The Whetstone of Witte/The Preface

by Robert Recorde

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THE PREFACE
to the gentle Reader.

The excellencie of nomber. Although nomber be infinite in increasyng: so that there is not in all the worlde, any thing that can excede the quantitie of it: Nother the grasse on the ground, nother the droppes of water in the sea, no not the small graines of Sande through the whole masse of the yearth: yet maie it seme by good reason, that noe man is so experte in Arithmetike, that can nōber the commodities of it. Wherefore I maie truely saie, that if any imperfection bee in nomber, it is bicause that nomber, can scarsely nomber, the commodities of it self. For the moare that any experte man, doeth weigh in his mynde the benifites of it, the more of them shall he see to remain behinde. And so shall he well perceiue, that as nomber is infinite, so are the commodities of it as infinite. And if any thyng doe or maie exceade the whole worlde, it is nomber, whiche so farre surmounteth the measure of the worlde, that if there were infinite worldes, it would at the full cōprehend them all. This nomber also hath other prerogatiues, aboue all naturalle thynges, for neither is there certaintie in any thyng without it, nother good argremente where it wanteth. Whereof no man can doubte, that hath been accustomed in the Bookes of Plato, Aristotell, and other aunciente Philosophers, where he shall see, how thei search all secrete knowledge and hid misteries, by the aide of nomber. For not onely the constitution of the whole worlde, dooe thei referre to nomber, but also the composition of manne, yea and the noble substaunce of the soule. Of whiche thei professe to knowe no moare, then thei cā by the benifite of nomber attaine. Furthermore, for knowledge and certaintie in any other thynge, that mannes witte can reche vnto, there is noe possibilitie without nomber. It is confessed amongeste all men, that knowe what learnyng meaneth, that beside the Mathematicalle artes, there is noe vnfallible knoweledge, excepte it bee borowed of them. And emongeste them, it is sufficiently knowen, and well declared by Nicomachus, and diuerse other writers, that Arithmetike is the fountaine of all the other, and their ground and bonde, as he calleth it. If any man will saie, that Diuinitie, Lawe, and Physike, maie be had without it: or that thei take litle aide therby. Although I haue before this tyme aunswered thereto, yet not I saie again: Diuninite. that in Diuinitie there are greate hidde secretes in nombers. So that diuerse excellente Diuines, haue written whole Bookes of the misteries of nombers. And some of their Bookes intituled: The Diuinitie of Nombers. But what Christen manne is ignoraunte, that betwene Trinitie and vnitie, doeth consiste the full grounde of al Diuninitie. Wherefore I neade not to allege the other hollie and sacred Nombers. Saue that .7. will not permitte me to passe it with silence. In whiche is contained, not onely the secretes of the creation of all thynges: and the consummation of the whole worlde againe, with the state of eternitie: But also by it is the Sabbothes reste, and therby the full life and conuersation of godlie persones, represented and insinuate. Lawe. In Lawe twoe kyndes of Iustice are the sommeof the studie: Iustice Distributiue, and Iustice Commutatiue, whiche termes I use, as beste knowen in that arte: But what is any of thē bothe without Nomber? I haue said in an other place (as I learned of that noble Philosopher Aristotell) that if the knowledge and distinction, of Geometricalle and Arithmeticall proportion bee not well obserued, there can noe Iustice well bee executed. And how often the ministers of the Lawe vse aide of Nomber, I neade not repete, bicause none but madde men doubt of it. Physike. And as for Physike, without knowledge and aide of nomber is nothynge. Wee see that nature in generation, bothe of manne and beastes, yea and of al thynges els doeth obserue nomber exactly. As well in the type of formation, as in the monethes of quickenyng, and of birthe. The misteries of the seuenth and nineth monethes are sufficiente testimonies therein. Beside that from the fourthe monethe til the seuenth many thynges bee permitted, that els bee not conueniente. For the vse of the pulse, and for criticalle dayes, beside the proportion in degrees in simple medicines, and mixture of compounde medicines, and other infinite maters, what nomber can doe and what aide it giueth, onely the ignoraunte doe doubte.

Astronomie. But where can there bee any better testimonie for Nomber, then that the celestialle bodies doe kepe an vnfallible nomber, in all their wonderfulle motions? By meanes whereof, mannes witte is habled to attaine the knowledge of them. As by the Arithmeticalle tables, of their motions it is easily knowen. Therefore and for that we see the yere, and all the distinction of times, beside the common vse of trafike betwene menne, to depende of nomber, wee muste neades not onely confesse it to bee, as it were the onely staie of all natures woorkes, and of all ciuilitie: but we must also honoure and reuerence it, as often as wee duely remember the excellencie and benifite of it. Was not Nomber, thinke you, wonderfullie honoured, when noe name was thought moare meter for God, then the name of Nomber? I meane .1. and .3. the name of the Trinitie. But to come to moare familiare maters, I will saie, as Plato saieth in his Booke De sum mo bono, Take awaie Arithmetike, with measure and weightes, from all other artes, and the reste that remaineth is but base, and of noe estimation. Where although Plato dooe name three thinges in appearaunce, that is Nomber, Measure, and Weighte. Measure.
weighte. What are Measure and Weighte, but nomber applied to seueralle vses? For Measure is but the nombryng of the partes of lengthe, bredthe, or depthe. And so weighte (as here it is taken) is nomberyng of the heuinesse of any thyng. So that if nomber were withdrawen, no manne could either measure, or weigh any quantitie. And therfore it must followe: that nomber onely maketh all artes perfecte, and worthie estimation: seyng that without it, all artes are but base, and without commendation. This maie suffice for the iuste cōmendation of Arithmetike. But yet one commoditie moare, whiche all menne that studie that arte, doe fele, I can not omitte. That is the filyng, sharpenyng, and quickenyng of the witte, that by practice of Arithmetike doeth insue. It teacheth menne and accustometh them, so certainly to remember thynges paste: So circumspectly to consider thynges presense: And so prouidently to forsee thynges that followe: that it maie truelie bee called the File of witte. Yea it maie aptly bee named the Scholehouse of reason. The like iudgemente had Plato of it, as appeareth by his woordes in the seuenth booke Dere publica. Where he saieth thus: Thei that be apte of nature to Arithmetike, bee readie and quicke to attaine all kindes of learnyng. And thei that bee dulle witted, and yet bee instructed and exercised init, though thei gette nothyng else, yet this shall thei all obtain, that thei shall bee moare sharpe witted, then thei were before. What a benifite that onely thyng is, to haue the witte whetted and sharpened, I neade not trauell to declare, sith all menne confesse it to be as greate as maie be. Excepte any witlesse persone thinke he maie bee to wise. But he that moste feateth that, is leaste in daunger of it. Wherefore to conclude, I see moare menne to acknowledge the benifite of nomber, then I can espie willyng to studie, to attaine the benifites of it. Many praise it, but fewe dooe greately practise it: onlesse it bee fore the vulgare practice, concernyng Merchaundes trade. Wherein the desire and hope of gain, maketh many willyng to sustaine some trauell. For aide of whom, I did sette forth the firste parte of Arithmetike. But if thei knewe how farre this seconde parte, dooeth excell the firste parte, thei would not accoumpte any tyme loste, that were imploied in it. Yea thei would not thinke any tyme well bestowed, till thei had gotten soche habilitie by it, that it might be their aide in al other studies. And if Plato doe require Arithmetike, as a specialle and a necessarie qualitie in hum, whom he would admitte as a citezein in his politike toune: How maie wee thinke of our selues, that desire to gouerne other, and yet can scante skille of common nomber? So farre are many, yea moste parte of vs from cunnyug in nomber. Plato thinketh noe manne hable to bee a good capitaine, excepte he bee skilfulle in this arte: And wee accoumpte it noe parte of those qualities, that bee required in any soche manne. Howbeit for the better trialle thereof, I haue in this Booke framed some of the questions in soche sorte, as thei maie approue the vse of this arte, not onely good for capitaines, but also moste necessarie for theim. So that without it, thei can not Marshall their battaile, nother vewe their enemies campe or forte. And if I shall saie as I thinke, without it a capitaine is noe capitaine. In this booke what I haue written, for the aide of all menne, and namely soche of my countrie menne, that vnderstand nothyng but Englishe, I neade not to repete perticularely, but remitte them to the booke it self, to see it at large. Onely this maie I saie: that as I haue doen in other artes, so in this I am the first venturer, in these darke maters. Wherfore I trust thei that be learned, and happen to reade this worke, wil beare the moare with me, if thei finde any thyng, that thei doe mislike: Wherein if thei will vse this curtesie, either by writynge to admonishe me thereof, either theim selfes to sette forthe a moare perfecter woorke, I will thynke them praise worthie. But if any manne will be so hastie, other to blame that, whiche he is not hable to amende, or to condempne that, whiche he did neuer vnderstande: As some ofte tyme doe of a fonde curiositie, I will wisshe hym a better witte, and moare modestie. And to preuente all soche seuere Iudges, I thought it good to adminisshe you before, that by occasion of trouble vnon trouble, I was hundered rom accomplishyng this worke, as I did intende. But yet is here moare, then any manne might well looke for at my handes, if thei did knowe and consider myne estate. And this moche moare I saie: that if I maie perceiue, that this Booke bee as well receiued, as the firste parte was, I will striue moche, to stele from my troubles so moche tyme, as to set out the reste of this arte, moare completely in Englishe, than euer I sawe it in any toungue, hetherto doen: trust thereto adsuredly. And wisshe hym good, that traueleth for thy benifite.

Of the rule of Cose.

 One thyng is nothyng, the prouerbe is,
whiche in some cases doeth not misse.
Yet here by woorkyng with one thyng,
Soche knowledge doeth from one roote spryng,
That one thyng maie with right good skille,
Compare with all thyng: And you will
The practice learne, you shall sone see,
what thynges by one thyng knowen maie bee.

To the curiouse scanner.

 If you ought finde, as some men maie,
That you can mende, I shall you praie,
To take some paine so grace maie sende,
This worke to growe to perfecte ende.
 But if you mende not that you blame,
I winne the praise, and you the shame.
Therfore be wise, and learne before,
Sith slaunder hurtes it self moste sore.