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Mathematics: A Cargo of Pepper (p. 1b)


Mathematics: A Cargo of Pepper (p.01b)


Michael's manuscript starts with 180 pages of commercial mathematics. Many entries demonstrate the different mathematical techniques Michael could use to solve problems. The problem here concerns the value of a cargo of pepper. Pepper was one of the most important commodities traded by the Venetians, for which medieval merchants often had to calculate prices and profits. In dealing with such problems, Michael typically uses three different methods of calculation to get the same answer. In this case, he starts with the rule of three. Next he uses algebra. Then he uses the method of double false position.

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+ Ihesus + El chargo del piper, el qual è libre 400, val ducati 49 1/2, per libre 315 quanti duchati averò? E per farla per la riegola del 3 diremo: “Se 400 libre me dà duchati 49 1/2, che me darà libre 315?” Primo moltipicha per lo muodo vedirì qui de sutto e puo' parti. [NOTE FOR TEAM: What is the best method for replacement?] 40049 1/231540099315315 283531185121992835 18840 800 2318840 314078531185 800 381570 880 1320 24 14080 440 32 14080 800 17 480/800Monta duchati 38, denari 23, pizulli 17 480/80018840 E per voler far la ditta raxion per la chossa, questo intra in lo primo cha- pitolo dove dize: “Chosa ingual al numero, se die partir lo numero per le chosse”. Esempio dela raxion sovra scritta. Pony che valese 1co. Adoncha se die dir: “Se 1co me dà libre 315, che me darà duchati 49 1/2, che son 99/2. Adoncha moltipicha 99/2 chon 315/1, fa- no 31185, e può moltipicha 400 fia 1co, fa 400co. Puo' par- ti 31185 per 2, serano 15592 1/2. Parti li numeri per le chose, zoè per 400co, insirà duchati 38. Lo romagnente moltipichado per 24 e par- tido per 400co serano denari 23. E lo ruto moltipichado per 32 e partido per 400co insirà pizulli 17. E questa serà ingual a quela de sovra. E per far la ditta raxion per impoxizion pony che avesemo posto ala pri- ma impoxizion 10, e diremo: “Se 400/1 me dà 99/2, che me darà 315/1?” Se moltipicho 315/1 unità chon 99/2 farano 15592 1/2.” Mo' si mo- ltipicho 400 ch'è lo partidor chon 10 che ò posto a l'inpoxizion, me die venir 15592 1/2, e mi so che non ò se non 4000. Adoncha sotra- zi 4000 de quello, vien a romanir 11592 1/2 e meto che questo sia men. E per la segonda inpoxizion mettemo che la fose 20, e per lo simile muodo moltipichemo 99/2 chon 315/1, fano 15592 1/2, e moltipicha 20 fia 400

+Jesus+ If a load of pepper which weighs 400 pounds is worth 49 1/2 ducats, for 315 pounds how many ducats will I have? And to do this by the rule of three, we will say, “If 400 pounds gives me 49 1/2 ducats, what will 315 pounds give me?” First multiply by the method you will see below and then divide. 400 49 1/2 315 400 99 315 315 2835 31185 1 2 1 99 2835 18840 800 23 18840 3140 785 31185 800 38 1570 880 1320 24 14080 440 32 14080 800 17 480/800 It results in 38 ducats, 23 denari, 17 480/800 piccoli. 18840 And to do this problem by algebra, this is covered in the first chap- ter where it says “unknown equal to the number, the number should be divided by the unknowns.” For example, the problem given above. Put that it was worth 1co. Then you should say, “If 1co gives me 315 pounds, what will give me 49 1/2 ducats, which is 99/2?” Then multiply 99/2 by 315/1, which makes 31185, and then multiply 400 times 1co, which makes 400co. Then di- vide 31185 by 2; it will be 15592 1/2. Divide the numbers by the unknowns--that is, by 400co--the result will be 38 ducats. The remainder multiplied by 24 and di- vided by 400co will be 23 denari. And the fraction multiplied by 32 and divided by 400co will result in 17. And this is equal to the solution above. And to solve the problem by false position, put that we had put 10 at the first false position, and we will say, “If 400/1 gives me 99/2, what will 315/1 give me?” If I multiply 315/1 digits with 99/2 it will make 15592 1/2. Now if I mul- tiply 400, which is the divisor with the 10 that I put at the false position, I should get 15592 1/2, and I have only 4000. So sub- tract 4000 from this, which leaves 11592 1/2 and put that this is minus. And for the second false position let's say that it was 20, and by a similar method we multiply 99/2 by 315/1, which makes 15,592 1/2, and multiply 20 by 400