Chapter 3

¶ Her{e} by-gynnes þe craft of Addicioñ. In þis craft þ{o}u most knowe foure thyng{es}. ¶ Fyrst þ{ou} most know what is addicioñ. Next þ{o}u most know how mony rewles of figurys þou most haue. ¶ Next þ{o}u most know how mony diue{r}s casys happes in þis craft of addicioñ. ¶ And next qwat is þe p{ro}fet of þis craft. ¶ As for þe first þou most know þat addicioñ is a castyng to-ged{ur} of twoo nomburys in-to on{e} nombr{e}. As yf I aske qwat is twene & thre. Þ{o}u wyl cast þese twene nomb{re}s to-ged{ur} & say þ{a}t it is fyue. ¶ As for þe secunde þou most know þ{a}t þou schall{e} haue tweyne rewes of figures, on{e} vndur a-nother, as her{e} þ{o}u mayst se.

1234 2168.

¶ As for þe thryd þou most know þ{a}t ther{e} ben foure diu{er}se cases. As for þe forthe þ{o}u most know þ{a}t þe p{ro}fet of þis craft is to telle what is þe hole nomb{ur} þ{a}t comes of diu{er}se nomburis. Now as to þe texte of oure verse, he teches ther{e} how þ{o}u schal worch in þis craft. ¶ He says yf þ{o}u wilt cast on{e} nomb{ur} to anoþ{er} nomb{ur}, þou most by-gynne on þis wyse. ¶ ffyrst write [*leaf 140b] two rewes of figuris & nombris so þat þ{o}u write þe first figur{e} of þe hyer nomb{ur} euen{e} vnd{ir} the first fig{ure} of þe nether nomb{ur}, And þe secunde of þe nether nomb{ur} euen{e} vnd{ir} þe secunde of þe hyer, & so forthe of eu{er}y fig{ur}e of both þe rewes as þ{o}u mayst se.

123 234.

[Headnote: The Cases of the Craft of Addition.]

¶ Inde duas adde p{ri}mas hac condic{i}one: Si digitus crescat ex addic{i}one prior{um}; P{ri}mo scribe loco digitu{m}, quicu{n}q{ue} sit ille.

[Sidenote: Add the first figures; rub out the top figure; write the result in its place. Here is an example.]

¶ Here he teches what þ{o}u schalt do when þ{o}u hast write too rewes of figuris on vnder an-oþ{er}, as I sayd be-for{e}. ¶ He says þ{o}u schalt take þe first fig{ur}e of þe heyer nomb{re} & þe fyrst figur{e} of þe neþ{er} nombre, & cast hem to-ged{er} vp-on þis condicioɳ. Thou schal loke qweþ{er} þe nombe{r} þat comys þ{ere}-of be a digit or no. ¶ If he be a digit þ{o}u schalt do away þe first fig{ur}e of þe hyer nomb{re}, and write þ{ere} in his stede þat he stode Inne þe digit, þ{a}t comes of þe ylke 2 fig{ur}es, & so wrich forth oɳ oþ{er} figures yf þ{ere} be ony moo, til þ{o}u come to þe ende toward þe lyft side. And lede þe nether fig{ure} stonde still eu{er}-mor{e} til þ{o}u haue ydo. ffor þ{ere}-by þ{o}u schal wyte wheþ{er} þ{o}u hast don{e} wel or no, as I schal tell þe aft{er}ward in þe ende of þis Chapt{er}. ¶ And loke allgate þat þou be-gynne to worch in þis Craft of [*leaf 141a] Addi[*]cioɳ in þe ryȝt side, here is an ensampul of þis case.

1234 2142.

Caste 2 to four{e} & þat wel be sex, do away 4. & write in þe same place þe fig{ur}e of sex. ¶ And lete þe fig{ur}e of 2 in þe nether rewe stonde stil. When þ{o}u hast do so, cast 3 & 4 to-ged{ur} and þat wel be seuen þ{a}t is a digit. Do away þe 3, & set þ{ere} seueɳ, and lete þe neþ{er} fig{ure} stonde still{e}, & so worch forth bakward til þ{o}u hast ydo all to-ged{er}.

Et si composit{us}, in limite scribe seque{n}te Articulum, p{ri}mo digitum; q{uia} sic iubet ordo.

[Sidenote: Suppose it is a Composite, set down the digit, and carry the tens. Here is an example.]

¶ Here is þe secunde case þ{a}t may happe in þis craft. And þe case is þis, yf of þe casting of 2 nomburis to-ged{er}, as of þe fig{ur}e of þe hyer rewe & of þe figure of þe neþ{er} rewe come a Composyt, how schalt þ{ou} worch. Þ{us} þ{o}u schalt worch. Thou shalt do away þe fig{ur}e of þe hyer nomb{er} þat was cast to þe figure of þe neþ{er} nomber. ¶ And write þ{ere} þe digit of þe Composyt. And set þe articul of þe composit next aft{er} þe digit in þe same rewe, yf þ{ere} be no mo fig{ur}es aft{er}. But yf þ{ere} be mo figuris aft{er} þat digit. And þere he schall be rekend for hym selfe. And when þ{o}u schalt adde þ{a}t ylke figure þ{a}t berys þe articull{e} ou{er} his hed to þe figur{e} vnd{er} hym, þ{o}u schalt cast þat articul to þe figure þ{a}t hase hym ou{er} his hed, & þ{ere} þat Articul schal tokeɳ hym selfe. lo an Ensampull [*leaf 141b] of all.

326 216.

Cast 6 to 6, & þ{ere}-of wil arise twelue. do away þe hyer 6 & write þ{ere} 2, þ{a}t is þe digit of þis composit. And þe{n} write þe articull{e} þat is ten ou{er} þe figuris hed of twene as þ{us}.

1 322 216.

Now cast þe articull{e} þ{a}t standus vpon þe fig{ur}is of twene hed to þe same fig{ur}e, & reken þat articul bot for on{e}, and þan þ{ere} wil arise thre. Þan cast þat thre to þe neþ{er} figure, þat is on{e}, & þat wul be four{e}. do away þe fig{ur}e of 3, and write þ{ere} a fig{ur}e of foure. and lete þe neþ{er} fig{ur}e stonde stil, & þan worch forth. vn{de} {ver}sus.

¶ Articulus si sit, in p{ri}mo limite cifram, ¶ Articulu{m} v{er}o reliquis inscribe figuris, Vel p{er} se scribas si nulla figura sequat{ur}.

[Sidenote: Suppose it is an Article, set down a cipher and carry the tens. Here is an example.]

¶ Her{e} he puttes þe thryde case of þe craft of Addicioɳ. & þe case is þis. yf of Addiciouɳ of 2 figuris a-ryse an Articull{e}, how schal þ{o}u do. thou most do away þe heer fig{ur}e þ{a}t was addid to þe neþ{er}, & write þ{ere} a cifre, and sett þe articuls on þe figuris hede, yf þ{a}t þ{ere} come ony aft{er}. And wyrch þan as I haue tolde þe in þe secunde case. An ensampull.

25. 15

Cast 5 to 5, þat wylle be ten. now do away þe hyer 5, & write þ{ere} a cifer. And sette ten vpon þe figuris hed of 2. And reken it but for on þus.] lo an Ensampull{e}

+----+ | 1 | | 2φ | | 15 | +----+

And [*leaf 142a] þan worch forth. But yf þ{ere} come no figure aft{er} þe cifre, write þe articul next hym in þe same rewe as here

+---+ | 5 | | 5 | +---+

cast 5 to 5, and it wel be ten. do away 5. þat is þe hier 5. and write þ{ere} a cifre, & write aft{er} hym þe articul as þus

+----+ | 1φ | | 5 | +----+

And þan þ{o}u hast done.

¶ Si tibi cifra sup{er}ueniens occurrerit, illa{m} Dele sup{er}posita{m}; fac illic scribe figura{m}, Postea procedas reliquas addendo figuras.

[Sidenote: What to do when you have a cipher in the top row. An example of all the difficulties.]

¶ Her{e} he putt{es} þe fourt case, & it is þis, þat yf þ{ere} come a cifer in þe hier rewe, how þ{o}u schal do. þus þ{o}u schalt do. do away þe cifer, & sett þ{ere} þe digit þ{a}t comes of þe addiciou{n} as þus

1φφ84. 17743

In þis ensampul ben all{e} þe four{e} cases. Cast 3 to foure, þ{a}t wol be seueɳ. do away 4. & write þ{ere} seueɳ; þan cast 4 to þe figur{e} of 8. þ{a}t wel be 12. do away 8, & sett þ{ere} 2. þat is a digit, and sette þe articul of þe composit, þat is ten, vpon þe cifers hed, & reken it for hym selfe þat is on. þan cast on{e} to a cifer, & hit wull{e} be but on, for noȝt & on makes but on{e}. þan cast 7. þ{a}t stondes vnd{er} þat on to hym, & þat wel be 8. do away þe cifer & þat 1. & sette þ{ere} 8. þan go forthermor{e}. cast þe oþ{er} 7 to þe cifer þ{a}t stondes ou{er} hy{m}. þ{a}t wul be bot seuen, for þe cifer betokens noȝt. do away þe cifer & sette þ{ere} seueɳ, [*leaf 142b] & þen go forþ{er}mor{e} & cast 1 to 1, & þat wel be 2. do away þe hier 1, & sette þ{ere} 2. þan hast þ{o}u do. And yf þ{o}u haue wel ydo þis nomber þat is sett her{e}-aft{er} wel be þe nomber þat schall{e} aryse of all{e} þe addicioɳ as her{e} 27827. ¶ Sequi{tu}r alia sp{eci}es.

[Headnote: The Craft of Subtraction.]

++A nu{mer}o num{er}u{m} si sit tibi demer{e} cura Scribe figurar{um} series, vt in addicione.

[Sidenote: Four things to know about subtraction: the first; the second; the third; the fourth.]

¶ This is þe Chapt{er} of subtraccioɳ, in the quych þou most know foure nessessary thyng{es}. the first what is subtraccioɳ. þe secunde is how mony nombers þou most haue to subt{ra}ccioɳ, the thryd is how mony maners of cases þ{ere} may happe in þis craft of subtraccioɳ. The fourte is qwat is þe p{ro}fet of þis craft. ¶ As for þe first, þ{o}u most know þ{a}t subtraccioɳ is drawyng{e} of on{e} nowmb{er} oute of anoþ{er} nomber. As for þe secunde, þou most knowe þ{a}t þou most haue two rewes of figuris on{e} vnd{er} anoþ{er}, as þ{o}u addyst in addicioɳ. As for þe thryd, þ{o}u moyst know þ{a}t four{e} man{er} of diu{er}se casis mai happe in þis craft. ¶ As for þe fourt, þou most know þ{a}t þe p{ro}fet of þis craft is whenne þ{o}u hasse taken þe lasse nomber out of þe mor{e} to telle what þ{ere} leues ou{er} þ{a}t. & þ{o}u most be-gynne to wyrch in þ{is} craft in þe ryght side of þe boke, as þ{o}u diddyst in addicioɳ. V{er}sus.

¶ Maiori nu{mer}o num{er}u{m} suppone minorem, ¶ Siue pari nu{mer}o supponat{ur} num{er}us par.

[Sidenote: Put the greater number above the less.]

[*leaf 143a] ¶ Her{e} he telles þat þe hier nomber most be mor{e} þen þe neþ{er}, or els eueɳ as mych. but he may not be lasse. And þe case is þis, þou schalt drawe þe neþ{er} nomber out of þe hyer, & þou mayst not do þ{a}t yf þe hier nomber wer{e} lasse þan þat. ffor þ{o}u mayst not draw sex out of 2. But þ{o}u mast draw 2 out of sex. And þou maiste draw twene out of twene, for þou schal leue noȝt of þe hier twene vn{de} v{er}sus.

[Headnote: The Cases of the Craft of Subtraction.]

¶ Postea si possis a prima subt{ra}he p{ri}ma{m} Scribens quod remanet.

[Sidenote: The first case of subtraction. Here is an example.]

Her{e} is þe first case put of subtraccioɳ, & he says þou schalt begynne in þe ryght side, & draw þe first fig{ure} of þe neþ{er} rewe out of þe first fig{ure} of þe hier rewe. qwether þe hier fig{ur}e be mor{e} þen þe neþ{er}, or eueɳ as mych. And þat is notified in þe vers when he says “Si possis.” Whan þ{o}u has þus ydo, do away þe hiest fig{ur}e & sett þ{ere} þat leues of þe subtraccioɳ, lo an Ensampull{e}

+-----+ | 234 | | 122 | +-----+

draw 2 out of 4. þan leues 2. do away 4 & write þ{ere} 2, & latte þe neþ{er} figur{e} sto{n}de stille, & so go for-by oþ{er} figuris till þ{o}u come to þe ende, þan hast þ{o}u do.

¶ Cifram si nil remanebit.

[Sidenote: Put a cipher if nothing remains. Here is an example.]

¶ Her{e} he putt{es} þe secunde case, & hit is þis. yf it happe þ{a}t qwen þ{o}u hast draw on neþ{er} fig{ure} out of a hier, & þ{er}e leue noȝt aft{er} þe subt{ra}ccioɳ, þus [*leaf 143b] þou schalt do. þ{o}u schall{e} do away þe hier fig{ur}e & write þ{ere} a cifer, as lo an Ensampull

+----+ | 24 | | 24 | +----+

Take four{e} out of four{e} þan leus noȝt. þ{er}efor{e} do away þe hier 4 & set þ{ere} a cifer, þan take 2 out of 2, þan leues noȝt. do away þe hier 2, & set þ{ere} a cifer, and so worch whar{e} so eu{er} þis happe.

Sed si no{n} possis a p{ri}ma dem{er}e p{ri}ma{m} P{re}cedens vnu{m} de limite deme seque{n}te, Quod demptu{m} p{ro} denario reputabis ab illo Subt{ra}he to{ta}lem num{er}u{m} qu{em} p{ro}posuisti Quo facto sc{ri}be super quicquid remaneb{i}t.

[Sidenote: Suppose you cannot take the lower figure from the top one, borrow ten; take the lower number from ten; add the answer to the top number. How to ‘Pay back’ the borrowed ten. Example.]

Her{e} he puttes þe thryd case, þe quych is þis. yf it happe þat þe neþ{er} fig{ur}e be mor{e} þen þe hier fig{ur}e þat he schall{e} be draw out of. how schall{e} þou do. þus þ{o}u schall{e} do. þou schall{e} borro .1. oute of þe next fig{ur}e þat comes aft{er} in þe same rewe, for þis case may neu{er} happ but yf þ{ere} come figures aft{er}. þan þ{o}u schalt sett þat on ou{er} þe hier figur{es} hed, of the quych þou woldist y-draw oute þe neyþ{er} fig{ur}e yf þ{o}u haddyst y-myȝt. Whane þou hase þus ydo þou schall{e} rekene þ{a}t .1. for ten. ¶. And out of þat ten þ{o}u schal draw þe neyþermost fig{ur}e, And all{e} þ{a}t leues þou schall{e} adde to þe figur{e} on whos hed þat .1. stode. And þen þ{o}u schall{e} do away all{e} þat, & sett þ{ere} all{e} that arisys of the addicioɳ of þe ylke 2 fig{ur}is. And yf yt [*leaf 144a] happe þat þe fig{ur}e of þe quych þ{o}u schalt borro on be hym self but 1. If þ{o}u schalt þat on{e} & sett it vppoɳ þe oþ{er} figur{is} hed, and sett in þ{a}t 1. place a cifer, yf þ{ere} come mony figur{es} aft{er}. lo an Ensampul.

+------+ | 2122 | | 1134 | +------+

take 4 out of 2. it wyl not be, þerfor{e} borro on{e} of þe next figur{e}, þ{a}t is 2. and sett þat ou{er} þe hed of þe fyrst 2. & rekene it for ten. and þere þe secunde stondes write 1. for þ{o}u tokest on out of hy{m}. þan take þe neþ{er} fig{ur}e, þat is 4, out of ten. And þen leues 6. cast to 6 þe fig{ur}e of þat 2 þat stode vnd{er} þe hedde of 1. þat was borwed & rekened for ten, and þat wylle be 8. do away þ{a}t 6 & þat 2, & sette þ{ere} 8, & lette þe neþ{er} fig{ur}e stonde stille. Whanne þ{o}u hast do þus, go to þe next fig{ur}e þ{a}t is now bot 1. but first yt was 2, & þ{ere}-of was borred 1. þan take out of þ{a}t þe fig{ur}e vnd{er} hym, þ{a}t is 3. hit wel not be. þer-for{e} borowe of the next fig{ur}e, þe quych is bot 1. Also take & sett hym ou{er} þe hede of þe fig{ure} þat þou woldest haue y-draw oute of þe nether figure, þe quych was 3. & þou myȝt not, & rekene þ{a}t borwed 1 for ten & sett in þe same place, of þe quych place þ{o}u tokest hy{m} of, a cifer, for he was bot 1. Whanne þ{o}u hast þ{us} ydo, take out of þat 1. þ{a}t is rekent for ten, þe neþ{er} figure of 3. And þ{ere} leues 7. [*leaf 144b] cast þe ylke 7 to þe fig{ur}e þat had þe ylke ten vpon his hed, þe quych fig{ur}e was 1, & þat wol be 8. þan do away þ{a}t 1 and þ{a}t 7, & write þ{ere} 8. & þan wyrch forth in oþ{er} figuris til þ{o}u come to þe ende, & þan þ{o}u hast þe do. V{er}sus.

¶ Facque nonenarios de cifris, cu{m} remeabis ¶ Occ{ur}rant si forte cifre; dum demps{er}is vnum ¶ Postea p{ro}cedas reliquas deme{n}do figuras.

[Sidenote: A very hard case is put. Here is an example.]

¶ Her{e} he putt{es} þe fourte case, þe quych is þis, yf it happe þat þe neþ{er} fig{ur}e, þe quych þ{o}u schalt draw out of þe hier fig{ur}e be mor{e} pan þe hier figur ou{er} hym, & þe next fig{ur}e of two or of thre or of foure, or how mony þ{ere} be by cifers, how wold þ{o}u do. Þ{o}u wost wel þ{o}u most nede borow, & þ{o}u mayst not borow of þe cifers, for þai haue noȝt þat þai may lene or spar{e}. Ergo[{4}] how woldest þ{o}u do. Certayɳ þus most þ{o}u do, þ{o}u most borow on of þe next figure significatyf in þat rewe, for þis case may not happe, but yf þ{ere} come figures significatyf aft{er} the cifers. Whan þ{o}u hast borowede þ{a}t 1 of the next figure significatyf, sett þ{a}t on ou{er} þe hede of þ{a}t fig{ur}e of þe quych þ{o}u wold haue draw þe neþ{er} figure out yf þ{o}u hadest myȝt, & reken it for ten as þo{u} diddest i{n} þe oþ{er} case her{e}-a-for{e}. Whaɳ þ{o}u hast þus y-do loke how mony cifers þ{ere} wer{e} bye-twene þat figur{e} significatyf, & þe fig{ur}e of þe quych þ{o}u woldest haue y-draw the [*leaf 145a] neþ{er} figure, and of eu{er}y of þe ylke cifers make a figur{e} of 9. lo an Ensampull{e} after.

+-----+ |40002| |10004| +-----+

Take 4 out of 2. it wel not be. borow 1 out of be next figure significatyf, þe quych is 4, & þen leues 3. do away þ{a}t figur{e} of 4 & write þ{ere} 3. & sett þ{a}t 1 vppon þe fig{ur}e of 2 hede, & þan take 4 out of ten, & þan þere leues 6. Cast 6 to the fig{ur}e of 2, þ{a}t wol be 8. do away þat 6 & write þ{er}e 8. Whan þ{o}u hast þus y-do make of eu{er}y 0 betweyn 3 & 8 a figure of 9, & þan worch forth in goddes name. & yf þ{o}u hast wel y-do þ{o}u[{5}] schalt haue þis nomb{er}

+-----+ |39998| Sic. |10004| +-----+

[Headnote: How to prove the Subtraction.]

¶ Si subt{ra}cc{i}o sit b{e}n{e} facta p{ro}bar{e} valebis Quas s{u}btraxisti p{ri}mas addendo figuras.

[Sidenote: How to prove a subtraction sum. Here is an example. He works his proof through, and brings out a result.]

¶ Her{e} he teches þe Craft how þ{o}u schalt know, whan þ{o}u hast subt{ra}yd, wheþ{er} þou hast wel ydo or no. And þe Craft is þis, ryght as þ{o}u subtrayd þe neþ{er} figures fro þe hier figures, ryȝt so adde þe same neþ{er} figures to þe hier figures. And yf þ{o}u haue well y-wroth a-for{e} þou schalt haue þe hier nombre þe same þ{o}u haddest or þou be-gan to worch. as for þis I bade þou schulde kepe þe neþ{er} figures stylle. lo an [*leaf 145b] Ensampull{e} of all{e} þe 4 cases toged{re}. worche well{e} þis case

+--------+ |40003468|. |20004664| +--------+

And yf þou worch well{e} whan þou hast all{e} subtrayd þe þ{a}t hier nombr{e} her{e}, þis schall{e} be þe nombre here foloyng whan þ{o}u hast subtrayd.

+--------+ |39998804|. [Sidenote: Our author makes a slip here (3 for 1).] |20004664| +--------+

And þou schalt know þ{us}. adde þe neþ{er} rowe of þe same nombre to þe hier rewe as þus, cast 4 to 4. þat wol be 8. do away þe 4 & write þ{ere} 8. by þe first case of addicioɳ. þan cast 6 to 0 þat wol be 6. do away þe 0, & write þere 6. þan cast 6 to 8, þ{a}t wel be 14. do away 8 & write þ{ere} a fig{ur}e of 4, þat is þe digit, and write a fig{ur}e of 1. þ{a}t schall be-token ten. þ{a}t is þe articul vpon þe hed of 8 next aft{er}, þan reken þ{a}t 1. for 1. & cast it to 8. þat schal be 9. cast to þat 9 þe neþ{er} fig{ur}e vnd{er} þat þe quych is 4, & þat schall{e} be 13. do away þat 9 & sett þ{er}e 3, & sett a figure of 1. þ{a}t schall be 10 vpon þe next figur{is} hede þe quych is 9. by þe secu{n}de case þ{a}t þ{o}u hadest in addicioɳ. þan cast 1 to 9. & þat wol be 10. do away þe 9. & þat 1. And write þ{ere} a cifer. and write þe articull{e} þat is 1. betokenyng{e} 10. vpon þe hede of þe next figur{e} toward þe lyft side, þe quych [*leaf 146a] is 9, & so do forth tyl þ{o}u come to þe last 9. take þe figur{e} of þat 1. þe quych þ{o}u schalt fynde ou{er} þe hed of 9. & sett it ou{er} þe next figures hede þat schal be 3. ¶ Also do away þe 9. & set þ{ere} a cifer, & þen cast þat 1 þat stondes vpon þe hede of 3 to þe same 3, & þ{a}t schall{e} make 4, þen caste to þe ylke 4 the figur{e} in þe neyþ{er} rewe, þe quych is 2, and þat schall{e} be 6. And þen schal þ{o}u haue an Ensampull{e} aȝeyɳ, loke & se, & but þ{o}u haue þis same þ{o}u hase myse-wroȝt.

+--------+ |60003468| |20004664| +--------+

Sequit{ur} de duplac{i}one

[Headnote: The Craft of Duplation.]

++Si vis duplar{e} num{er}u{m}, sic i{n}cipe p{rim}o Scribe fig{ur}ar{um} serie{m} q{ua}mcu{n}q{ue} vel{is} tu.

[Sidenote: Four things must be known in Duplation. Here they are. Mind where you begin. Remember your rules.]

¶ This is the Chaptur{e} of duplacioɳ, in þe quych craft þ{o}u most haue & know 4 thing{es}. ¶ Þe first þ{a}t þ{o}u most know is what is duplacioɳ. þe secu{n}de is how mony rewes of fig{ur}es þ{o}u most haue to þis craft. ¶ þe thryde is how many cases may[{6}] happe in þis craft. ¶ þe fourte is what is þe p{ro}fet of þe craft. ¶ As for þe first. duplacioɳ is a doublyng{e} of a nombre. ¶ As for þe secu{n}de þ{o}u most [*leaf 146b] haue on nombre or on rewe of figures, the quych called nu{merus} dupland{us}. As for þe thrid þ{o}u most know þat 3 diu{er}se cases may hap in þis craft. As for þe fourte. qwat is þe p{ro}fet of þis craft, & þ{a}t is to know what a-risyȝt of a nombre I-doublyde. ¶ fforþ{er}-mor{e}, þ{o}u most know & take gode hede in quych side þ{o}u schall{e} be-gyn in þis craft, or ellis þ{o}u mayst spyl all{e} þ{i} lab{er} þ{er}e aboute. c{er}teyn þ{o}u schalt begyɳ in the lyft side in þis Craft. thenke wel ou{er} þis verse. ¶ [{7}]A leua dupla, diuide, m{u}ltiplica.[{7}] [[Subt{ra}has a{u}t addis a dext{ri}s {ve}l medi{a}b{is}]] The sentens of þes verses afor{e}, as þ{o}u may see if þ{o}u take hede. As þe text of þis verse, þat is to say, ¶ Si vis duplare. þis is þe sentence. ¶ If þ{o}u wel double a nombre þus þ{o}u most be-gynɳ. Write a rewe of figures of what nomb{re} þou welt. v{er}sus.

Postea p{ro}cedas p{ri}ma{m} duplando figura{m} Inde q{uo}d excrescit scribas vbi iusserit ordo Iuxta p{re}cepta tibi que dant{ur} in addic{i}one.

[Sidenote: How to work a sum.]

¶ Her{e} he telles how þ{o}u schalt worch in þis Craft. he says, fyrst, whan þ{o}u hast writen þe nombre þ{o}u schalt be-gyn at þe first figur{e} in the lyft side, & doubull{e} þat fig{ur}e, & þe nombre þat comes þ{ere}-of þ{o}u schalt write as þ{o}u diddyst in addicioɳ, as ¶ I schal telle þe in þe case. v{er}sus.

[Headnote: The Cases of the Craft of Duplation.]

[*leaf 147a]

¶ Nam si sit digitus in primo limite scribas.

[Sidenote: If the answer is a digit, write it in the place of the top figure.]

¶ Her{e} is þe first case of þis craft, þe quych is þis. yf of duplacioɳ of a figur{e} arise a digit. what schal þ{o}u do. þus þ{o}u schal do. do away þe fig{ur}e þat was doublede, & sett þ{ere} þe diget þat comes of þe duplacioɳ, as þus. 23. double 2, & þ{a}t wel be 4. do away þe figur{e} of 2 & sett þ{ere} a figur{e} of 4, & so worch forth till{e} þ{o}u come to þe ende. v{er}sus.

¶ Articul{us} si sit, in p{ri}mo limite cifram, ¶ Articulu{m} v{er}o reliquis inscribe figuris; ¶ Vel p{er} se scribas, si nulla figura sequat{ur}.

[Sidenote: If it is an article, put a cipher in the place, and ‘carry’ the tens. If there is no figure to ‘carry’ them to, write them down.]

¶ Here is þe secunde case, þe quych is þis yf þ{ere} come an articull{e} of þe duplacioɳ of a fig{ur}e þ{o}u schalt do ryȝt as þ{o}u diddyst in addicioɳ, þat is to wete þat þ{o}u schalt do away þe figur{e} þat is doublet & sett þ{ere} a cifer, & write þe articull{e} ou{er} þe next figur{is} hede, yf þ{ere} be any aft{er}-warde toward þe lyft side as þus. 25. begyn at the lyft side, and doubull{e} 2. þat wel be 4. do away þat 2 & sett þere 4. þan doubul 5. þat wel be 10. do away 5, & sett þ{ere} a 0, & sett 1 vpon þe next figur{is} hede þe quych is 4. & þen draw downe 1 to 4 & þat woll{e} be 5, & þen do away þ{a}t 4 & þat 1, & sett þ{ere} 5. for þat 1 schal be rekened in þe drawyng{e} toged{re} for 1. wen [*leaf 147b] þou hast ydon þou schalt haue þis nomb{r}e 50. yf þ{ere} come no figur{e} aft{er} þe fig{ur}e þ{a}t is addit, of þe quych addicioɳ comes an articull{e}, þ{o}u schalt do away þe figur{e} þ{a}t is dowblet & sett þ{ere} a 0. & write þe articul next by in þe same rewe toward þe lyft syde as þus, 523. double 5 þat woll be ten. do away þe figur{e} 5 & set þ{ere} a cifer, & sett þe articul next aft{er} in þe same rewe toward þe lyft side, & þou schalt haue þis nombre 1023. þen go forth & double þe oþ{er} nombers þe quych is lyȝt y-nowȝt to do. v{er}sus.

¶ Compositus si sit, in limite sc{ri}be seq{uen}te Articulu{m}, p{ri}mo digitu{m}; q{uia} sic iubet ordo: Et sic de reliq{ui}s facie{n}s, si sint tibi plures.

[Sidenote: If it is a Composite, write down the digit, and ‘carry’ the tens. Here is an example.]

¶ Her{e} he putt{es} þe Thryd case, þe quych is þis, yf of duplacioɳ of a fig{ur}e come a Composit. þ{o}u schalt do away þe fig{u}re þ{a}t is doublet & set þ{ere} a digit of þe Composit, & sett þe articull{e} ou{er} þe next figures hede, & aft{er} draw hym downe w{i}t{h} þe figur{e} ou{er} whos hede he stondes, & make þ{ere}-of an nombre as þ{o}u hast done afore, & yf þ{ere} come no fig{ur}e aft{er} þat digit þat þ{o}u hast y-write, þa{n} set þe articull{e} next aft{er} hym in þe same rewe as þus, 67: double 6 þat wel be 12, do away 6 & write þ{ere} þe digit [*leaf 148a] of 12, þe quych is 2, and set þe articull{e} next aft{er} toward þe lyft side in þe same rewe, for þ{ere} comes no figur{e} aft{er}. þan dowble þat oþ{er} figur{e}, þe quych is 7, þat wel be 14. the quych is a Composit. þen do away 7 þat þ{o}u doublet & sett þe þe diget of hy{m}, the quych is 4, sett þe articull{e} ou{er} þe next figur{es} hed, þe quych is 2, & þen draw to hym þat on, & make on nombre þe quych schall{e} be 3. And þen yf þ{o}u haue wel y-do þ{o}u schall{e} haue þis nombre of þe duplacioɳ, 134. v{er}sus.

¶ Si super ext{re}ma{m} nota sit monade{m} dat eid{em} Quod t{ibi} {con}tingat si p{ri}mo dimidiabis.

[Sidenote: How to double the mark for one-half. This can only stand over the first figure.]