[Albrecht Heeffer]
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Sources in the history of algebra: arithmetical and recreational problems

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Conspectus of problems from: Tractatus algorismi.
Transcription by: Høyrup, Jens (2000) Jacobus de Florentia, Tractatus algorismi (1307), the chapter on algebra (Vat. Lat. 4826, fols 36v–45v), Centaurus, .



JFA002
Make two parts of 10 for me, so that when the larger is divided by the lesser, 100 results from it.
(p. 28v)



JFA003
There are three companions, who have gained 30 libre. The first companion put in 10 libre. The second put in 20 libre. The third put in so much that 15 libre of this gain went to him. I want to know how much the third companion put in, and how much of the gain goes to each of the other two companions.
(p. 36v-37r)



JFA005
And I shall say thus: find me two numbers that are in the same proportion as is 2 of 3: and when each of them is multiplied by itself, and one multiplication is detracted from the other, 20 remains. I want to know which are these numbers.
(p. 37v)



JFA007
Find me 2 numbers that are in the same proportion as is 4 of 9. And when one is multiplied against the other, it makes as much as when they are joined together. I want to know which are these numbers.
(p. 37v-38r)



JFA009
One lends to another 100 libre at the term of 2 years, to do at the end of year. And when the two years came to an end he gave back to him 150 libre. I want to know at which rate the libra was lent a month.
(p. 38r-38v)



JFA010
And there are two men that have denari. The first says to the second: If you gave me 14 of your denari, and I threw them together with mine, I would have 4 times as much as you. The second says to the first: if you gave me the root of your denari, I would have 30 denari. I want to know how much each man had.
(p. 39r)



JFA012
Make two parts of 10 for me, so that when the larger is multiplied against the lesser, it shall make 20. I ask how much will be each part.
(p. 39r)



JFA013
Somebody makes two voyages, and in the first voyage he gains 12. And in the second voyage he gains at that same rate as he did in the first. And when his voyages were completed, he found to have 54, gains and capital together. I want to know with how much he set out.
(p. 39r)



JFA014
Make two parts of 10 for me, so that when one is multiplied against the other and above the said multiplication is joined the difference which there is from one part to the other, it make 22. I ask, how much will be each part.
(p. 40v)



JFA016
Somebody has 40 gold florins and changed them to Venetians. And then from these Venetians he withdrew 60 and changed them back into florins at one Venetian more per florin than he changed them at first for me, and when he has changed thus, he found that the Venetians which remained with him when he detracted 60, and the florins he got for the 60 Venetians, joined together made 100. I want to know how much was worth the florin in Venetians.
(p. 41v)



JFA031
A man has 100 staia of grain that is worth 20 soldi the staio, and grain that is worth 12 soldi the staio. Now it happens accidentally that he wants to put, of that which is worth 12 soldi the staio, so much above that which is worth 20 soldi the staio that, thus blended, it be worth 18 soldi the staio. I want to know how much of it he will put to it.
(p. 42v)



JFA032
Somebody is in a warehouse 3 years, and in the first and third year together he gets a salary of 20 florins. And the second year he gets 8 florins. I want to know precisely what he received the first year and the third year, each one by itself.
(p. 43v)



JFA033
Somebody is in a warehouse 4 years, and in the first year he got 15 gold florins, and the fourth he got 60 florins. I want to know how much he got the second year and the third at that same rate.
(p. 44r)



JFA034
Somebody is in a warehouse 4 years. And in the first year and the fourth year together he got 90 gold florins. And in the second year and the third year together he got 60 gold florins. I want to know what resulted for him, each one by itself.
(p. 44r)



JFA035
Somebody is in a warehouse 4 years. And in the first year and the third together he got 20 gold florins. And in the second and the fourth year he got 30 gold florins. I want to know what went to him the first year and the second and the third and the fourth. And that the first be such part of the second as the third is of the fourth.
(p. 45r)