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A12970 Disme: the art of tenths, or decimall arithmetike teaching how to perform all computations whatsoeuer, by whole numbers without fractions, by the foure principles of common arithmeticke: namely addition, subtraction, multiplication, and diuision. Inuented by the excellent mathematician, Simon Steuin. Published in English with wholesome additions by Robert Norton, Gent.; Thiende. English Stevin, Simon, 1548-1620.; Norton, Robert, d. 1635. 1608 (1608) STC 23264; ESTC S104599 15,830 36

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because of the explicatiō of these vtilities out of doubt he sheweth himselfe to haue neyther iudgemēt vnderstanding nor knowledge to discerne simple things from ingenious inuentions but he rather seemeth enuious of the common benefite yet howsoeuer it were not fit to omit the benefit hereof for the inconuenience of such calumny But as the Mariner hauing by hap found a certaine vnknowne Island spareth not to declare to his Prince the riches and profits thereof as the fayre fruits precious mineralls pleasant champions c. and that without imputation of Philautry euen so shall we speake freely of the great vse of this inuention I call it great being greater then any of you expect to come from me Seeing then that the matter of this Disme the cause of the name whereof shal be declared by the first difinition following is number the vse and effects of which yourselues shall sufficiently witnes by your continuall experiences therefore it were not necessary to vse many words thereof for the Astrologer knoweth that the world is become by computation Astronomicall seing it teacheth the Pilot the eleuation of the Equator and of the Pole by meanes of the declination of the Sunne to describe the true Longitudes Lātitudes situatiōs distances of places c. a Paradise aboūding in some places with such things as the Earth cannot bring forth in other But as the sweet is neuer without the sowre so the trauayle in such computations cannot be vnto him hidden namely in the busy multiplications and diuisions which proceed of the 60 progression of degrees minutes seconds thirds c. And the Surueyor or Land-meater knoweth what great benefite the world receyueth from his science by which many dissensions and difficulties are auoyded which otherwise would arise by reason of the vnknowne capacity of Land besides he is not ignorant especially whose busines and imployment is great of the troublesome multiplications of Roods Feete and oftentimes of ynches the one by the other which not onely molesteth but also often though he be very well experienced causeth error tending to the dāmage of both parties as also to the discredit of Land-meater or surueyor and so for the Money-masters Marchants and each one in his busines therefore how much they are more worthy and the meanes to attayne them the more laborious so much the greater and better is this Disme taking away those difficulties But howe it teacheth to speake in a word the easy performance of all reckonings computations accounts without broken numbers which can happen in mans busines in such sort as that the foure Principles of Arithmetick namely Addition Substractiō Multiplication Devisiō by whole numbers may satisfie these effects affording the like facility vnto those that vse Coūters Now if by those meanes wee gaine the time which is precious if hereby that be saued which otherwise should be lost if so the paines controuersy error dammage and other inconueniences commonly hapning therin be eased or taken away then I leaue it willingly vnto your iudgements to be censured and for that that some may say that certaine inuentions at the first seeme good which when they come to be practized effect nothing of worth as it often hapneth to the serchers of strong mouing which seeme good in small proofes and modells when in great or comming to the effect they are not worth a Button whereto we answere that herein is no such doubt for experience dayly sheweth the same namely by the practize of diuers expert Land-meaters of Holland vnto whom we haue shewed it who laying aside that which each of them had according to his owne manner inuented to lessen their paines in their computations do vse the same to their great contentment and by such fruit as the nature of it witnesseth the due effect necessarily followeth The like shall also happen to each of your selues vsing the same as they doe meane while liue in all felicity The Argument THe Disme hath two parts that is Definitions Operations by the first definition is declared what Disme is by the second third and fourth what Comencement Prime Second c. and Disme numbers are the Operation is declared by foure propositions The Addition Substraction Multiplication and Deuision of Disme numbers The order whereof may be successiuely represented by this Table The Disme hath two parts Definitions as what is Disme Comencement Prime Second c. Disme nomber Operations or Practize of the Addition Substraction Multiplication Deuision And to y● end the premises may the better be explaned there shal be hereunto an Appendix adioyned declaring the vse of the Disme in many things by certaine examples and also definitions and operations to teach such as doe not already know the vse and practize of Numeration and the foure principles of common Arithmetick in whole numbers namely Addition Substraction Multiplication Diuision together with the Golden Rule sufficient to instruct the most ignorant in the vsuall practize of this Art of Disme or Decimall Arithmeticke The first Part. Of the Definitions of the Dismes The first Definition DIsme is a kind of Arithmeticke inuented by the tenth progression consisting in Characters of Cyphers whereby a certaine number is described and by which also all accounts which happen in humane affayres are dispatched by whole numbers without fractions or broken numbers Explication LEt the certaine number be one thousand one hundred and eleuen described by the Characters of Cyphers thus 1111 in which it apeareth that ech 1 is the 10th part of his precedent character 1 likewise in 2378 each vnity of 8 is the tenth of each vnity of 7 and so of all the others But because it is conueniēt that the things whereof we would speake haue names and that this maner of computation is found by the consideration of such tenth or disme progression that is that it consisteth therein entirely as shall hereafter appeare Wee call this Treatise fitly by the name of Disme whereby all accounts hapning in the affayres of man may be wrought and effected without fractions or broken numbers as hereafter appeareth The second Definition EVery number propounded is called Comencement wose signe is thus 0 Explication BY example a certaine number is propounded of three hundred sixty foure we call the 364 Comencements described thus 364 0 and so of all other like The third Definition ANd each tenth part of the vnity of the Comencement wee call the Prime whose signe is thus 1 and each tenth part of the vnity of the Prime we call the Second whose signe is 2 and so of the other each tenth part of the vnity of the precedent signe alwayes in order one further Explication AS 3 1 7 2 5 3 9 4 that is to say 3 Primes 7 Seconds 5 Thirds 9 Fourths and so proceeding infinitly but to speake of their valew you may note that according to this definition the sayd numbers are 3 10 7 100 5 1000 9 10000 together 3759 10000 and likewise 8 0 9