Chapter 5

[*leaf 157a] ¶ Now m{u}ltiply 4, þe quych comes next aft{er} 6, by þe last 2 of þe neþ{er} nounbur toward þe lyft side. as 2 tymes 4, þat wel be 8. sette þat 8 ou{er} þe figure the quych stondes ou{er} þe hede of þat 2, þe quych is þe last figur{e} of þe neþ{er} nounbre; þan multiplie þat same 4 by 3, þat comes in þe neþ{er} rewe, þat wol be 12. sette þe digit of þe composyt ou{er} þe figure þe quych stondes ou{er} þe hed of þat 3, & sette þe articule of þis co{m}posit ou{er} al þe figures þat stondes ou{er} þe neþ{er} 2 hede. þen m{u}ltiplie þe same 4 by þe 2 in þe ryȝt side in þe neþ{er} nounbur, þat wol be 8. do away 4. & sette þ{ere} 8. Eu{er} mor{e} qwen þ{o}u m{u}ltiplies þe hier figur{e} by þat figur{e} þe quych stondes vnd{er} hym, þou schalt do away þat hier figur{e}, & sett þer þat nounbre þe quych comes of m{u}ltiplicacioɳ of ylke digittes. Whan þou hast done as I haue byde þe, þ{o}u schalt haue suych an ord{er} of figur{e} as is her{e},

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þen take and ant{er}y þi neþ{er} figures. And sett þe fyrst fig{ur}e of þe neþ{er} figures[{11}] vndre be figur{e} of 6. ¶ And draw al þe oþ{er} figures of þe same rewe to hym-warde, [*leaf 157b] as þ{o}u diddyst afore. þen m{u}ltiplye 6 be 2, & sett þat þe quych comes ou{er} þ{ere}-of ou{er} al þe oþ{er} figures hedes þat stondes ou{er} þat 2. þen m{u}ltiply 6 be 3, & sett all{e} þat comes þ{ere}-of vpon all{e} þe figur{e}s hedes þat standes ou{er} þat 3; þa{n} m{u}ltiplye 6 be 2, þe quych stondes vnd{er} þat 6, þen do away 6 & write þ{ere} þe digitt of þe composit þat schal come þ{ere}of, & sette þe articull ou{er} all{e} þe figures þat stondes ou{er} þe hede of þat 3 as her{e},

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þen ant{er}y þi figures as þou diddyst afor{e}, and m{u}ltipli 5 be 2, þat wol be 10; sett þe 0 ou{er} all þe figures þ{a}t stonden ou{er} þat 2, & sett þ{a}t 1. ou{er} the next figures hedes, all{e} on hye towarde þe lyft side. þen m{u}ltiplye 5 be 3. þat wol be 15, write 5 ou{er} þe figures hedes þat stonden ou{er} þ{a}t 3, & sett þat 1 ou{er} þe next figur{e}s hedes toward þe lyft side. þen m{u}ltiplye 5 be 2, þat wol be 10. do away þat 5 & sett þ{ere} a 0, & sett þat 1 ou{er} þe figures hedes þat stonden ou{er} 3. And þen þou schalt haue such a nounbre as here stondes aftur.[*leaf 158a]

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¶ Now draw all{e} þese figures downe toged{er} as þus, 6.8.1. & 1 draw to-gedur; þat wolle be 16, do away all{e} þese figures saue 6. lat hym stonde, for þow þ{o}u take hym away þou most write þer þe same aȝene. þ{ere}for{e} late hym stonde, & sett 1 ou{er} þe figur{e} hede of 4 toward þe lyft side; þen draw on to 4, þat woll{e} be 5. do away þat 4 & þat 1, & sette þ{ere} 5. þen draw 4221 & 1 toged{ur}, þat wol be 10. do away all{e} þat, & write þere þat 4 & þat 0, & sett þat 1 ou{er} þe next figur{es} hede toward þe lyft side, þe quych is 6. þen draw þat 6 & þat 1 togedur, & þat wolle be 7; do away 6 & sett þ{ere} 7, þen draw 8810 & 1, & þat wel be 18; do away all{e} þe figures þ{a}t stondes ou{er} þe hede of þat 8, & lette 8 stonde stil, & write þat 1 ou{er} þe next fig{u}r{is} hede, þe quych is a 0. þen do away þat 0, & sett þ{ere} 1, þe quych stondes ou{er} þe 0. hede. þen draw 2, 5, & 1 toged{ur}, þat woll{e} be 8. þen do away all{e} þat, & write þ{ere} 8. ¶ And þen þou schalt haue þis nounbre, 571880.

[Headnote: The Cases of this Craft.]

[*leaf 158b]

¶ S{ed} cu{m} m{u}ltiplicabis, p{ri}mo sic e{st} op{er}andu{m}, Si dabit articulu{m} tibi m{u}ltiplicacio solu{m}; P{ro}posita cifra su{m}ma{m} t{ra}nsferre meme{n}to.

[Sidenote: What to do if the first multiplication results in an article.]

¶ Her{e} he puttes þe fyrst case of þis craft, þe quych is þis: yf þ{ere} come an articulle of þe m{u}ltiplicacioɳ ysette befor{e} the articull{e} in þe lyft side as þus

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multiplye 5 by 2, þat wol be 10; sette ou{er} þe hede of þat 2 a 0, & sett þat on, þat is þe articul, in þe lyft side, þat is next hym, þen þ{o}u schalt haue þis nounbre

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¶ And þen worch forth as þou diddist afore. And þ{o}u schalt vnd{er}stonde þat þ{o}u schalt write no 0. but whan þat place where þou schal write þat 0 has no figure afore hy{m} noþ{er} aft{er}. v{er}sus.

¶ Si aut{em} digitus excreu{er}it articul{us}q{ue}. Articul{us}[{12}] sup{ra}p{osit}o digito salit vltra.

[Sidenote: What to do if the result is a composite number.]

¶ Her{e} is þe secunde case, þe quych is þis: yf hit happe þat þ{ere} come a composyt, þou schalt write þe digitte ou{er} þe hede of þe neþ{er} figur{e} by þe quych þ{o}u multipliest þe hier figure; and sett þe articull{e} next hym toward þe lyft side, as þou diddyst afore, as þ{us}

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Multiply 8 by 8, þat wol be 64. Write þe 4 ou{er} 8, þat is to say, ou{er} þe hede of þe neþ{er} 8; & set 6, þe quych [*leaf 159a] is an articul, next aft{er}. And þen þou schalt haue such a nounb{r}e as is her{e},

+-----------+ | 6483[{13}]|, | 83 | +-----------+

And þen worch forth.

¶ Si digitus t{amen} ponas ip{su}m sup{er} ip{s}am.

[Sidenote: What if it be a digit.]

¶ Her{e} is þe thryde case, þe quych is þis: yf hit happe þat of þi m{u}ltiplicaciouɳ come a digit, þ{o}u schalt write þe digit ou{er} þe hede of þe neþ{er} figur{e}, by the quych þou m{u}ltipliest þe hier{e} figur{e}, for þis nedes no Ensampul.

¶ Subdita m{u}ltiplica non hanc que [incidit] illi Delet ea{m} penit{us} scribens quod p{ro}uenit inde.

[Sidenote: The fourth case of the craft.]

¶ Her{e} is þe 4 case, þe quych is: yf hit be happe þat þe neþ{er} figur{e} schal multiplye þat figur{e}, þe quych stondes ou{er} þat figures hede, þou schal do away þe hier figur{e} & sett þ{er}e þat þ{a}t comys of þ{a}t m{u}ltiplicacioɳ. As yf þ{er}e come of þat m{u}ltiplicacioɳ an articuls þou schalt write þere þe hier figur{e} stode a 0. ¶ And write þe articuls in þe lyft side, yf þat hit be a digit write þ{er}e a digit. yf þat h{i}t be a composit, write þe digit of þe composit. And þe articul in þe lyft side. al þis is lyȝt y-nowȝt, þ{er}e-for{e} þer nedes no Ensampul.

¶ S{ed} si m{u}ltiplicat alia{m} ponas sup{er} ip{s}am Adiu{n}ges num{er}u{m} que{m} p{re}bet duct{us} ear{um}.

[Sidenote: The fifth case of the craft.]

¶ Her{e} is þe 5 case, þe quych is þis: yf [*leaf 159b] þe neþ{er} figur{e} schul m{u}ltiplie þe hier, and þat hier figur{e} is not recte ou{er} his hede. And þat neþ{er} figur{e} hase oþ{er} figures, or on figure ou{er} his hede by m{u}ltiplicacioɳ, þat hase be afor{e}, þou schalt write þat nounbre, þe quych comes of þat, ou{er} all{e} þe ylke figures hedes, as þus here:

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Multiply 2 by 2, þat wol be 4; set 4 ou{er} þe hede of þat 2. þen[{14}] m{u}ltiplies þe hier 2 by þe neþ{er} 3, þat wol be 6. set ou{er} his hede 6, multiplie þe hier 2 by þe neþ{er} 4, þat wol be 8. do away þe hier 2, þe quych stondes ou{er} þe hede of þe figur{e} of 4, and set þ{er}e 8. And þou schalt haue þis nounb{re} here

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And antery þi figur{e}s, þat is to say, set þi neþ{er} 4 vnd{er} þe hier 3, and set þi 2 other figures ner{e} hym, so þat þe neþ{er} 2 stonde vnd{ur} þe hier 6, þe quych 6 stondes in þe lyft side. And þat 3 þat stondes vndur 8, as þus aftur ȝe may se,

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Now worch forthermor{e}, And m{u}ltiplye þat hier 3 by 2, þat wol be 6, set þ{a}t 6 þe quych stondes ou{er} þe hede of þat 2, And þen worch as I taȝt þe afore.

[*leaf 160a]

¶ Si sup{ra}posita cifra debet m{u}ltiplicar{e} Prorsus ea{m} deles & ibi scribi cifra debet.

[Sidenote: The sixth case of the craft.]

¶ Her{e} is þe 6 case, þe quych is þis: yf hit happe þat þe figur{e} by þe quych þou schal m{u}ltiplye þe hier figur{e}, þe quych stondes ryght ou{er} hym by a 0, þou schalt do away þat figur{e}, þe quych ou{er} þat cifre hede. ¶ And write þ{ere} þat nounbre þat comes of þe m{u}ltiplicacioɳ as þus, 23. do away 2 and sett þ{er}e a 0. vn{de} v{er}sus.

¶ Si cifra m{u}ltiplicat alia{m} posita{m} sup{er} ip{s}am Sitq{ue} locus sup{ra} vacu{us} sup{er} hanc cifra{m} fiet.

[Sidenote: The seventh case of the craft.]

¶ Her{e} is þe 7 case, þe quych is þis: yf a 0 schal m{u}ltiply a figur{e}, þe quych stondes not recte ou{er} hym, And ou{er} þat 0 stonde no thyng, þou schalt write ou{er} þat 0 anoþ{er} 0 as þus:

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multiplye 2 be a 0, it wol be nothyng{e}. write þere a 0 ou{er} þe hede of þe neþ{er} 0, And þen worch forth til þou come to þe ende.

¶ Si sup{ra}[{15}] fuerit cifra sem{per} e{st} p{re}t{er}eunda.

[Sidenote: The eighth case of the craft.]

¶ Her{e} is þe 8 case, þe quych is þis: yf þ{ere} be a 0 or mony cifers in þe hier rewe, þ{o}u schalt not m{u}ltiplie hem, bot let hem stonde. And antery þe figures beneþe to þe next figur{e} sygnificatyf as þus:

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Ou{er}-lepe all{e} þese cifers & sett þat [*leaf 160b] neþ{er} 2 þat stondes toward þe ryght side, and sett hym vnd{ur} þe 3, and sett þe oþ{er} nether 2 nere hym, so þat he stonde vnd{ur} þe thrydde 0, þe quych stondes next 3. And þan worch. vnd{e} v{er}sus.

¶ Si dubites, an sit b{e}n{e} m{u}ltiplicac{i}o facta, Diuide totalem nu{mer}u{m} p{er} multiplicante{m}.

[Sidenote: How to prove the multiplication.]

¶ Her{e} he teches how þou schalt know wheþ{er} þou hase wel I-do or no. And he says þat þou schalt deuide all{e} þe nounb{r}e þat comes of þe m{u}ltiplicacioɳ by þe neþ{er} figures. And þen þou schalt haue þe same nounbur þat þ{o}u hadyst in þe begynnyng{e}. but ȝet þou hast not þe craft of dyuisioɳ, but þ{o}u schalt haue hit aft{er}warde.

¶ P{er} num{er}u{m} si vis nu{mer}u{m} q{u}oq{ue} m{u}ltiplicar{e} ¶ T{antu}m p{er} normas subtiles absq{ue} figuris Has normas pot{er}is p{er} v{er}sus scir{e} sequentes.

[Sidenote: Mental multiplication.]

¶ Her{e} he teches þe to m{u}ltiplie be þowȝt figures in þi mynde. And þe sentence of þis v{er}se is þis: yf þo{u} wel m{u}ltiplie on nounbre by anoþ{er} in þi mynde, þ{o}u schal haue þ{er}eto rewles in þe v{er}ses þat schal come aft{er}.

¶ Si tu p{er} digitu{m} digitu{m} vis m{u}ltiplicar{e} Re{gula} p{re}cedens dat qualit{er} est op{er}andu{m}.

[Sidenote: Digit by digit is easy.]

¶ Her{e} he teches a rewle as þou hast afor{e} to m{u}ltiplie a digit be anoþ{er}, as yf þou wolde wete qwat is sex tymes 6. þou [*leaf 161a] schalt wete by þe rewle þat I taȝt þe befor{e}, yf þou haue mynde þ{er}of.

¶ Articulu{m} si p{er} reliquu{m} reliquu{m} vis m{u}lti{plica}r{e} In p{ro}p{r}iu{m} digitu{m} debet vt{er}q{ue} resolui. ¶ Articul{us} digitos post se m{u}ltiplicantes Ex digit{us} quociens retenerit m{u}ltipli{ca}r{i} Articuli faciu{n}t tot centu{m} m{u}ltiplicati.

[Sidenote: The first case of the craft. Article by article; an example: another example:]

[Headnote: How to work subtly without Figures.]

[Sidenote: Mental multiplication. Another example. Another example. Notation. Notation again. Mental multiplication.]

¶ Her{e} he teches þe furst rewle, þe quych is þis: yf þou wel m{u}ltiplie an articul be anoþ{er}, so þat both þe articuls bene w{i}t{h}-Inne an hundreth, þus þ{o}u schalt do. take þe digit of bothe the articuls, for eu{er}y articul hase a digit, þen m{u}ltiplye þat on digit by þat oþ{er}, and loke how mony vnytes ben in þe nounbre þat comes of þe m{u}ltiplicacioɳ of þe 2 digittes, & so mony hundrythes ben in þe nounb{re} þat schal come of þe m{u}ltiplicacioɳ of þe ylke 2 articuls as þus. yf þ{o}u wold wete qwat is ten tymes ten. take þe digit of ten, þe quych is 1; take þe digit of þat oþ{er} ten, þe quych is on. ¶ Also m{u}ltiplie 1 be 1, as on tyme on þat is but 1. In on is but on vnite as þou wost welle, þ{er}efor{e} ten tymes ten is but a hundryth. ¶ Also yf þou wold wete what is twenty tymes 30. take þe digit of twenty, þat is 2; & take þe digitt of thrytty, þat is 3. m{u}ltiplie 3 be 2, þat is 6. Now in 6 ben 6 vnites, ¶ And so mony hundrythes ben in 20 tymes 30[*leaf 161b], þ{ere}for{e} 20 tymes 30 is 6 hundryth eueɳ. loke & se. ¶ But yf it be so þat on{e} articul be w{i}t{h}-Inne an hundryth, or by-twene an hundryth and a thowsande, so þat it be not a þowsande fully. þen loke how mony vnytes ben in þe nounbur þat comys of þe m{u}ltiplicacioɳ [{16}]And so mony tymes[{16}] of 2 digitt{es} of ylke articuls, so mony thowsant ben in þe nounbre, the qwych comes of þe m{u}ltiplicacioɳ. And so mony tymes ten thowsand schal be in þe nounbre þat comes of þe m{u}ltiplicacion of 2 articuls, as yf þ{o}u wold wete qwat is 4 hundryth tymes [two hundryth]. Multiply 4 be 2,[{17}] þat wol be 8. in 8 ben 8 vnites. ¶ And so mony tymes ten thousand be in 4 hundryth tymes [2][{17}] hundryth, þ{a}t is 80 thousand. Take hede, I schall telle þe a gen{e}rall{e} rewle whan þ{o}u hast 2 articuls, And þou wold wete qwat comes of þe m{u}ltiplicacioɳ of hem 2. m{u}ltiplie þe digit of þ{a}t on articuls, and kepe þat nounbre, þen loke how mony cifers schuld go befor{e} þat on articuls, and he wer{e} write. Als mony cifers schuld go befor{e} þat other, & he wer{e} write of cifers. And haue all{e} þe ylke cifers toged{ur} in þi mynde, [*leaf 162a] a-rowe ychoɳ aftur other, and in þe last plase set þe nounbre þat comes of þe m{u}ltiplicacioɳ of þe 2 digittes. And loke in þi mynde in what place he stondes, wher{e} in þe secunde, or in þe thryd, or in þe 4, or wher{e} ellis, and loke qwat þe figures by-token in þat place; & so mych is þe nounbre þat comes of þe 2 articuls y-m{u}ltiplied to-ged{ur} as þus: yf þ{o}u wold wete what is 20 thousant tymes 3 þowsande. m{u}ltiply þe digit of þat articull{e} þe quych is 2 by þe digitte of þat oþ{er} articul þe quych is 3, þat wol be 6. þen loke how mony cifers schal go to 20 thousant as hit schuld be write in a tabul. c{er}tainly 4 cifers schuld go to 20 þowsant. ffor þis figure 2 in þe fyrst place betokenes twene. ¶ In þe secunde place hit betokenes twenty. ¶ In þe 3. place hit betokenes 2 hundryth. .¶. In þe 4 place 2 thousant. ¶ In þe 5 place h{i}t betokenes twenty þousant. þ{ere}for{e} he most haue 4 cifers a-for{e} hym þat he may sto{n}de in þe 5 place. kepe þese 4 cifers in thy mynde, þen loke how mony cifers goɳ to 3 thousant. Certayn to 3 thousante [*leaf 162b] goɳ 3 cifers afor{e}. Now cast ylke 4 cifers þat schuld go to twenty thousant, And thes 3 cifers þat schuld go afor{e} 3 thousant, & sette hem in rewe ychoɳ aft{er} oþ{er} in þi mynde, as þai schuld stonde in a tabull{e}. And þen schal þou haue 7 cifers; þen sett þat 6 þe quych comes of þe m{u}ltiplicacioɳ of þe 2 digitt{es} aft{u}r þe ylke cifers in þe 8 place as yf þat hit stode in a tabul. And loke qwat a figur{e} of 6 schuld betoken in þe 8 place. yf hit wer{e} in a tabul & so mych it is. & yf þat figure of 6 stonde in þe fyrst place he schuld betoken but 6. ¶ In þe 2 place he schuld betoken sexty. ¶ In the 3 place he schuld betokeɳ sex hundryth. ¶ In þe 4 place sex thousant. ¶ In þe 5 place sexty þowsant. ¶ In þe sext place sex hundryth þowsant. ¶ In þe 7 place sex þowsant thousant{es}. ¶ In þe 8 place sexty þowsant thousantes. þ{er}for{e} sett 6 in octauo loco, And he schal betoken sexty þowsant thousantes. And so mych is twenty þowsant tymes 3 thousant, ¶ And þis rewle is gen{er}all{e} for all{e} man{er} of articuls, Whethir þai be hundryth or þowsant; but þ{o}u most know well þe craft of þe wryrchyng{e} in þe tabull{e} [*leaf 163a] or þou know to do þus in þi mynde aftur þis rewle. Thou most þat þis rewle holdyþe note but wher{e} þ{ere} ben 2 articuls and no mo of þe quych ayther of hem hase but on figur{e} significatyf. As twenty tymes 3 thousant or 3 hundryth, and such oþ{ur}.

¶ Articulum digito si m{u}ltiplicare o{portet} Articuli digit[i sumi quo multiplicate] Debem{us} reliquu{m} quod m{u}ltiplicat{ur} ab ill{is} P{er} reliq{u}o decuplu{m} sic su{m}ma{m} later{e} neq{ui}b{i}t.

[Sidenote: The third case of the craft; an example.]

¶ Her{e} he puttes þe thryde rewle, þe quych is þis. yf þ{o}u wel m{u}ltiply in þi mynde, And þe Articul be a digitte, þou schalt loke þat þe digitt be w{i}t{h}-Inne an hundryth, þen þou schalt m{u}ltiply the digitt of þe Articulle by þe oþer digitte. And eu{er}y vnite in þe nounbre þat schall{e} come þ{ere}-of schal betoken ten. As þus: yf þat þ{o}u wold wete qwat is twyes 40. m{u}ltiplie þe digitt{e} of 40, þe quych is 4, by þe oþ{er} diget, þe quych is 2. And þat wolle be 8. And in þe nombre of 8 ben 8 vnites, & eu{er}y of þe ylke vnites schuld stonde for 10. þ{ere}-fore þ{ere} schal be 8 tymes 10, þat wol be 4 score. And so mony is twyes 40. ¶ If þe articul be a hundryth or be 2 hundryth And a þowsant, so þat hit be notte a thousant, [*leaf 163b] worch as þo{u} dyddyst afor{e}, saue þ{o}u schalt rekene eu{er}y vnite for a hundryth.

¶ In nu{mer}u{m} mixtu{m} digitu{m} si ducer{e} cures Articul{us} mixti sumat{ur} deinde resoluas In digitu{m} post fac respectu de digitis Articul{us}q{ue} docet excrescens in diriua{n}do In digitu{m} mixti post ducas m{u}ltiplica{n}te{m} ¶ De digitis vt norma [{18}][docet] de [hunc] Multiplica si{mu}l et sic postea summa patebit.

[Sidenote: The fourth case of the craft: Composite by digit. Mental multiplication.]

Here he puttes þe 4 rewle, þe quych is þis: yf þou m{u}ltipliy on composit be a digit as 6 tymes 24, [{19}]þen take þe diget of þat composit, & m{u}ltiply þ{a}t digitt by þat oþ{er} diget, and kepe þe nomb{ur} þat comes þ{ere}-of. þen take þe digit of þat composit, & m{u}ltiply þat digit by anoþ{er} diget, by þe quych þ{o}u hast m{u}ltiplyed þe diget of þe articul, and loke qwat comes þ{ere}-of. þen take þ{o}u þat nounbur, & cast hit to þat other nounbur þat þ{o}u secheste as þus yf þou wel wete qwat comes of 6 tymes 4 & twenty. multiply þat articull{e} of þe composit by þe digit, þe quych is 6, as yn þe thryd rewle þ{o}u was tauȝt, And þat schal be 6 scor{e}. þen m{u}ltiply þe diget of þe {com}posit, [*leaf 164a] þe quych is 4, and m{u}ltiply þat by þat other diget, þe quych is 6, as þou wast tauȝt in þe first rewle, yf þ{o}u haue mynde þ{er}of, & þat wol be 4 & twenty. cast all ylke nounburs to-ged{ir}, & hit schal be 144. And so mych is 6 tymes 4 & twenty.

[Headnote: How to multiply without Figures.]

¶ Duct{us} in articulu{m} num{erus} si {com}posit{us} sit Articulu{m} puru{m} comites articulu{m} q{u}o{que} Mixti pro digit{is} post fiat [et articulus vt] Norma iubet [retinendo quod extra dicta ab illis] Articuli digitu{m} post tu mixtu{m} digitu{m} duc Re{gula} de digitis nec p{re}cipit articul{us}q{ue} Ex quib{us} exc{re}scens su{m}me tu iunge p{ri}ori Sic ma{n}ifesta cito fiet t{ibi} su{m}ma petita.

[Sidenote: The fifth case of the craft: Article by Composite. An example.]

¶ Her{e} he puttes þe 5 rewle, þe quych is þis: yf þ{o}u wel m{u}ltiply an Articul be a composit, m{u}ltiplie þat Articul by þe articul of þe composit, and worch as þou wos tauȝt in þe secunde rewle, of þe quych rewle þe v{er}se begynnes þus. ¶ Articulu{m} si p{er} Relicu{m} vis m{u}ltiplicare. þen m{u}ltiply þe diget of þe composit by þat oþ{ir} articul aft{ir} þe doctrine of þe 3 rewle. take þ{er}of gode hede, I p{ra}y þe as þus. Yf þ{o}u wel wete what is 24 tymes ten. Multiplie ten by 20, þat wel be 2 hundryth. þen m{u}ltiply þe diget of þe 10, þe quych is 1, by þe diget of þe composit, þe quych is 4, & þ{a}t [*leaf 164b] wol be 4. þen reken eu{er}y vnite þat is in 4 for 10, & þat schal be 40. Cast 40 to 2 hundryth, & þat wol be 2 hundryth & 40. And so mych is 24 tymes ten.

[Headnote: How to work without Figures.]

¶ Compositu{m} num{er}u{m} mixto si[c] m{u}ltiplicabis Vndecies tredeci{m} sic e{st} ex hiis op{er}andum In reliquu{m} p{rimu}m demu{m} duc post in eund{em} Vnu{m} post den{u}m duc in t{ri}a dei{n}de p{er} vnu{m} Multiplices{que} dem{u}m int{ra} o{mn}ia m{u}ltiplicata In su{m}ma decies q{ua}m si fu{er}it t{ibi} doces Multiplicandor{um} de normis sufficiunt h{ec}.

[Sidenote: The sixth case of the craft: Composite by Composite. Mental multiplication. An example of the sixth case of the craft.]

¶ Here he puttes þe 6 rewle, & þe last of all{e} multiplicacioɳ, þe quych is þis: yf þ{o}u wel m{u}ltiplye a {com}posit by a-noþ{er} composit, þou schalt do þus. m{u}ltiplie þ{a}t on composit, qwych þ{o}u welt of the twene, by þe articul of þe toþ{er} composit, as þ{o}u wer{e} tauȝt in þe 5 rewle, þen m{u}ltiplie þ{a}t same composit, þe quych þou hast m{u}ltiplied by þe oþ{er} articul, by þe digit of þe oþ{er} composit, as þ{o}u was tauȝt in þe 4 rewle. As þus, yf þou wold wete what is 11 tymes 13, as þ{o}u was tauȝt in þe 5 rewle, & þat schal be an hundryth & ten, aft{er}warde m{u}ltiply þat same co{m}posit þ{a}t þ{o}u hast m{u}ltiplied, þe quych is a .11. And m{u}ltiplye hit be þe digit of þe oþ{er} composit, þe quych is 3, for 3 is þe digit of 13, And þat wel be 30. þen take þe digit of þat composit, þe quych composit þou m{u}ltiplied by þe digit of þ{a}t oþ{er} {com}posit, [*leaf 165a] þe quych is a 11. ¶ Also of the quych 11 on is þe digit. m{u}ltiplie þat digitt by þe digett of þat oth{er} composit, þe quych diget is 3, as þ{o}u was tauȝt in þe first rewle i{n} þe begynnyng{e} of þis craft. þe quych rewle begynn{es} “In digitu{m} cures.” And of all{e} þe m{u}ltiplicacioɳ of þe 2 digitt comys thre, for onys 3 is but 3. Now cast all{e} þese nounbers toged{ur}, the quych is þis, a hundryth & ten & 30 & 3. And al þat wel be 143. Write 3 first in þe ryght side. And cast 10 to 30, þat wol be 40. set 40 next aft{ur} towarde þe lyft side, And set aftur a hundryth as her{e} an Ensampull{e}, 143.

(Cetera desunt.)

FOOTNOTES (The Crafte of Nombrynge):

[1: In MS, ‘awiy.’] [2: ‘ben’ repeated in MS.] [3: In MS. ‘thausandes.’] [4: Perhaps “So.”] [5: ‘hali’ marked for erasure in MS.] [6: ‘moy’ in MS.] [7: ‘Subt{ra}has a{u}t addis a dext{ri}s {ve}l medi{a}b{is}’ added on margin of MS.] [8: After ‘craft’ insert ‘the .4. what is þe p{ro}fet of þis craft.’] [9: After ‘sythes’ insert ‘& þis wordes fyue sithe & sex sythes.’] [10: ‘t’l’ marked for erasure before ‘tyl’ in MS.] [11: Here ‘of þe same rew’ is marked for erasure in MS.] [12: ‘s{ed}’ deleted in MS.] [13: 6883 in MS.] [14: ‘þen’ overwritten on ‘þat’ marked for erasure.] [15: ‘Supra’ inserted in MS. in place of ‘cifra’ marked for erasure.] [16--16: Marked for erasure in MS.] [17: 4 in MS.] [18: docet. decet MS.] [19: ‘4 times 4’ in MS.]

+The Art of Nombryng.+

A TRANSLATION OF

+John of Holywood’s De Arte Numerandi.+

[_Ashmole MS. 396, fol. 48._]

+Boys seying in the begynnyng of his Arsemetrik{e}:--All{e} [*Fol. 48.] thynges that ben{e} fro the first begynnyng of thynges have p{ro}ceded{e}, and come forth{e}, And by reso{u}n of nombre ben formed{e}; And in wise as they ben{e}, So oweth{e} they to be knowen{e}; wherfor in vniu{er}sall{e} knowlechyng of thynges the Art of nombrynge is best, and most operatyf{e}.+

[Sidenote: The name of the art. Derivation of Algorism. Another. Another. Kinds of numbers. The 9 rules of the Art.]