations do excell Englishmen: But I cannot impute the cause to any other thing, then to be contempt, or misregard of learning. For as Englishmen are inferiour to no men in mother wit, so they passe all men in vain pleasures, to which they may attain with great pain and labour: and are as slack to any never so great commodity; if there hang of it any painfull study or travelsome labour.
Howbeit, yet all men are not of that sort, though the most part be, the more pity it is: but of them that are so glad, not onely with painfull study, and studious pain to attain learning, but also with as great study and pain to communicate their learning to other, and make all England (if it might be) partakers of the same; the most part are such, that unneath they can support their own necessary charges, so that they are not able to bear any charges in doing of that good, that else they desire to do.
But a greater cause of lamentation is this, that when learned men have taken pains to do things for the aid of the unlearned, scarce they shall be allowed for their wel-doing, but derided and scorned, and so utterly discouraged to take in hand any like enterprise again. The following is "The declaration of the profit of Arithmeticke" and constitutes the first ten pages of the text. It may be said to represent the influence of this text upon establishing for a long period what educators at present speak of as "the objectives" of elementary arithmetic.
A DIALOGUE BETWEEN THE MASTER AND THE SCHOLAR: TEACHING THE ART AND USE OF ARlTHMETICK WITH PEN.
THE SCHOLAR SPEAKETH. SIR, such is your authority in mine estimation, that I am content to consent to your saying, and to receive it as truth, though I see none other reason that doth lead me thereunto: whereas else in mine own conceit it appeareth but vain, to bestow any time privately in learning of that thing, that every chi/de may. and doth learn at all times and hours. when he doth any thing himself alone, and much more when he talketh or reasoneth with others.
Master. Lo, this is the fashion and chance of all them that seek to defend their blinde ignorance, that when they think they have made strong reason for themselves, then have they proved quite contrary. For if numbring be so common (as you grant it to be) that no man can do anything alone, and much lesse talk or bargain with other, but he shall still have to do with number: this proveth not number to be contemptible and vile, but rather right excellent and of high reputation, sith it is the ground of all mens affairs, in that without it no tale can be told, no communication without it can be continued, no bargaining without it can duely be ended, or no businesse that man hath, justly completed, These commodities, if there were none other, are sufficient to approve the worthinesse of number. But there are other innumerable, farre passing all these, which declare number to exceed all praise. Wherefore in all great works ere Clerks so much desired? Wherefore are Auditors so richly fed? What causeth Geometricians so highly to be enhaunsed? Why are Astronomers so greatly advanced? Because that by number such things they finde, which else would farre excell mans minde.
Scholar. Verily, sir, if it bee so, that these men by numbring, their cunning do attain, at whose great works most men do wonder, then I see well I was much deceived, and numbring is a more cunning thing then I took it to be.
Master. If number were so vile a thing as you did esteem it, then need it DOt to be used so much in mens communication. Exclude number, and answer to this question: How many years old are you?
Scholar. Mum.
Master. How many dayes in a weeke? How many weeks in a year? What lands hath your Father? How many men doth hee keep? How long is it since you came from him to me?
Scholar. Mum.
Master, So that if number want, you answer all by Mummes: How many miles to London?
Scholar. A poak full of plums.
Master. Why, thus you may see, what rule number beareth, and that if number bee lacking it maketh men dumb, so that to most questions they must answer Mum.
Scholar, This is the cause, sir, that I judged it so vile, because it is so common in talking every while: Nor plenty is not dainty, as the common saying is.
Master. No, nor store is no sore, perceive you this? The more common that the thing is, being needfully required, the better is the thing, and the more to be desired. But in numbring, as some of it is light and plain, so the most part is difficult, and not easie to attain. The easier part serveth all men in common, and the other requireth some learning. Wherefore as without numbring a man can do almost nothing, so with the help of it, you may attain to all things.
Scholar. Yes, sir, why then it were best to learn the Art of numbring, first of all other learning, and then a man need learn no more, if all other come with it.
Master. Nay not so: but if it be first learned, then shall a man be able (I mean) to learn, perceive, and attain to other Sciences; which without it he could never get.
Scholar. I perceive by your former words, that Astronomy and Geometry depend much on the help of numbring: but that other Sciences, as Musick, Physick, Law, Grammer, and such like, have any help of Arithmetick, I perceive not.
Master, I may perceive your great Clerk-linesse by the ordering of your Sciences: but I will let that passe now, because it toucheth not the matter that I intend, and I will shew you how Arithmetick doth profit in all these somewhat grosly, according to your small understanding, omitting other reasons more substantial!.
First (as you reckon them) Musick hath not onely great help of Arithmetic, but is made, and hath his perfectnesse of it: for all Musick standeth by number and proportion: And in Physick, beside the calculation of criticall dayes, with other things, which I omit, how can any man judge the pulse rightly, that is ignorant of the proportion of numbers? And so for the Law, it is plain, that the man that is ignorant of Arithmetick, is neither meet to be a Judge, neither an Advocate, nor yet a Proctor. For how can hee well understand another mans cause, appertaining to distribution of goods, or other debts, or of summes of money, if he be ignorant of Arithmetick? This oftentimes causeth right to bee hindered, when the Judge either delighteth not to hear of a matter that hee perceiveth not, or cannot judge for lack of understanding: this commeth by ignorance of Arithmetick. Now, as for Grammer, me thinketh you would not doubt in what it needeth number, sith you have learned that Nouns of all sorts, Pronouns,The Declaration of the Profit of Arithmeticke Verbs, and Participles are distinct diversly by numbers: besides the variety of Nouns of Numbers, and Adverbs, And if you take away number from Grammer, then is all the quantity of Syllables lost, And many other ways doth number help Grammer. Whereby were all kindes of Meeters found and made? was it not by number? But how need full Arithmetick is to all parts of Philosophy, they may soon see, that do read either Aristotle, Plato, or any other Philosophers writings. For all their examples almost, and their probations, depend of Arithmetick. It is the saying of Aristotle, that hee that is ignorant of Arithmetick, is meet for no Science. And Plato his Master wrote a little sentence over his Schoolhouse door, Let none enter in hither (quoth he) that is ignorant of Geometry. Seeing hee would have all his Scholars expert in Geometry, much rather he would the same in Arithmetick, without which Geometry cannot stand. And how needfull Arithmetick is to Divinity, it appeareth, seeing so many Doctors gather so great mysteries out of number, and so much do write of it. And if I should go about to write all the commodities of Arithmetick in civill acts, as in governance of Common-weales in time of peace, and in due provision & order of Armies, in time of war, for numbering of the Host, summing of their wages, provision of victuals, viewing of Artillery, with other Armour; beside the cunningest point of all, for casting of ground, for encamping of men, with such other like: And how many wayes also Arithmetick is conducible for all private Weales, of Lords and all Possessioners, of Merchants, and all other occupiers, and generally for all estates of men, besides Auditors, Treasurers, Receivers, Stewards, Bailiffes, and such like, whose Offices without Arithmetick are nothing: If I should (I say) particularly repeat all such commodities of the noble Science of Arithmetick, it were enough to make a very great book.
Scholar. No, no sir, you shall not need: For I doubt not, but this, that you have said, were enough to perswade any man to think this Art to be right excellent and good, and so necessary for man, that (as I think now) so much as a man lacketh of it, so much hee lacketh of his sense and wit.
Master. What, are you so farre changed since, by hearing these few commodities in generall: by likelihood you would be farre changed if you knew all the particular Commodities.
Scholar, I beseech you Sir, reserve those Commodities that rest yet behinde unto their place more convenient: and if yee will bee so good as to utter at this time this excellent treasure, so that I may be somewhat inriched thereby, if ever I shall be able, I will requite your pain.
Master. I am very glad of your request, and will do it speedily, sith that to learn it you bee so ready.
Scholar. And I to your authority my wit do subdue; whatsoever you say, I take it for true.
Master. That is too much; and meet for no man to bee beleeved in all things, without shewing of reason. Though I might of my Scholar some credence require, yet except I shew reason, I do it not desire. But now sith you are so earnestly set this Art to attaine, best it is to omit no time, lest some other passion coole this great heat, and then you leave off before you see the end.
Scholar, Though many there bee so unconstant of mind, that flitter and turn with every winde, which often begin, and never come to the end, I am none of this sort, as I trust you partly know. For by my good will what I once begin, till I have it fully ended, I would never blin.
Master. So have I found you hitherto indeed, and I trust you will increase rather then go back. For, better it were never to assay, then to shrink and flie in the mid way: But I trust you will not do so; therefore tell mee briefly: What call you the Science that you desire so greatly.
Scholar: Why sir, you know.
Master. That maketh no matter, I would hear whether you know, and therefore I ask you. For great rebuke it were to have studied a Science, and yet cannot tell how it is named.
Scholar. Some call it Arsemetrick, and some Augrime.
Master. And what do these names betoken?
Scholar. That, if it please you, of you would I learn.
Master. Both names are corruptly written: Arsemetrick for Arithmetick, as the Greeks call it, and Augrime for Algorisme, as the Arabians found it: which both betoken the Science of Numbring: for Arithmos in Greek is called Number: and of it commeth Arithmetick, the Art of Numbring. So that Arithmetick is a Science or Art teaching the manner and use of Numbring: This Art may be wrought diversly, with Pen or with Counters. But I will first shew you the working with the Pen, and then the other in order.
Scholar, This I will remember. But how many things are to bee learned to attain this Art fully?
Master. There are reckoned commonly seven parts or works of it. Numeration, Addition, Subtraction, Multiplication, Division, Progression, and Extraction of roots: to these some men adde Duplication, Triplation, and Mediation, But as for these three last they are contained under the other seven, For Duplication, and Triplation are contained under Multiplication; as it shall appear in their place: And Mediation is contained under Division, as I will declare in his place also.
Scholar. Yet then there remain the first seven kinds of Numbring.
Master. So there doth: Howbeit if I shall speak exactly of the parts of Numbring, I must make but five of them: for Progression is a compound operation of Addition, Multiplication and Division. And so is the Extractions of roots. But it is no harme to name them as kindes severall, seeing they appear to have some severall working. For it forceth not so much to contend for the number of them, as for the due knowledge and practising of them.
Scholar. Then you will that I shall name them as seven kindes distinct. But now I desire you to instruct mee in the use of each of them.
Master. So I will, but it must be done in order: for you may not learn the last so soon as the first, but you must learn them in that order, as I did rehearse them, if you will learn them speedily, and well.
Scholar. Even as you please. Then to begin; Numeration is the first in order: what shall I do with it?
Master. First, you must know what the thing is, and then after learn the use of the same.