Qui sequitur numerum scriptum quiscunque figuris.
How to multiply one number by another. ¶ Here he teches how þou schalt wyrch in þis craft. þou schalt multiplye þe last figure of þe nombre, and quen þou hast so ydo þou schalt draw alle þe figures of þe neþer nounbre more [taward] þe ryȝt side, so qwen þou hast multiplyed þe last figure of þe heyer nounbre by alle þe neþer figures. Multiply the ‘last’ figure of the higher by the ‘first’ of the lower number. And sette þe nounbir þat comes þer-of ouer þe last figure of þe neþer nounbre, & þen þou schalt sette al þe oþer figures of þe neþer nounbre more nere to þe ryȝt side. ¶ And whan þou hast multiplied þat figure þat schal be multiplied þe next after hym by al þe neþer figures. And worch as þou dyddyst afore til leaf 156 b. *þou come to þe ende. And þou schalt vnderstonde þat euery figure of þe hier nounbre schal be multiplied be alle þe figures of the neþer nounbre, yf þe hier nounbre be any figure þen one. Set the answer over the first of the lower: lo an Ensampul here folowynge. 2465.
232 þou schalt begyne to multiplye in þe lyft side. Multiply 2 be 2, and twyes 2 is 4. set 4 then multiply the second of the lower, and so on. ouer þe hed of þat 2, þen multiplie þe same hier 2 by 3 of þe nether nounbre, as thryes 2 þat schal be 6. set 6 ouer þe hed of 3, þan multiplie þe same hier 2 by þat 2 þe quych stondes vnder hym, þat wol be 4; do away þe hier 2 & sette þere 4. Then antery the lower number: ¶ Now þou most [antery] þe nether nounbre, þat is to say, þou most sett þe neþer nounbre more towarde þe ryȝt side, as þus. Take þe neþer 2 toward þe ryȝt side, & sette it eueɳ vnder þe 4 of þe hyer nounbre, & antery alle þe figures þat comes after þat 2, as þus; sette 2 vnder þe 4. þen sett þe figure of 3 þere þat þe figure of 2 stode, þe quych is now vndur þat 4 in þe hier nounbre; þen sett þe oþer figure of 2, þe quych is þe last figure toward þe lyft side of þe neþer nomber þere þe figure of 3 stode. as thus. þen þou schalt haue such a nombre. 464465
232 leaf 157 a. * ¶ Now multiply 4, þe quych comes next after 6, by þe last 2 of þe neþer nounbur toward þe lyft side. as 2 tymes 4, þat wel be 8. sette þat 8 ouer þe figure the quych stondes ouer þe hede of þat 2, þe quych is þe last figure of þe neþer nounbre; þan multiplie þat same 4 by 3, þat comes in þe neþer rewe, þat wol be 12. sette þe digit of þe composyt ouer þe figure þe quych stondes ouer þe hed of þat 3, & sette þe articule of þis composit ouer al þe figures þat stondes ouer þe neþer 2 hede. Now multiply by the last but one of the higher: þen multiplie þe same 4 by þe 2 in þe ryȝt side in þe neþer nounbur, þat wol be 8. do away 4. & sette þere 8. Euer more qwen þou multiplies þe hier figure by þat figure þe quych stondes vnder hym, þou schalt do away þat hier figure, & sett þer þat nounbre þe quych comes of multiplicacioɳ of ylke digittes. as thus. Whan þou hast done as I haue byde þe, þou schalt haue suych an order of figure as is here, 1
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232. þen take and antery þi neþer figures. And sett þe fyrst figure of þe neþer figures[11] vndre be figure of 6. ¶ And draw al þe oþer figures of þe same rewe to hym-warde, leaf 157 b. *as þou diddyst afore. þen multiplye 6 be 2, & sett þat þe quych comes ouer þere-of ouer al þe oþer figures hedes þat stondes ouer þat 2. þen multiply 6 be 3, & sett alle þat comes þere-of vpon alle þe figures hedes þat standes ouer þat 3; þan multiplye 6 be 2, þe quych stondes vnder þat 6, þen do away 6 & write þere þe digitt of þe composit þat schal come þereof, & sette þe articull ouer alle þe figures þat stondes ouer þe hede of þat 3 as here, 11
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232 Antery the figures again, and multiply by five: þen antery þi figures as þou diddyst afore, and multipli 5 be 2, þat wol be 10; sett þe 0 ouer all þe figures þat stonden ouer þat 2, & sett þat 1. ouer the next figures hedes, alle on hye towarde þe lyft side. þen multiplye 5 be 3. þat wol be 15, write 5 ouer þe figures hedes þat stonden ouer þat 3, & sett þat 1 ouer þe next figures hedes toward þe lyft side. þen multiplye 5 be 2, þat wol be 10. do away þat 5 & sett þere a 0, & sett þat 1 ouer þe figures hedes þat stonden ouer 3. And þen leaf 158 a. þou schalt haue such a nounbre as here stondes aftur.* 11
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232 ¶ Now draw alle þese figures downe togeder as þus, 6.8.1. & 1 draw to-gedur; þat wolle be 16, do away alle þese figures saue 6. lat hym stonde, for [þow] þou take hym away þou most write þer þe same aȝene. þerefore late hym stonde, & sett 1 ouer þe figure hede of 4 toward þe lyft side; þen draw on to 4, þat wolle be 5. Then add all the figures above the line: do away þat 4 & þat 1, & sette þere 5. þen draw 4221 & 1 togedur, þat wol be 10. do away alle þat, & write þere þat 4 & þat 0, & sett þat 1 ouer þe next figures hede toward þe lyft side, þe quych is 6. þen draw þat 6 & þat 1 togedur, & þat wolle be 7; do away 6 & sett þere 7, þen draw 8810 & 1, & þat wel be 18; do away alle þe figures þat stondes ouer þe hede of þat 8, & lette 8 stonde stil, & write þat 1 ouer þe next figuris hede, þe quych is a 0. þen do away þat 0, & sett þere 1, þe quych stondes ouer þe 0. hede. þen draw 2, 5, & 1 togedur, þat wolle be 8. þen do away alle þat, & write þere 8. and you will have the answer. ¶ And þen þou schalt haue þis nounbre, 571880.
The Cases of this Craft.
* ¶ Sed cum multiplicabis, primo sic est operandum,
Si dabit articulum tibi multiplicacio solum;
Proposita cifra summam transferre memento.
What to do if the first multiplication results in an article. ¶ Here he puttes þe fyrst case of þis craft, þe quych is þis: yf þere come an articulle of þe multiplicacioɳ ysette before the articulle in þe lyft side as þus 51
23. multiplye 5 by 2, þat wol be 10; sette ouer þe hede of þat 2 a 0, & sett þat on, þat is þe articul, in þe lyft side, þat is next hym, þen þou schalt haue þis nounbre 1051.
23 ¶ And þen worch forth as þou diddist afore. And þou schalt vnderstonde þat þou schalt write no 0. but whan þat place where þou schal write þat 0 has no figure afore hym noþer after. versus.
¶ Si autem digitus excreuerit articulusque.
Articulus[12] supraposito digito salit vltra.
What to do if the result is a composite number. ¶ Here is þe secunde case, þe quych is þis: yf hit happe þat þere come a composyt, þou schalt write þe digitte ouer þe hede of þe neþer figure by þe quych þou multipliest þe hier figure; and sett þe articulle next hym toward þe lyft side, as þou diddyst afore, as þus 83.
83 Multiply 8 by 8, þat wol be 64. Write þe 4 ouer 8, þat is to say, ouer þe hede of þe neþer 8; & set 6, þe quych leaf 159 a. *is an articul, next after. And þen þou schalt haue such a nounbre as is here, 6483[13],
83 And þen worch forth.