Therfore [sithen] the science of the whiche at this tyme we The name of the art. intendene to write of standithe alle and about nombre: ffirst we most se, what is the propre name therofe, and fro whens the name come: Afterwarde what is nombre, And how manye spices of nombre ther ben. The name is clepede Algorisme, Derivation of Algorism. hade out of Algore, other of Algos, in [grewe], That is clepide in englisshe art [other] craft, And of Rithmus that is callede nombre. So [algorisme] is clepede the art of nombryng, Another. other it is had ofe en or in, and gogos that is introduccioun, and Rithmus nombre, that is to say Interduccioun of nombre. Another. And thirdly it is hade of the name of a kyng that is clepede Algo and Rythmus; So callede Algorismus. Kinds of numbers. Sothely .2. manere of nombres ben notifiede; Formalle,[1] as nombre is vnitees gadrede to-gedres; Materialle,[2] as nombre is a colleccioun of vnitees. Other nombre is a multitude hade out of vnitees, vnitee is that thynge wher-by euery thynge is callede oone, other [o] thynge. Of nombres, that one is clepede [digitalle], that othere Article, Another a nombre [componede] oþer myxt. Another digitalle is a nombre with-in .10.; Article is þat nombre that may be dyvydede in .10. parties egally, And that there leve no residue; Componede or [medlede] is that nombre that is come of a digite and of an [article]. And vndrestande wele that alle nombres betwix .2. articles next is a nombre componede. The 9 rules of the Art. Of this art bene .9. [spices], that is forto sey, numeracioun, addicioun, Subtraccioun, Mediacioun, Duplacioun, Multipliacioun, Dyvysioun, Progressioun, And of Rootes the extraccioun, and that may be hade in .2. maners, that is to sey in nombres quadrat, and in cubices: Amonge the whiche, ffirst of Numeracioun, and afterwarde of þe oþers by [ordure], y entende to write.
Chapter I. Numeration.
*For-sothe numeracioun is of euery numbre by competent figures an artificialle representacioun.
Figures, differences, places, and limits. Sothly figure, difference, places, and [lynes] supposen o thyng other the same, But they ben sette here for dyuers resons. ffigure is clepede for protraccioun of figuracioun; Difference is callede for therby is shewede euery figure, how it hathe difference fro the figures before them: place by cause of space, where-in [me] writethe: [lynees], for that is ordeynede for the presentacioun of euery figure. The 9 figures. And vnderstonde that ther ben .9. [lymytes] of figures that representen the .9. digites that ben these. 0. 9. 8. 7. 6. 5. 4. 3. 2. 1. The cipher. The .10. is clepede theta, or a cercle, other a cifre, other a figure of nought for nought it signyfiethe. Nathelesse she holdyng that place givethe others for to signyfie; for withe-out cifre or cifres a pure article may not be writte. The numeration And sithen that by these .9. figures significatifes Ioynede with cifre or with cifres alle nombres ben and may be representede, It was, [nether] is, no nede to fynde any more figures. of digits, And note wele that euery digite shalle be writte with [oo] figure allone to it [aproprede]. of articles, And alle articles by a cifre, ffor euery article is namede for oone of the digitis as .10. of 1.. 20. of. 2. and so of the others, &c. And alle nombres digitalle owen to be sette in the first difference: Alle articles in the seconde. Also alle nombres fro .10. til an .100. [which] is excludede, with .2. figures mvst be writte; And yf it be an article, by a cifre first put, and the figure y-writte towarde the lift honde, that signifiethe the digit of the whiche the article is namede; of composites. And yf it be a nombre componede, ffirst write the digit that is a part of that componede, and write to the lift side the article as it is seide be-fore. Alle nombre that is fro an hundrede tille a thousande [exclusede], owithe to be writ by .3. figures; and alle nombre that is fro a thousande til .x. Mł. mvst be writ by .4. figures; And so forthe. The value due to position. And vnderstonde wele that euery figure sette in the first place signyfiethe his digit; In the seconde place .10. tymes his digit; In the .3. place an hundrede so moche; In the .4. place a thousande so moche; In the .5. place .x. thousande so moche; In the .6. place an hundrede thousande so moche; In the .7. place a thousande thousande. And so infynytly mvltiplying by Fol. 49. *these .3. 10, 100, 1000. And vnderstande wele that [competently] me may sette vpon figure in the place of a thousande, a prike to shewe how many thousande the last figure shalle represent. Numbers are written from right to left. We writene in this art to the lift side-warde, as arabiene writene, that weren fynders of this science, othere for this resoun, that for to kepe a custumable ordre in redyng, Sette we alle-wey the more nombre before.
Chapter II. Addition.
Definition. Addicioun is of nombre other of nombres vnto nombre or to nombres aggregacioun, that me may see that that is come therof as [excressent]. In addicioun, 2. ordres of figures and .2. nombres ben necessary, that is to sey, a nombre to be addede and the nombre wherto the addicioun sholde be made to. The nombre to be addede is that þat sholde be addede therto, and shalle be vnderwriten; the nombre vnto the whiche addicioun shalle be made to is that nombre that resceyuethe the addicion of þat other, and shalle be writen above; How the numbers should be written. and it is convenient that the lesse nombre be vnderwrit, and the more addede, than the contrary. But whether it happe one [other] other, the same comythe of, Therfor, yf þow wilt adde nombre to nombre, write the nombre wherto the addicioun shalle be made in the [omest] ordre by his differences, so that the first of the lower ordre be vndre the first of the [omyst] ordre, and so of others. The method of working. That done, adde the first of the lower ordre to the first of the omyst ordre. And of suche addicioun, other þere growith therof a digit, An article, other a composede. Begin at the right. If it be digitus, In the place of the omyst shalt thow write the digit excrescyng, as thus:—
| The resultant | 2 |
| To whom it shal be addede | 1 |
| The nombre to be addede | 1 |
The Sum is a digit, If the article; in the place of the omyst put a-way by a cifre writte, and the digit transferrede, of þe whiche the article toke his name, towarde the lift side, and be it addede to the next figure folowyng, yf ther be any figure folowyng; or no, and yf it be not, leve it [in the] voide, as thus:—
| The resultant | 10 |
| To whom it shalle be addede | 7 |
| The nombre to be addede | 3 |
| Resultans | 2 | 7 | 8 | 2 | 7 |
| Cui debet addi | 1 | 0 | 0 | 8 | 4 |
| Numerus addendus | 1 | 7 | 7 | 4 | 3 |