The grounde of artes teaching the perfect vvorke and practise of arithmetike, both in whole nu[m]bers and fractions, after a more easie ane exact sort, than hitherto hath bene set forth. Made by M. Robert Recorde, D. in Physick, and afterwards augmented by M. Iohn Dee. And now lately diligently corrected, [and] beautified with some new rules and necessarie additions: and further endowed with a thirde part, of rules of practize, abridged into a briefer methode than hitherto hath bene published: with diverse such necessary rules, as are incident to the trade of merchandize. Whereunto are also added diuers tables [and] instructions ... By Iohn Mellis of Southwark, scholemaster.

TO THE MOSTE mightie Prince Edwarde the sixt, by the grace of God King of Englande, Fraunce, and Irelande. &c.

THe excellencie of mans na∣ture, being such, as it is by Gods diuine fauoure (most mightie Prince) not onely created in highnesse of de∣gree farre aboue all other corporall things, but by per∣fection of reason and search of wit, much approching to∣ward the image of God, as not onely the holy Scriptures doe testifie, but also those naturall Philosophers, which exactly did consider the na∣ture of man, and namely the farre reach and infinite com∣passe of the workes of the minde, were inforced to con∣fesse, that man scarcely was able to knowe himselfe. And if he would duly ponder the nature of himselfe, he woulde finde it so strange, that it might seeme vnto him a verie miracle. And thereof sprang that saying: magnum mi∣raculum est homo, maximum mariculum sapiens homo.

For vndoubtedly as man is one of the greatest mira∣cles that euer God wrought, so a wise man is plainely the greatest.

And therefore was it that some did account the heade of a man the greatest miracle in the worlde, because not onely of the straunge workemanshippe that is in it, but much more of the efficacie of reason, witte, memorie, ima∣gination, and such other powers and works of the mind, which can more easily conceiue any thing in a manner, than vnderstande it selfe. And amongst all the creatures of God it findeth none more difficult to be perceiued than these same powers of it selfe, whereby it doth conceiue and iudge as it may be well coniectured by the diuersitie of opinions, that the wisest Philosophers did vtter tou∣ching the spirite of man and the substance of it: whereof at this present I intende to make no rehearsall, but who so sisteth to reade thereof, may finde it largely set forth not onely in Aristotle his bookes De anima; but also in Galene his booke called Historia philosophica, & againe in Plutarch his worke, De philosophorum placitis, whose wordes are also repeared of Eusebius in the xv. booke, 〈 in non-Latin alphabet 〉〈 in non-Latin alphabet 〉, vnto whom I remi•• them that haue desired to vnderstande the intricate diffi∣cultie of knowing our owne selues, as touching our best part, and that part whereby we deserue to beare the name of men.

This matter seemed so obscure and difficulte, in know∣ledge, that Galen, who for his excellent wisedome and iudgement in naturall workes, is called of many men a Miracle in nature, yet in searching the nature and sub∣stance of the spirite of man, he not onely confesseth him∣selfe ignorant, but counteth it plaine temeritie to attempt to finde it: so farre aboue the hope of mans knowledge is that parte, whereby man doth knowe and iudge of

things. And although the ignorant sort (which hate all things that they knowe not) doe little esteeme the pro∣foundnesse of mans spirit and of reason, the chiefe power and facultie of it, yet as there is a kind of feare and obedi∣ence of vnreasonable beastes vnto man by the working power of God, so is there in those small reasoned persons a certaine kinde of reuerence towarde wisedome and re∣asons, which they doe shewe oftentimes, and by power of persuasion are inforced to obey reason, will they nil they.

And hereby came it to passe, that y^e rudenesse of the first age of man was brought vnto some more ciuill trade, as it is well declared by Cicero in the beginning of his first booke De inuentione Rethorica, where he saith thus:

Nam suit quoddam tempus quum in agris homines passion bestiarum more vagahantur, & sibi victu ferino vitam pro∣pagabant, nec ratione animi quicquam, sed plera{que} viribus corporis administrabant. N••ndum diuine religionis, non hu∣mani officij ratio colebatur: Nemo legitimas viderat nuptias, non cer••os quisquam inspexerat liberos, n••n ius aequabile quid vnlitatis haberet, acceperat: ita propter errorem atque insci∣tiam. caeca ac ••emeraria dominatrix animi cupiditas, ad se ex∣ple••dam viribus corporis abutebatur, perniciosissimis satelli∣tibus.

Quo tempore quidam, magnus videlicet vir & sapiens, cog∣nouit quae ma••••ria esset, & quanta ad maximas res oportunitas in animis iness•• th••ninum, si quis eam posset elicere, & praeci∣piendo me••••••r••n reddere: Qui dispersos homines in agris, & in tectis syluestribus abditos ratione quadam compulit in v∣num locum, & congregauit: & eos in vnamquamque rem in∣ducens v••ilē atque honestam primo propter insolentiam recla∣mantes, deinde propter rationem atque orationem studiosius au∣dientes, ex feris & immanibus mites reddidit, & mansue∣tos.

This long repetition of Tullies wordes will seeme te∣dious

to them which loue but little, and care much lesse for the knowledge of reason, but vnto your Maiestie (I dare say) it is a delectable remembrance, and vnto mee it seemed so pleasant, that I coulde scarse staye my penne from writing all that mine eyes did so greedily reade.

This sentence of Cicero am I lothe to translate into Englishe, partly for that vnto your Maiestie it needeth no translation, but especially knowing howe farre that grace of Tullies eloquence doth excell any English mans tongue, and much more exceedeth the basenesse of my bar∣barous style, yet for the fruite of the sentence, I had ra∣ther vnto my meere English Countrymen vtter the rude∣nesse of my translation, than to defraud them of the bene∣fite of so good a lesson, trusting they will also gladly and greedily imbrace all good sciences that may helpe to the iust furniture of the same, when they consider that infor∣med reason was the onely Instrument, or ar least y^e chiefe meane to bring men vnto Ciuile regiment, from barba∣rous manners and beastly conditions.

For the time was (saith Tullie) that men wandered a∣broad in the fields vp and downe like beasts, and vsed no better order in feeding than they, so that by reasons rule they wrought nothing, but moste of their doing did they atchiue by force of strēgth. At this time there was no iust regarde of religion towarde God, nor of duetie towarde man. No man had seene right vse of mariage, neither did any man knowe their owne children from other, nor no man had felt the commodity of iust lawes: so that through errour and ignorance, wilfull lust, like a blinde and heady ruler, abused bodily strength as a most mortall minister for the satisfying of his desire. At that time was there one, which not onely in power, but also in wisedome was great: and he considered, howe that in the mindes of men was bothe apte instrumentes, and greate occasion to the

due accomplishment of most weightie affaires, if a man coulde applie them to vse, and by teaching of rules frame them to better trade. This man with persuasion of rea∣son, gathered into one place the people that were wan∣dring about the fieldes, and lay lurking in wilde cotages and woods: And bringing them into one common socie∣tie, did trade them to all such things, as either were pro∣fitable or honest, although not without repyning at y^e first, by reason that they had not beene so accustomed before. Yet at length through reason and persuasion of wordes they obeyed him more diligently, and so of a wilde and cruell people, he made them curteous and gentle.

Thus hath Tullie set forth the efficacie of reason and persuasion, howe it was able to conuert wilde people to a mildenesse, and to change their furious cruelnesse into gen••le cur••••e. Were it not nowe a great reproch in this our time (when knowledge raigneth so large) that men should shewe themselues lesse obsequious to reason? vn∣lesse it may be thought, that now euery man hauing suffi∣cient knowledge of himselfe, needeth not to hearken to the persuasion of others.

Indeede he that thinketh himself wise, will not esteeme the reason of any other, be he neuer so wise, so that of such one it may well be saide, He that thinketh himselfe wiser than he is, may iustly be counted a double foole: where∣fore such men are not to bee permitted in open audience to talke, but must be put to silence, and made to giue eare to reason, which reason consisteth not in a multitude of words, heaped rashly together, and applyed for one pur∣pose, but reason is the expressing of a iust matter with wittie persuasions, furnished with learned knowledge. Such knowledge had Moses being expert in all learning of the Aegyptians, as the Scriptures declare, and there∣fore was able to persuade the stubborne people of the

Iewes, although not without great paine.* 1.1 Such know∣ledge and such reasons did Druys shewe, which was the first lawe maker of all the West partes of Europe. Like reason and wisedome did Xamolxis vse amongest the Gothes: Lycurgus vnto the Lacedemonians, Zeleucus to the Locrians, Solon to the Athenienses, and Donwallo Molmitius two thousande yeares past, amongst the olde Britanes of this realme. And therby ti came to passe, that their lawes continued long, till more perfite reason alte∣red many of them, and wilfull power oppressed moste of them.

At the beginning when these wise men perceiued howe harde it was to bring the rude people to vnderstande rea∣son, they iudged the best meanes to attaine this honest purpose to depende of learning in euerie kind, for by lear∣ning, as Ouid saith: Pectora moiles••unt, asperitas{que} fugit: Stoute stomackes doe waxe milde, and sharpe fiercenesse is exiled. Therefore as Berosus doth testifie, Sarron▪ that was the thirde King ouer all this West parte of Eu∣rope, for to bring the people from beastly rage to manly reason, did erect Schooles of liberall Artes which tooke so good successe, that his name continued in that sort fa∣mous aboue two thousand yeares after: for Diodorus Si∣culus, which was in the time of Iulius Caesar maketh mē¦tion of the learned men of the Gothes, and named them Sarronides, that is to say, Sarron his Scholers and fo••∣lowers.

Among these Artes that then were taught, some did in forme the tongue, and make men able both to vtter aptly their minde, and also to persuade, as Grammer, Logike, and Rhethorike, although not so couriously as in this time: some other did appertaine to the iust order of parti∣tion of Landes, the true vsing of waights, measures, and reckenings in all sorts of bargaines, and for order of buil∣ding

and sundrie other vses, those were Arithmerike and Geometrie. Againe, to incourage men to the honour of God, they taught Astronomie, whereby the wonderfull workes of God were so manifestly set forth, that no mans tongue nor pen can in like sort expresse his infinite pow∣er, his vnspeakable wisedome, and his exceeding good∣nesse toward man, wherby he doth bauntifully prouide for man all necessaries, not onely to liue, but also to liue plea∣santly. And so was their confidence in Gods prouidence strongly stayed, knowing his goodnesse to be such, that he woulde helpe man as he coulde, and his power to bee so great, that he could doe what he woulde: and thirdly his wisedome to be so pure, that he would doe nothing, but that was best. Beside these Sciences they taught also Mu∣sike, which most commonly they did apply partely to reli∣gious Sciences, to drawe men to delight therein, & part∣ly to songs made of the maners of men in praise of Ver∣tue, and discommendation of Vice, whereby it came to passe, that no man would displease them, nor do any thing euill that might come to their hearing:* 1.2 for their Songs did make euill men more abhorred in that time, than any excommunication doeth in this time. The posteritle of these Musitians continue yet both in Wales and Ireland called Bardes vnto this day, by the auncient name of Bar∣dus, their first founder.

And as these Sciences did encrease, so did vertue in∣crease thereby. Againe, as these sciences did decaye, so vertue lost hir estimation, and consequently was little in vse: whereof to make a ful declaration, were a thing meet for a Prince to heare, but it woulde require a peculiar treatise. Wherefore at this present I count it sufficient lightly to haue touched this matter in generall wordes, and to say no more of the particularitie thereof, but onely touching one of those sciences, that is, Arithmetike, by

which not onely iust partition of landes was made, but also touching buying an selling, all assises, weights, and measures were deuised, and all reckenings and accounts driuen: yea by proportion of it, were the true orders of Iu∣stice limited, as (Aristotle in his Ethikes doth declare) & the degrees of estates in the common wealth established. Although that proportion be called Geometricall, and not Arithmeticall, yet doth that proportion appertaine to the Art of Arithmetike: & in Arithmetike is taught the Pro∣gression of such proportions, and all things thereto be∣longing. Wherefore I may well say, that seeing Arith∣metike is so many wayes needefull vnto the first planting of a common wealth, it must needes be as much required to the preseruation of it also: for by the same meanes is any common wealth continued, by which it was erected and established. And if I shall in smal matters in appea∣rance, but in deede verie waightie, put one example or two, what shall we say for the statutes of this realme, which be the onely staie of good order in maner nowe? As touching the mesuring of ground by length and bredth, there is a good and an auncient statute made by Arte of Arithmetike, and now it shalbe to little vse, if by the same Art it be not practised and tried. For the assyse of breade and drinke, the two most common and most necessarie thinges for the sustentation of man, there was a goodly ordinance in the Lawe made, which by ignorance hath so growen out of knowledge and vse, that fewe men doe vn∣derstand it, and therefore the statute bookes wonderfully corrupted, & the commons cruelly oppressed: notwithstan∣ding some mē haue written, that it is too doubtful a mat∣ter to execute those Assises by those statutes, by reason they depend of the standerd of the coine, whiche is muche chaunged from the state of that time when those statutes were made. Thus shall euerie man reade that listeth in

the Abridgement of Statutes in the title of Waightes and Measures, in the seauenth number of the Englishe Booke, where hee shoulde haue translated a good ordi∣nance, which is set forth in the French booke: but no maruaile if the Abridgement doth omit it, seeing the great booke of Statutes doth omitte the same Statute, as it hath done diuers other verie good lawes. And this is the fruite of ignorance, to reiect all that it vnderstan∣deth not, although they vse some clokes for it: but such clokes, as being allowed, might serue to repell all good lawes, which God forbid.

Againe there is an auncient order for assise of fyre wood, and coales, which was renued not many yeares past, and nowe howe Auarice and Ignorance doth canuas the statute, it is too pitifull to talke of, and more misera∣ble to feele.

Furthermore, for the Statute of Coinage, and the standerd thereof, if the people vnderstoode rightly the statute, they shoulde not, nor woulde not (as they often doe) gather an excuse for their follie therby, but as I said, these statutes by wisedome and good knowledge of Arith∣metike were made, & by the same must they be continued. And let Ignorance no more meddle with the vse of them, than it did with the making of them. Oh in how misera∣ble case is that Realme, where the Ministers and inter∣preters of the Lawes are destitute of all good sciences, which be the keyes of the laws? How can they either make good Laws, or maintaine them, that lack that true know∣ledge wherby to iudge them? And happie may that realme be accounted where the Prince himselfe is studious of learning, and desireth to vnderstande equitie in all lawes. Therefore most happy are we the louing subiectes of your Maiestie which may see in your highnesse not onely such towardnesse, but also such knowledge of diuers Artes as

seldome hath bene seene in any Prince of such yeares, whereby we are inforced to conceiue this hope: Certain∣ly, that he which in those yeares seeketh knowledge when knowledge is least esteemed, and of such an age can di∣scerne them, to be enimes both to his royall person, and to his realme, which labour to withdrawe him from know∣ledge to exeessiue pastime, and from reasonable studie to ydle or noysome pleasures, he must needes, when he com∣meth to more mature yeares, be a most prudent Prince, a most iust Gouernour, and a right Iudge, not onely of his subiectes commonly, but also of the ministers of his lawes, yea, and of the Lawes themselues. And to be able to conceiue the true equitie and exact vnderstanding of al his Lawes and Statutes, to the comfort of his good sub∣iectes, and the confusion and reproch of them which labour to obscure or peruerte the equitie of the same lawes and statutes. Howe some of those statutes may bee applied to vse, as well in our time, as in any other time, I haue particularly declared in this Booke, & some other I haue omitted for iust considerations, till I may of∣fer them first vnto your Maiestie, to weigh them, as to your Highnesse shall seeme good: for many things in them are not to be published without your highnesse knowledge and approbation, namely because in them is declared all the rates of alloyes for all standerds from one ounce vp∣warde, with other mysteries of Mynte matters, and also most part of the varieties of coynes, that haue beene cur∣rant in this your Maiesties realme by the space of sixe hundred yeares last past, and many of them that were cur∣rant in the time that the Romaines ruled here.

All which, with the auncient description of Englande and Irelande and my simple censure of the same, I haue almost compleated to be exhibited to your Highnesse.

In the meane season most humbly beseeching your Ma∣iestie,

to accept this simple treatise, not worthy to be pre∣sented to so high a Prince, but that my lowly request to your maiestie is, that this amongst other of my bookes may passe vnder the protection of your highnesse, whom I beseeche God most earnestly and dayly, according to my duetie, to aduaunce in all honour and prince∣ly regalitie, and to increase in all know∣ledge, iustice, and godly policie. Amen.

Your Maiesties most obedient subiect and seruant, ROBERT RECORDE.

Notes

• * 1.1

  Druis vvas sonne to K. Sarron, & succeeded him in his kingdome.
• * 1.2

  This Bar∣dus Drui∣dius the v. king of the Celtes, raig¦ned 69. yeres, and died 1832. yeares be∣fore Christ.