Articuli faciunt tot centum multiplicati.
The first case of the craft. ¶ Here he teches þe furst rewle, þe quych is þis: yf þou wel multiplie an articul be anoþer, so þat both þe articuls bene with-Inne an hundreth, þus þou schalt do. Article by article; take þe digit of bothe the articuls, for euery articul hase a digit, þen multiplye þat on digit by þat oþer, and loke how mony vnytes ben in þe nounbre þat comes of þe multiplicacioɳ of þe 2 digittes, & so mony hundrythes ben in þe nounbre þat schal come of þe multiplicacioɳ of þe ylke 2 articuls as þus. an example: yf þou wold wete qwat is ten tymes ten. take þe digit of ten, þe quych is 1; take þe digit of þat oþer ten, þe quych is on. ¶ Also multiplie 1 be 1, as on tyme on þat is but 1. In on is but on vnite as þou wost welle, þerefore ten tymes ten is but a hundryth. another example: ¶ 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. multiplie 3 be 2, þat is 6. Now in 6 ben 6 vnites, ¶ And so mony hundrythes ben in 20 tymes 30*, leaf 161 b. þerefore 20 tymes 30 is 6 hundryth eueɳ. loke & se. ¶ But yf it be so þat one articul be with-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 multiplicacioɳ [16]And so mony tymes[16] of 2 digittes of ylke articuls, so mony thowsant ben in þe nounbre, the qwych comes of þe multiplicacioɳ. And so mony tymes ten thowsand schal be in þe nounbre þat comes of þe multiplicacion of 2 articuls, as yf þou wold wete qwat is 4 hundryth tymes [two hundryth]. Multiply 4 be 2,[17] þat wol be 8. in 8 ben 8 vnites. How to work subtly without Figures. Mental multiplication. ¶ And so mony tymes ten thousand be in 4 hundryth tymes [2][17] hundryth, þat is 80 thousand. Take hede, I schall telle þe a Another example. generalle rewle whan þou hast 2 articuls, And þou wold wete qwat comes of þe multiplicacioɳ of hem 2. multiplie þe digit of þat on [articuls], and kepe þat nounbre, þen loke how mony cifers schuld go before þat on articuls, [and] he were [write]. Als mony cifers schuld go before þat other, & he were write of cifers. And haue alle þe ylke cifers togedur in þi mynde, leaf 162 a. *[a-rowe] [ychoɳ] aftur other, and in þe last plase set þe nounbre þat comes of þe multiplicacioɳ of þe 2 digittes. And loke in þi mynde in what place he stondes, [where] in þe secunde, or in þe thryd, or in þe 4, or where ellis, and loke qwat þe figures by-token in þat place; & so mych is þe nounbre þat Another example. comes of þe 2 articuls y-multiplied to-gedur as þus: yf þou wold wete what is 20 thousant tymes 3 þowsande. multiply þe digit of þat articulle þe quych is 2 by þe digitte of þat oþer 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. certainly 4 cifers schuld go to 20 þowsant. ffor þis figure 2 in þe fyrst place betokenes twene. Notation. ¶ 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 hit betokenes twenty þousant. þerefore he most haue 4 cifers a-fore hym þat he may stonde 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 162 b. *goɳ 3 cifers afore. Now cast ylke 4 cifers þat schuld go to twenty thousant, And thes 3 cifers þat schuld go afore 3 thousant, & sette hem in rewe ychoɳ after oþer in þi mynde, as þai schuld stonde in a tabulle. And þen schal þou haue 7 cifers; þen sett þat 6 þe quych comes of þe multiplicacioɳ of þe 2 digittes aftur þe ylke cifers in þe 8 place as yf þat hit stode in a tabul. And loke qwat a figure of 6 schuld betoken in þe 8 place. yf hit were 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. Notation again. ¶ 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 thousantes. ¶ In þe 8 place sexty þowsant thousantes. þerfore sett 6 in octauo loco, And he schal betoken sexty þowsant thousantes. Mental multiplication. And so mych is twenty þowsant tymes 3 thousant, ¶ And þis rewle is generalle for alle maner of articuls, Whethir þai be hundryth or þowsant; but þou [most] know well þe craft of þe [wryrchynge] in þe tabulle leaf 163 a. *or þou know to do þus in þi mynde aftur þis rewle. Thou most þat þis rewle [holdyþe] [note] but where þere ben 2 articuls and no mo of þe quych ayther of hem hase but on figure significatyf. As twenty tymes 3 thousant or 3 hundryth, and such oþur.
¶ Articulum digito si multiplicare oportet
Articuli digit[i sumi quo multiplicate]
Debemus reliquum quod multiplicatur ab illis
Per reliquo decuplum sic summam latere nequibit.
The third case of the craft; ¶ Here he puttes þe thryde rewle, þe quych is þis. yf þou wel multiply in þi mynde, And þe Articul be a digitte, þou schalt loke þat þe digitt be with-Inne an hundryth, þen þou schalt multiply the digitt of þe Articulle by þe oþer digitte. And euery vnite in þe nounbre þat schalle come þere-of schal betoken ten. As þus: an example. yf þat þou wold wete qwat is twyes 40. multiplie þe digitte of 40, þe quych is 4, by þe oþer diget, þe quych is 2. And þat wolle be 8. And in þe nombre of 8 ben 8 vnites, & euery of þe ylke vnites schuld stonde for 10. þere-fore þere 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 163 b. *worch as þou dyddyst afore, saue þou schalt rekene euery vnite for a hundryth.
¶ In numerum mixtum digitum si ducere cures
Articulus mixti sumatur deinde resoluas
In digitum post fac respectu de digitis