Chapter 4

¶ Her{e} he says, yf ou{er} þe fyrst fig{ur}e in þe ryȝt side be such a merke as is her{e} made, ʷ, þ{o}u schall{e} fyrst doubull{e} þe figur{e}, the quych stondes vnd{er} þ{a}t merke, & þen þou schalt doubul þat merke þe quych stond{es} for haluendel on. for too haluedels makes on, & so þ{a}t wol be on. cast þ{a}t on to þat duplacioɳ of þe figur{e} ou{er} whos hed stode þat merke, & write it in þe same place þ{ere} þat þe figur{e} þe quych was doublet stode, as þus 23ʷ. double 3, þat wol be 6; doubul þat halue on, & þat wol be on. cast on to 6, þ{a}t wel be 7. do away 6 & þat 1, & sett þ{ere} 7. þan hase þou do. as for þat figur{e}, þan go [*leaf 148b] to þe oþ{er} fig{ure} & worch forth. & þ{o}u schall neu{er} haue such a merk but ou{er} þe hed of þe furst figure in þe ryght side. And ȝet it schal not happe but yf it were y-halued a-for{e}, þus þ{o}u schalt vnd{er}stonde þe verse. ¶ Si sup{er} ext{re}ma{m} &c. Et nota, talis fig{ur}a ʷ significans medietate{m}, unitat{is} veniat, {i.e.} contingat u{e}l fiat sup{er} ext{re}ma{m}, {i.e.} sup{er} p{ri}ma{m} figura{m} in ext{re}mo sic v{er}sus dextram ars dat: {i.e.} reddit monade{m}. {i.e.} vnitate{m} eide{m}. {i.e.} eidem note & declina{tur} hec monos, d{i}s, di, dem, &c. ¶ Quod {er}g{o} to{tum} ho{c} dabis monade{m} note {con}ting{et}. {i.e.} eveniet tibi si dimidiasti, {i.e.} accipisti u{e}l subtulisti medietatem alicuius unius, in cuius principio sint figura nu{mer}u{m} denotans i{m}pare{m} p{rim}o {i.e.} principiis.

[Headnote: The Craft of Mediation.]

¶ Sequit{ur} de mediacione.

++Incipe sic, si vis alique{m} nu{me}ru{m} mediar{e}: Sc{ri}be figurar{um} seriem sola{m}, velut an{te}.

[Sidenote: The four things to be known in mediation: the first the second; the third; the fourth. Begin thus.]

¶ In þis Chapter is taȝt þe Craft of mediaciouɳ, in þe quych craft þ{o}u most know 4 thynges. ffurst what is mediacioɳ. the secunde how mony rewes of figur{es} þ{o}u most haue in þe wyrchyng{e} of þis craft. þe thryde how mony diu{er}se cases may happ in þis craft.[{8}] [[the .4. what is þe p{ro}fet of þis craft.]] ¶ As for þe furst, þ{o}u schalt vndurstonde þat mediacioɳ is a takyng out of halfe a nomber out of a holle nomber, [*leaf 149a] as yf þ{o}u wolde take 3 out of 6. ¶ As for þe secunde, þ{o}u schalt know þ{a}t þ{o}u most haue on{e} rewe of figures, & no moo, as þ{o}u hayst in þe craft of duplacioɳ. ¶ As for the thryd, þou most vnd{er}stonde þat 5 cases may happe in þis craft. ¶ As for þe fourte, þou schall{e} know þat the p{ro}fet of þis craft is when þ{o}u hast take away þe haluendel of a nomb{re} to telle qwat þer{e} schall{e} leue. ¶ Incipe sic, &c. The sentence of þis verse is þis. yf þ{o}u wold medye, þat is to say, take halfe out of þe holle, or halfe out of halfe, þou most begynne þ{us}. Write on{e} rewe of figur{es} of what nombre þou wolte, as þ{o}u dyddyst be-for{e} in þe Craft of duplacioɳ. v{er}sus.

¶ Postea p{ro}cedas medians, si p{ri}ma figura Si par aut i{m}par videas.

[Sidenote: See if the number is even or odd.]

¶ Her{e} he says, when þ{o}u hast write a rewe of figures, þ{o}u schalt take hede wheþ{er} þe first figur{e} be eueɳ or odde in nombre, & vnd{er}stonde þ{a}t he spekes of þe first figure in þe ryȝt side. And i{n} the ryght side þ{o}u schall{e} begynne in þis Craft.

¶ Quia si fu{er}it par, Dimidiab{is} eam, scribe{n}s quicq{ui}d remanebit:

[Sidenote: If it is even, halve it, and write the answer in its place.]

¶ Her{e} is the first case of þis craft, þe quych is þis, yf þe first figur{e} be euen. þou schal take away fro þe figur{e} euen halfe, & do away þat fig{ur}e and set þ{ere} þat leues ou{er}, as þus, 4. take [*leaf 149b] halfe out of 4, & þan þ{ere} leues 2. do away 4 & sett þ{ere} 2. þis is lyght y-nowȝt. v{er}sus.

[Headnote: The Mediation of an Odd Number.]

¶ Impar si fu{er}it vnu{m} demas mediar{e} Quod no{n} p{re}sumas, s{ed} quod sup{er}est mediabis Inde sup{er} tractu{m} fac demptu{m} quod no{ta}t vnu{m}.

[Sidenote: If it is odd, halve the even number less than it. Here is an example. Then write the sign for one-half over it. Put the mark only over the first figure.]

Her{e} is þe secunde case of þis craft, the quych is þis. yf þe first figur{e} betoken{e} a nombre þat is odde, the quych odde schal not be mediete, þen þ{o}u schalt medye þat nombre þat leues, when the odde of þe same nomb{re} is take away, & write þat þ{a}t leues as þ{o}u diddest in þe first case of þis craft. Whaɳ þ{o}u hayst write þat. for þ{a}t þat leues, write such a merke as is her{e} ʷ vpon his hede, þe quych merke schal betokeɳ halfe of þe odde þat was take away. lo an Ensampull. 245. the first figur{e} her{e} is betokenyng{e} odde nombre, þe quych is 5, for 5 is odde; þ{er}e-for{e} do away þat þ{a}t is odde, þe quych is 1. þen leues 4. þen medye 4 & þen leues 2. do away 4. & sette þ{ere} 2, & make such a merke ʷ upon his hede, þat is to say ou{er} his hede of 2 as þus. 242.ʷ And þen worch forth in þe oþ{er} figures tyll þ{o}u come to þe ende. by þe furst case as þ{o}u schalt vnd{er}stonde þat þ{o}u schalt [*leaf 150a] neu{er} make such a merk but ou{er} þe first fig{ur}e hed in þe riȝt side. Wheþ{er} þe other fig{ur}es þat comyɳ aft{er} hym be eueɳ or odde. v{er}sus.

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

¶ Si monos, dele; sit t{ibi} cifra post no{ta} supra.

[Sidenote: If the first figure is one put a cipher.]

¶ Here is þe thryde case, þe quych yf the first figur{e} be a figur{e} of 1. þ{o}u schalt do away þat 1 & set þ{ere} a cifer, & a merke ou{er} þe cifer as þus, 241. do away 1, & sett þ{ere} a cifer w{i}t{h} a merke ou{er} his hede, & þen hast þ{o}u ydo for þat 0. as þus 0ʷ þen worch forth in þe oþer fig{ur}ys till þ{o}u come to þe ende, for it is lyght as dyche water. vn{de} v{er}sus.

¶ Postea p{ro}cedas hac condic{i}one secu{n}da: Imp{ar} si fu{er}it hinc vnu{m} deme p{ri}ori, Inscribens quinque, nam denos significabit Monos p{re}d{ict}am.

[Sidenote: What to do if any other figure is odd. Write a figure of five over the next lower number’s head. Example.]

¶ Her{e} he putt{es} þe fourte case, þe quych is þis. yf it happeɳ the secunde figur{e} betoken odde nombre, þou schal do away on of þat odde nombre, þe quych is significatiue by þ{a}t figure 1. þe quych 1 schall be rekende for 10. Whan þ{o}u hast take away þ{a}t 1 out of þe nombre þ{a}t is signifiede by þat figur{e}, þ{o}u schalt medie þ{a}t þat leues ou{er}, & do away þat figur{e} þat is medied, & sette in his styde halfe of þ{a}t nombre. ¶ Whan þ{o}u hase so done, þ{o}u schalt write [*leaf 150b] a figure of 5 ou{er} þe next figur{es} hede by-for{e} toward þe ryȝt side, for þat 1, þe quych made odd nombr{e}, schall stonde for ten, & 5 is halfe of 10; so þ{o}u most write 5 for his haluendell{e}. lo an Ensampull{e}, 4678. begyɳ in þe ryȝt side as þ{o}u most nedes. medie 8. þen þ{o}u schalt leue 4. do away þat 8 & sette þ{ere} 4. þen out of 7. take away 1. þe quych makes odde, & sett 5. vpon þe next figur{es} hede afor{e} toward þe ryȝt side, þe quych is now 4. but afor{e} it was 8. for þat 1 schal be rekenet for 10, of þe quych 10, 5 is halfe, as þou knowest wel. Whan þ{o}u hast þus ydo, medye þ{a}t þe quych leues aft{er} þe takying{e} away of þat þat is odde, þe quych leuyng{e} schall{e} be 3; do away 6 & sette þ{er}e 3, & þou schalt haue such a nombre

5 4634.

aft{er} go forth to þe next fig{ur}e, & medy þat, & worch forth, for it is lyȝt ynovȝt to þe c{er}tayɳ.

¶ Si v{er}o s{e}c{un}da dat vnu{m}. Illa deleta, sc{ri}bat{ur} cifra; p{ri}ori ¶ Tradendo quinque pro denario mediato; Nec cifra sc{ri}batur, nisi dei{n}de fig{ur}a seq{u}at{ur}: Postea p{ro}cedas reliq{ua}s mediando figuras Vt sup{ra} docui, si sint tibi mille figure.

[Sidenote: If the second figure is one, put a cipher, and write five over the next figure. How to halve fourteen.]

¶ Her{e} he putt{es} þe 5 case, þe quych is [*leaf 151a] þis: yf þe secunde figur{e} be of 1, as þis is here 12, þou schalt do away þat 1 & sett þ{ere} a cifer. & sett 5 ou{er} þe next fig{ur}e hede afor{e} toward þe riȝt side, as þou diddyst afor{e}; & þat 5 schal be haldel of þat 1, þe quych 1 is rekent for 10. lo an Ensampull{e}, 214. medye 4. þ{a}t schall{e} be 2. do away 4 & sett þ{ere} 2. þe{n} go forth to þe next figur{e}. þe quych is bot 1. do away þat 1. & sett þ{ere} a cifer. & set 5 vpon þe figur{es} hed afor{e}, þe quych is nowe 2, & þen þou schalt haue þis no{m}b{re}

5 202,

þen worch forth to þe nex fig{ur}e. And also it is no mayst{er}y yf þ{ere} come no figur{e} after þat on is medyet, þ{o}u schalt write no 0. ne nowȝt ellis, but set 5 ou{er} þe next fig{ur}e afor{e} toward þe ryȝt, as þus 14. medie 4 then leues 2, do away 4 & sett þ{ere} 2. þen medie 1. þe q{ui}ch is rekende for ten, þe halue{n}del þ{ere}-of wel be 5. sett þ{a}t 5 vpon þe hede of þ{a}t figur{e}, þe quych is now 2, & do away þ{a}t 1, & þou schalt haue þis nombre yf þ{o}u worch wel,

5 2.

vn{de} v{er}sus.

[Headnote: How to prove the Mediation.]

¶ Si mediacio sit b{e}n{e} f{ac}ta p{ro}bar{e} valeb{is} ¶ Duplando num{er}u{m} que{m} p{ri}mo di{m}ediasti

[Sidenote: How to prove your mediation. First example. The second. The third example. The fourth example. The fifth example.]

¶ Her{e} he telles þe how þou schalt know wheþ{er} þou hase wel ydo or no. doubul [*leaf 151b] þe nombre þe quych þ{o}u hase mediet, and yf þ{o}u haue wel y-medyt after þe dupleacioɳ, þou schalt haue þe same nombre þat þ{o}u haddyst in þe tabull{e} or þ{o}u began to medye, as þus. ¶ The furst ensampull{e} was þis. 4. þe quych I-mediet was laft 2, þe whych 2 was write in þe place þ{a}t 4 was write afor{e}. Now doubull{e} þat 2, & þ{o}u schal haue 4, as þ{o}u hadyst afor{e}. þe secunde Ensampull{e} was þis, 245. When þ{o}u haddyst mediet all{e} þis nomb{re}, yf þou haue wel ydo þou schalt haue of þ{a}t mediacioɳ þis nombre, 122ʷ. Now doubull{e} þis nombre, & begyn in þe lyft side; doubull{e} 1, þat schal be 2. do away þat 1 & sett þ{ere} 2. þen doubull{e} þ{a}t oþ{er} 2 & sett þ{ere} 4, þen doubull{e} þat oþ{er} 2, & þat wel be 4. þe{n} doubul þat merke þat stondes for halue on. & þat schall{e} be 1. Cast þat on to 4, & it schall{e} be 5. do away þat 2 & þat merke, & sette þ{ere} 5, & þen þ{o}u schal haue þis nombre 245. & þis wos þe same nombur þ{a}t þ{o}u haddyst or þ{o}u began to medye, as þ{o}u mayst se yf þou take hede. The nombre þe quych þou haddist for an Ensampul in þe 3 case of mediacioɳ to be mediet was þis 241. whan þ{o}u haddist medied all{e} þis nombur truly [*leaf 152a] by eu{er}y figur{e}, þou schall haue be þ{a}t mediacioɳ þis nombur 120ʷ. Now dowbul þis nomb{ur}, & begyn in þe lyft side, as I tolde þe in þe Craft of duplacioɳ. þus doubull{e} þe fig{ur}e of 1, þat wel be 2. do away þat 1 & sett þ{ere} 2, þen doubul þe next figur{e} afore, the quych is 2, & þat wel be 4; do away 2 & set þ{ere} 4. þen doubul þe cifer, & þat wel be noȝt, for a 0 is noȝt. And twyes noȝt is but noȝt. þ{ere}for{e} doubul the merke aboue þe cifers hede, þe quych betokenes þe halue{n}del of 1, & þat schal be 1. do away þe cifer & þe merke, & sett þ{ere} 1, & þen þ{o}u schalt haue þis nombur 241. And þis same nombur þ{o}u haddyst afore or þ{o}u began to medy, & yf þ{o}u take gode hede. ¶ The next ensampul þat had in þe 4 case of mediacioɳ was þis 4678. Whan þ{o}u hast truly ymedit all{e} þis nombur fro þe begynnyng{e} to þe endyng{e}, þ{o}u schalt haue of þe mediacioɳ þis nombur

5 2334.

Now doubul this nombur & begyn in þe lyft side, & doubull{e} 2 þat schal be 4. do away 2 and sette þere 4; þen doubul{e} 3, þ{a}t wol be 6; do away 3 & sett þ{ere} 6, þen doubul þat oþ{er} 3, & þat wel be 6; do away 3 & set þ{ere} [*leaf 152b] 6, þen doubul þe 4, þat welle be 8; þen doubul 5. þe quych stondes ou{er} þe hed of 4, & þat wol be 10; cast 10 to 8, & þ{a}t schal be 18; do away 4 & þat 5, & sett þ{ere} 8, & sett that 1, þe quych is an articul of þe Composit þe quych is 18, ou{er} þe next figur{es} hed toward þe lyft side, þe quych is 6. drav þ{a}t 1 to 6, þe quych 1 in þe dravyng schal be rekente bot for 1, & þ{a}t 1 & þ{a}t 6 togedur wel be 7. do away þat 6 & þat 1. the quych stondes ou{er} his hede, & sett ther 7, & þen þou schalt haue þis nombur 4678. And þis same nombur þ{o}u hadyst or þ{o}u began to medye, as þ{o}u mayst see in þe secunde Ensampul þat þou had in þe 4 case of mediacioɳ, þat was þis: when þ{o}u had mediet truly all{e} the nombur, a p{ri}ncipio usque ad fine{m}. þ{o}u schalt haue of þat mediacioɳ þis nombur

5 102.

Now doubul 1. þat wel be 2. do away 1 & sett þ{ere} 2. þen doubul 0. þ{a}t will be noȝt. þ{ere}for{e} take þe 5, þe quych stondes ou{er} þe next figur{es} hed, & doubul it, & þat wol be 10. do away þe 0 þat stondes betwene þe two fig{u}r{i}s, & sette þ{ere} in his stid 1, for þ{a}t 1 now schal stonde in þe secunde place, wher{e} he schal betoken 10; þen doubul 2, þat wol be 4. do away 2 & sett þere 4. & [*leaf 153a] þou schal haue þus nombur 214. þis is þe same nu{m}bur þat þ{o}u hadyst or þ{o}u began to medye, as þ{o}u may see. And so do eu{er} mor{e}, yf þ{o}u wil knowe wheþ{er} þou hase wel ymedyt or no. ¶. doubull{e} þe nu{m}bur þat comes aft{er} þe mediaciouɳ, & þ{o}u schal haue þe same nombur þ{a}t þ{o}u hadyst or þ{o}u began to medye, yf þ{o}u haue welle ydo. or els doute þe noȝt, but yf þ{o}u haue þe same, þ{o}u hase faylide in þ{i} Craft.

+Sequitur de multiplicatione.+

[Headnote: The Craft of Multiplication.]

[Headnote: To write down a Multiplication Sum.]

++Si tu p{er} num{er}u{m} num{er}u{m} vis m{u}ltiplicar{e} Scribe duas q{ua}scu{nque} velis series nu{me}ror{um} Ordo s{er}vet{ur} vt vltima m{u}ltiplicandi Ponat{ur} sup{er} ant{er}iorem multiplicant{is} A leua reliq{u}e sint scripte m{u}ltiplicantes.

[Sidenote: Four things to be known of Multiplication: the first: the second: the third: the fourth. How to set down the sum. Two sorts of Multiplication: mentally, and on paper.]

¶ Her{e} be-gynnes þe Chapt{r}e of m{u}ltiplicatioɳ, in þe quych þou most know 4 thynges. ¶ Ffirst, qwat is m{u}ltiplicacioɳ. The secunde, how mony cases may hap in multiplicacioɳ. The thryde, how mony rewes of figur{es} þ{ere} most be. ¶ The 4. what is þe p{ro}fet of þis craft. ¶ As for þe first, þ{o}u schal vnd{er}stonde þat m{u}ltiplicacioɳ is a bryngyng{e} to-ged{er} of 2 thyng{es} in on nombur, þe quych on nombur {con}tynes so mony tymes on, howe [*leaf 153b] mony tymes þ{ere} ben vnytees in þe nowmb{re} of þat 2, as twyes 4 is 8. now her{e} ben þe 2 nomb{er}s, of þe quych too nowmbr{e}s on is betokened be an adu{er}be, þe quych is þe worde twyes, & þis worde thryes, & þis worde four{e} sythes,[{9}] [[& þis wordes fyue sithe & sex sythes.]] & so furth of such other lyke wordes. ¶ And tweyn nombres schal be tokenyde be a nowne, as þis worde four{e} showys þes tweyɳ nombres y-broth in-to on hole nombur, þat is 8, for twyes 4 is 8, as þ{o}u wost wel. ¶ And þes nomb{re} 8 conteynes as oft tymes 4 as þ{ere} ben vnites in þ{a}t other nomb{re}, þe quych is 2, for in 2 ben 2 vnites, & so oft tymes 4 ben in 8, as þ{o}u wottys wel. ¶ ffor þe secu{n}de, þ{o}u most know þat þ{o}u most haue too rewes of figures. ¶ As for þe thryde, þ{o}u most know þ{a}t 8 man{er} of diu{er}se case may happe in þis craft. The p{ro}fet of þis Craft is to telle when a nomb{re} is m{u}ltiplyed be a noþ{er}, qwat co{m}mys þ{ere} of. ¶ fforthermor{e}, as to þe sentence of our{e} verse, yf þ{o}u wel m{u}ltiply a nombur be a-noþ{er} nomb{ur}, þou schalt write [*leaf 154a] a rewe of figures of what nomb{ur}s so eu{er} þ{o}u welt, & þat schal be called Num{erus} m{u}ltiplicand{us}, Anglice, þe nomb{ur} the quych to be m{u}ltiplied. þen þ{o}u schalt write a-nother rewe of figur{e}s, by þe quych þ{o}u schalt m{u}ltiplie the nombre þat is to be m{u}ltiplied, of þe quych nomb{ur} þe furst fig{ur}e schal be write vnd{er} þe last figur{e} of þe nomb{ur}, þe quych is to be m{u}ltiplied. And so write forthe toward þe lyft side, as her{e} you may se,

+----------+ | 67324 | | 1234 | +----------+

And þis on{e} nomb{ur} schall{e} be called nu{meru}s m{u}ltiplicans. An{gli}ce, þe nomb{ur} m{u}ltipliyng{e}, for he schall{e} m{u}ltiply þe hyer nounb{ur}, as þus on{e} tyme 6. And so forth, as I schal telle the aft{er}warde. And þou schal begyn in þe lyft side. ¶ ffor-þ{ere}-more þou schalt vndurstonde þat þ{ere} is two man{ur}s of m{u}ltiplicacioɳ; one ys of þe wyrchyng{e} of þe boke only in þe mynde of a mon. fyrst he teches of þe fyrst man{er} of duplacioɳ, þe quych is be wyrchyng{e} of tabuls. Aft{er}warde he wol teche on þe secunde man{er}. vn{de} v{er}sus.

[Headnote: To multiply one Digit by another.]

In digitu{m} cures digitu{m} si duc{er}e ma{i}or [*leaf 154b.] P{er} qua{n}tu{m} distat a denis respice debes ¶ Namq{ue} suo decuplo totiens deler{e} mi{n}ore{m} Sitq{ue} tibi nu{meru}s veniens exinde patebit.

[Sidenote: How to multiply two digits. Subtract the greater from ten; take the less so many times from ten times itself. Example.]

¶ Her{e} he teches a rewle, how þ{o}u schalt fynde þe nounb{r}e þat comes by þe m{u}ltiplicacioɳ of a digit be anoþ{er}. loke how mony [vny]tes ben. bytwene þe mor{e} digit and 10. And reken ten for on vnite. And so oft do away þe lasse nounbre out of his owne decuple, þat is to say, fro þat nounb{r}e þat is ten tymes so mych is þe nounb{re} þ{a}t comes of þe m{u}ltiplicacioɳ. As yf þ{o}u wol m{u}ltiply 2 be 4. loke how mony vnitees ben by-twene þe quych is þe mor{e} nounb{re}, & be-twene ten. C{er}ten þ{ere} wel be vj vnitees by-twene 4 & ten. yf þ{o}u reken þ{ere} w{i}t{h} þe ten þe vnite, as þou may se. so mony tymes take 2. out of his decuple, þe quych is 20. for 20 is þe decuple of 2, 10 is þe decuple of 1, 30 is þe decuple of 3, 40 is þe decuple of 4, And þe oþ{er} digetes til þ{o}u come to ten; & whan þ{o}u hast y-take so mony tymes 2 out of twenty, þe quych is sex tymes, þ{o}u schal leue 8 as þ{o}u wost wel, for 6 times 2 is twelue. take [1]2 out of twenty, & þ{ere} schal leue 8. bot yf bothe þe digett{es} [*leaf 155a] ben y-lyech mych as her{e}. 222 or too tymes twenty, þen it is no fors quych of hem tweyn þ{o}u take out of here decuple. als mony tymes as þ{a}t is fro 10. but neu{er}-þe-lesse, yf þ{o}u haue hast to worch, þ{o}u schalt haue her{e} a tabul of figures, wher{e}-by þ{o}u schalt se a-nonɳ ryght what is þe nounbre þ{a}t comes of þe multiplicacioɳ of 2 digittes. þus þ{o}u schalt worch in þis fig{ur}e.

[Sidenote: Better use this table, though. How to use it. The way to use the Multiplication table.]

1| ----- 2| 4| -------- 3| 6| 9| ----------- 4| 8|12|16| -------------- 5|10|15|20|25| ----------------- 6|12|18|24|30|36| -------------------- 7|14|21|28|35|42|49| ----------------------- 8|16|24|32|40|48|56|64| -------------------------- 9|18|27|36|45|54|63|72|81| ---------------------------- 1| 2| 3| 4| 5| 6| 7| 8| 9| ----------------------------

yf þe fig{ur}e, þe quych schall{e} be m{u}ltiplied, be euen{e} as mych as þe diget be, þe quych þat oþ{er} figur{e} schal be m{u}ltiplied, as two tymes twayɳ, or thre tymes 3. or sych other. loke qwer{e} þat fig{ur}e sittes in þe lyft side of þe t{ri}angle, & loke qwer{e} þe diget sittes in þe neþ{er} most rewe of þe triangle. & go fro hym vpwarde in þe same rewe, þe quych rewe gose vpwarde til þ{o}u come agaynes þe oþ{er} digette þat sittes in þe lyft side of þe t{ri}angle. And þat nounbre, þe quych þou [*leaf 155b] fyn[*]des þ{ere} is þe nounbre þat comes of the m{u}ltiplicacioɳ of þe 2 digittes, as yf þou wold wete qwat is 2 tymes 2. loke quer{e} sittes 2 in þe lyft side i{n} þe first rewe, he sittes next 1 in þe lyft side al on hye, as þ{o}u may se; þe[{n}] loke qwer{e} sittes 2 in þe lowyst rewe of þe t{ri}angle, & go fro hym vpwarde in þe same rewe tyll{e} þou come a-ȝenenes 2 in þe hyer place, & þer þou schalt fynd ywrite 4, & þat is þe nounb{r}e þat comes of þe multiplicacioɳ of two tymes tweyn is 4, as þow wotest well{e}. yf þe diget. the quych is m{u}ltiplied, be mor{e} þan þe oþ{er}, þou schalt loke qwer{e} þe mor{e} diget sittes in þe lowest rewe of þe t{ri}angle, & go vpwarde in þe same rewe tyl[{10}] þ{o}u come a-nendes þe lasse diget in the lyft side. And þ{ere} þ{o}u schalt fynde þe no{m}b{r}e þat comes of þe m{u}ltiplicacioɳ; but þ{o}u schalt vnd{er}stonde þat þis rewle, þe quych is in þis v{er}se. ¶ In digitu{m} cures, &c., noþ{er} þis t{ri}angle schall{e} not s{er}ue, bot to fynde þe nounbres þ{a}t comes of the m{u}ltiplicacioɳ þat comes of 2 articuls or {com}posites, þe nedes no craft but yf þou wolt m{u}ltiply in þi mynde. And [*leaf 156a] þere-to þou schalt haue a craft aft{er}warde, for þou schall wyrch w{i}t{h} digettes in þe tables, as þou schalt know aft{er}warde. v{er}sus.

[Headnote: To multiply one Composite by another.]

¶ Postea p{ro}cedas postrema{m} m{u}ltiplica{n}do [Recte multiplicans per cu{n}ctas i{n}feriores] Condic{i}onem tamen t{a}li q{uod} m{u}ltiplicant{es} Scribas in capite quicq{ui}d p{ro}cesserit inde Sed postq{uam} fuit hec m{u}ltiplicate fig{ur}e Anteriorent{ur} serei m{u}ltiplica{n}t{is} Et sic m{u}ltiplica velut isti m{u}ltiplicasti Qui sequit{ur} nu{mer}u{m} sc{ri}ptu{m} quiscu{n}q{ue} figur{is}.

[Sidenote: How to multiply one number by another. Multiply the ‘last’ figure of the higher by the ‘first’ of the lower number. Set the answer over the first of the lower: then multiply the second of the lower, and so on. Then antery the lower number: as thus. Now multiply by the last but one of the higher: as thus. Antery the figures again, and multiply by five: Then add all the figures above the line: and you will have the answer.]

¶ Her{e} he teches how þ{o}u schalt wyrch in þis craft. þou schalt m{ul}tiplye þe last figur{e} of þe nombre, and quen þ{o}u hast so ydo þou schalt draw all{e} þe figures of þe neþ{er} nounbre mor{e} taward þe ryȝt side, so qwe{n} þ{o}u hast m{u}ltiplyed þe last figur{e} of þe heyer nounbre by all{e} þe neþ{er} figures. And sette þe nounbir þat comes þer-of ou{er} þe last figur{e} of þe neþ{er} nounb{re}, & þen þou schalt sette al þe oþ{er} fig{ur}es of þe neþ{er} nounb{re} mor{e} ner{e} to þe ryȝt side. ¶ And whan þou hast m{u}ltiplied þat figur{e} þat schal be m{u}ltiplied þe next aft{er} hym by al þe neþ{er} figures. And worch as þou dyddyst afor{e} til [*leaf 156b] þou come to þe ende. And þou schalt vnd{er}stonde þat eu{er}y figur{e} of þe hier nounb{re} schal be m{u}ltiplied be all{e} þe figur{e}s of the neþ{er} nounbre, yf þe hier nounb{re} be any figur{e} þen on{e}. lo an Ensampul her{e} folowyng{e}.

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þou schalt begyne to m{u}ltiplye in þe lyft side. M{u}ltiply 2 be 2, and twyes 2 is 4. set 4 ou{er} þe hed of þ{a}t 2, þen m{u}ltiplie þe same hier 2 by 3 of þe nether nounbre, as thryes 2 þat schal be 6. set 6 ou{er} þe hed of 3, þan m{u}ltiplie þe same hier 2 by þat 2 þe quych stondes vnd{er} hym, þ{a}t wol be 4; do away þe hier 2 & sette þ{ere} 4. ¶ Now þ{o}u most antery þe nether nounbre, þat is to say, þ{o}u most sett þe neþ{er} nounbre more towarde þe ryȝt side, as þus. Take þe neþ{er} 2 toward þe ryȝt side, & sette it eueɳ vnd{er} þe 4 of þe hyer nounb{r}e, & ant{er}y all{e} þe figures þat comes aft{er} þat 2, as þus; sette 2 vnd{er} þe 4. þen sett þe figur{e} of 3 þ{ere} þat þe figure of 2 stode, þe quych is now vndur þ{a}t 4 in þe hier nounbre; þen sett þe oþer figur{e} of 2, þe quych is þe last fig{ur}e toward þe lyft side of þe neþ{er} nomb{er} þ{ere} þe figur{e} of 3 stode. þen þ{o}u schalt haue such a nombre.

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