Title , preface , whole numbers , operation , rule of 3 , Stevin , argument , definitions , operation , appendix

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The Art of Tenths,

OR,

Teaching how to performe all Computations

Fractions, by the foure Principles of

dition, Substraction, Multiplication,

and Division.

Simon Stevin.

Published in English with some additions

by

Imprinted at London by

Saint Magnus corner. 1608.

[ A2 ]
[ A2v ] which few or none have done before me: yet the respect I have to the publike good, that you my Countrymen, such as either want leisure or language, may become partakers of these excellent inventions of that famous forraigne Authour, more prevailing with mee, then the carelesse regard I have of such iniuries could hinder, I have, as you see, adventured to provide for this worthy stranger, this English welcome, and have preferred some few of mine owne friends (though unworthy) to accompany him:[ A3 ] [ A3v ] [ A4 ] [ A4v ] to the fourth, saying, 1 and 7 make 8, and 4 make 12, which shall be wholly placed in their rank thus.[ B ] stracted, as that the 4 stand directly under the 7, and the 0 under the 0, and so of the rest, drawing a line betweene the numbers given, and another under the number which is to be substracted, as hereunder appeareth.[ Bv ] or Number to be multiplied 546, and the Multiplicator or number to multiply 37.[ B2 ] which shall be placed in order under the line, as you see.[ B2v ] hereafter why we must say but three times) set downe 3 for the first Character of the Quotient, behynd the crooked line [error: 6], and the 3 remayning of the 9 cancelling the 2 & 9: then multiply 8 by the divisor, by 3, the Quotient it maketh 24, which substract from 39 (here appeareth the occasion why we sayd that 2 is but onely 3 times in 9: for if wee had sayd 4 times, resting of the 9, and had multiplied 8 by 4 it would have bene 32 which should be substracted from 19 which then remayned of the divident, which is impossible; therefore there must be such a number taken, & placed behind the crooked line, as that the product thereof may be substracted from the remaynder) resteth 15, which place over 39, cancelling the 39, and the 8, so shall the disposition of the Characters be in this manner.[ B3 ] and one for divisor given, we have found their Quotient required.
[ B4 ] simple things from ingenious inventions, but he (rather) seemeth envious of the common benefite; yet howsoever, it were not fit to omit the benefit hereof, for the inconvenience of such calumny. But as the Mariner, having by hap found a certaine unknowne 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: even so shall we speake freely of the great use of this invention; 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 shalbe declared by the first definition following) is number, the use and effects of which your selves shall sufficiently witnes by your continuall experiences, therefore it were not necessary to use many words thereof: for the Astrologer knoweth, that the world is become by computation Astronomicall (seing it teacheth the Pilot the elevation of the Equator and of the Pole, by meanes of the declination of the Sunne, to describe the true Longitudes, Latitudes, situations & distances of places, &c.) a Paradise, abounding in some places with such things as the Earth cannot bring forth in other. But as the sweet is never without the sowre: so the travayle in such computations cannot be unto him hidden, namely, in the busy multiplications and divisions which proceed of the 60 progression of degrees, minutes, seconds, thirds, &c. And the Surveyor or Land-meater knoweth, what great benefite the world[ B4v ] receyveth from his science, by which many dissensions and difficulties are avoyded, which otherwise would arise by reason of the unknowne 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 damage of both parties, as also to the discredit of Land-meater or surveyor, 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,[ C ] effect nothing of worth, as it often hapneth to the serchers of strong moving, 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 divers expert Land-meaters of[ Cv ] And to the end the premises may the better be explaned, there shalbe hereunto an Appendix adioyned, declaring the use of the Disme in many things by certaine examples, and also definitions and operations, to teach such as doe not already know the use and practize of[ C2 ] 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[ C2v ] fractions, and that the multitude of signes, except ([ C3 ] [ C3v ] [ C4] [ C4v ] [ D ] and divisor, we have found the Quotient required.[ Dv ] halfe of the latter signe of the numbers given, is alwayes the latter signe of the roote: wherefore if the latter signe given were of a number imper: the signe of the next following shalbe added, and then it shalbe a number per: and then extract the Roote as afore. Likewise in the extraction of the Cubique Roote, the third part of the latter signe given shalbe alwayes the signe of the Roote: and so of all other kind of Roots.[ D2 ] into 10 equall parts, each of which shalbe 1 ([ D2v ] upon the Pole how many feete and fingers (which are marked, ioyning the tenth part upon another side of the Rood) accord with themselves.[ D3 ] the demonstrations of all these examples are alreadie made in their propositions.[ D3v ] Now the Rod being so devided, to know the content of the Tunne, multiply and worke as in the precedent first Article, of which (being sufficiently manifest) we will not speake here any farther.[ D4 ] are the desired ([ D4v ] [ E ] [ Ev ] minutes, seconds, &c. of the 60. progression, into primes, seconds, &c. of the tenth progression: the use whereof followeth.[ E2 ] [ E2v ] of Gold value 36 lib. 5 ([ E3 ] But if all this be not put in practize so soone as we could wish, yet it will first content us, that it wil be beneficiall to our successors, if future men shal hereafter be of such nature as our predecessors, who were never negligent of so great advantage. Secondly, that it is not unnecessary for each in particular, for so much as concerneth him, for that they may all deliver them selves when they will, from so much and so great labour. |

Simon Stevin | Arithmetic | Robert Norton (top)