Sources in the history of algebra: arithmetical and recreational problems

Conspectus of problems from: Kitāb, fī al-jābr wa’l- muqābala.
Transcription by: Levey, Martin (1966) The Algebra of Abu Kamil. Kitab, fi al-jabr wa’l- muqabala in a Commentary by Mordecai Finzi, The University of Wisconsin Press, Madison, Wis..

AKH01 Multiply one by the other. Multiply the larger part by itself. The part multiplied by itself equals the product of the one part by the other plus its ½. (p. 110v)
AKH02 The second question is that 10 is divided into two parts. Multiply one of them by itself. Multiply 10 by itself, [it is] equal to the result of the multiplication of one of its parts by itself multiplied by 6 ¼ . (p. 111v)
AKH03 The third question is that 10 is divided into two parts. Divide the larger by the smaller part, it is equal to 4. (p. 112r)
AKH04 The fourth question is that 10 is divided into two parts, the smaller part multiplied by 9 and the larger by itself. They are then equal. (p. 112r)
AKH05 The fifth question is that 10 is divided into two parts. Multiply one by the other to get 21. (p. 113r)
AKH06 In the sixth question, add 8 to a root and multiply the sum by 4. It equals the square multiplied by itself. (p. 113v)
AKH07 If one should ask that 10 be divided into two parts, multiply every part by itself and subtract the product of the smaller part from the product of the larger, there remains 80. (p. 114r)
AKH08 If one says that 10 be divided into two parts, divide one by the other and the fractions come to 4 and ¼. (p. 114v)
AKH09 A problem is one says 10 is divided into two parts. Every one of them is divided by the other. Subtract one from the other to get 5/6. (p. 117r)
AKH10 A problem is if one says that 50 was divided among a certain number of men. Increase the number of men by 3 and divide 50 among all of them. For every one of the last ones, it comes out to less than what would come out for each of the first ones by 3 ¾. (p. 117v)
AKH11 One says that 10 be divided among men so that every one receives something. Add 4 men and divide 30 among them. For every one of them, the share is 4 less than what came to the former. (p. 118v)
AKH12 If one says that 10 be divided among men, every portion is a thing. Increase them by 4 men and divide 60 among them. Then each one receives 5 more than each of the former would have. (p. 119r)
AKH13 If one says that 60 is divided [among men] equally. Add 3 men and divide 20 among them. Then each portion is less than the first by 26. (p. 120r)
AKH14 When one says that 20 is divided among men equally, add 2 men to these and divide 60 among them, there then comes as a portion to each of the men, 5 more than each of the former received (p. 121r)
AKH15 If one says 10 is divided among men equally, when 6 men are added, then they share 40 among them and each receives as much as each of the former. (p. 121r)
AKH16 One says that 10 garments were purchased by 2 men at a price of 72 dirhams. Each one gave 36. The garments are varied in value. One of the men buys 36 dirhams worth of the garments and the other buys the remainder of the garments for 36 dirhams. The price of each garment of one man is 3 dirhams more than the price for each gar­ment of the other. (p. 121v-122r)
AKH17 If one says, 10 is divided into two parts, and also one part is multiplied by 6, and the product is divided by the other part, then take 3 the quotient and add it to the product of the one part by 6, then it equals 56 (p. 122v)
AKH18 One says : a value less its 1/3 and 2, then all of it multiplied by itself gives the value plus 24. (p. 123r)
AKH19 One says : 3 roots of. a magnitude plus 4 roots of the difference between the magnitude and the 3 roots equals 20. (p. 123r)
AKH20 One says to subtract its 1/3 from an amount, then multiply the difference by 3 roots of the first amount, then it equals the first amount (p. 124r)
AKH21 One says that its 1/3 is subtracted from an amount and the difference multiplied by 3 roots of the remainder of the amount, then the amount is obtained. One knows that when one subtracts its 1/3 from an amount, then the remainder is its 2/3. (p. 124r)
AKH22 If one says that there are 3 roots of an amount, then 2 roots of the remainder of this from the amount equals the difference. (p. 124v)
AKH24 If one says that 10 is divided into two parts, and one part is divided by the other, then the divisor added to the fraction equals 5 ½ . (p. 124v)
AKH25 If one says that 10 is divided into two parts, and one part is divided by the other part, and the fraction taken and added to the number which was divided, and then the sum multiplied by the divisor, it equals 30 (p. 125r)
AKH26 If one says that 10 is divided into two parts, and one part is divided by the other and the fraction multiplied by its numerator, it gives 9 (p. 125r)
AKH27 If one says that if 10 is divided into two parts and one is divided by the other, then the quotient is multiplied by itself and then by the divisor, it equals 32 (p. 125r)
AKH28 If one says that 10 is divided into two parts, and one part is divided by the other, and the quotient multiplied by the difference between the dividend and divisor, it equals 24. (p. 125v)
AKH29 If one says that 10 is divided into two parts, each of them divided by the other, then the sum of the two quotients multiplied by one of the two parts of 10 is equal to 34. (p. 126r)
AKH30 If one says that 10 is divided into two parts, and the larger part is divided by the smaller, add the result of the quotient to 10 and multiply the sum by the smaller part to give 46. (p. 126v)
AKH31 If one says that 10 is divided into two parts, the larger part is divided by the smaller, and the quotient is added to 10, and the sum is multiplied by the larger part, then it is equal to 69. (p. 127r)
AKH32 If one says to you that 10 is divided into two parts, and the larger is divided by the smaller, and the smaller by the larger, and the sum of the quotients is added to 10, and the sum multiplied by the larger part, all this is equal to 73 (p. 127v)
AKH33 If one says that 10 is divided into two parts, each of them divided by the other, [take the difference between one part and the other], multiply it by the other and it will come to 5. (p. 128v)
AKH34 One says that 10 is divided into two parts, and the larger is divided by the smaller, and the quotient is then added to the larger, the smaller divided by the larger and the quotient added to the smaller. Multiply one by the other to get 35. (p. 129r)
AKH35 If one says that 10 is divided into two parts, and the larger is divided by the smaller and the result added to 10, [and the smaller divided by the larger and the result added to 10], then each sum is multiplied one by the other, it comes to 122 2/3. (p. 130r)
AKH36 If one says that 10 is divided into two parts, the larger being divided by the smaller, and the result added to 10, and then the smaller is divided by the larger and the quotient subtracted from 10, and theft one is multiplied by the other, it will equal 107 1/3. (p. 130r-130v)
AKH37 If one says that 10 is divided into two parts, and one part multiplied by itself and the other by the root of 8, and subtract the quantity of the product of one part times the root of 8 from the quantity the product of the other part multiplied by itself, it gives 40 (p. 130v)
AKH38 One says that 10 is divided into two parts, and the products­, one by the root of 10, and the other by itself are equal. (p. 131r)
AKH39 If one says that 10 is added to an amount, and the sum is multiplied by the root of 5, then one gets the product of the amount by itself. (p. 131v)
AKH40 If one says to you that two magnitudes have a difference between them of 5, multiply the larger number by itself and by 10 and take the root of the product, then it will equal the product of the smaller by itself. (p. 131v)
AKH41 If one says that if a magnitude be multiplied by 2 magnitudes like it and its root taken and 2 added to it, then the total, multiplied by the magnitude, is equal to 30. (p. 132r)
AKH42 If one says that 10 is divided into two parts, each one is divided by the other, then the sum of the quotients equals the root of 5. (p. 132v)
AKH43 If one says that 10 is divided into two parts, each is divided by the other, and the products of each of the quotients by itself, then when added, gives 3 as a sum (p. 134r)
AKH44 If one says that 10 is divided into two parts, each of which is divided by the other, and when [the quotient of the smaller divided by the larger] is subtracted from the quotient of the larger divided by the smaller, then there remains 6. (p. 134r-134v)
AKH45 One says that 10 is divided into two parts, each of which is divided by the other, and when each of the quotients is multiplied by itself, and the smaller is subtracted from the larger, then there remains 2. (p. 134v)
AKH46 One says that 2 of its roots plus 10 is subtracted from an amount, then the difference multiplied by itself to equal 8 amounts. (p. 135v)
AKH47 If one says that 2 of the roots of an amount plus a root of 2 the amount plus a root of its 3 is equal to the amount, how large is the amount (p. 136r)
AKH48 If one says that 2 roots of an amount plus a root of its 2 plus a root of its a equals 20, how much is the amount? For the solution, make the amount as a square, take 2 of its roots plus the root of its 2 plus the root of its 3. It will be 2 things plus the root of its 2 plus the root of its 3 equal to 20. Subtract (p. 136r)
AKH49 If one says that an amount is added to 4 of its roots plus the root of its 2 plus the root of its 3, and then it equals 10, what is the amount ? (p. 136r)
AKH50 If one says that to an amount add its root and the root of its 2, and multiply the sum by itself, then it is 5 times the amount. (p. 136v)
AKH51 If one says that to an amount is added its root, and the root of its 2, and the sum is multiplied by itself, then this equals 20. (p. 136v)
AKH52 If one says that to an amount, the root of its 2 is added and the result multiplied by itself, then it gives 4 times the amount. (p. 136v)
AKH53 If one says that 2 amounts are equal, and the root of 3 is added to one of them, and the root of 2 to the other, and one sum is multiplied by the other, then it equals 20. (p. 137v)
AKH54 If one says that 7 is added to an amount, and the sum multiplied by the root of 3 times the amount, then it is equal to 10 times the amount. (p. 137v)
AKH55 If one says that to an amount is added the root of 3 times [of] it, and the sum multiplied by the root of 2 amounts, it will equal 4 times the amount. (p. 138v)
AKH56 If one says that 3 is added to the root of 2 an amount, and to the root of its 2, 2 is added, then the multiplication of one by the other is 20. (p. 139v)
AKH57 One says that an amount is multiplied by the root of 10 and then divided by the sum of 2 plus the root of 3, then it comes to the amount less 10 (p. 141r)
AKH58 If one says that there are two amounts, and that one is 3 times the other, add to each one its root and then multiply the sums, then it will equal 10 times the larger square. (p. 142r)
AKH59 If one says to take an amount then its root plus the root of its root plus the root of 2 of its roots plus the root of 5 times the amount is equal to 10. (p. 142v-143r)
AKH60 If one says that there are three unequal amounts and if the small one is multiplied by itself and the middle one multiplied by itself is added, it equals the large one by itself, and if the small one is multi­plied by the large one it equals the middle one multiplied by itself, and if the small one is multiplied by the middle one it equals 10. (p. 143v)
AKH61 One says that 10 is divided into three parts, and if [the small one is multiplied by itself and added to the middle one multiplied by itself, it equals the large one multiplied by itself], and when the small is multiplied by the large, it equals the middle multiplied by itself. (p. 144r)
AKH62 One says that 10 is divided into two parts. Add 2 of its roots to one part and subtract 2 of its roots from the other part. The results are equal. (p. 146r)
AKH63 One says that 10 is divided into two parts, and that 10 is divided by each of them. Their sum is 61. (p. 148v)
AKH64 One says that 10 is divided into two parts, and 10 is divided by each of the parts, then the quotients are multiplied one by the other to get 64. (p. 150v)
AKH65 It is known from what was said that when 10 is divided into two parts, and 40 is divided by each of the two parts, and then the quo­tients are multiplied, one by the other, it will equal 100. (p. 152v)
AKH66 If 10 is divided into two parts, and 50 is divided by one part, and 40 by the other, [and when the quo­tients are multiplied] it equals 125. (p. 152v)
AKH67 One says that 10 is divided into two parts, 10 is divided by each of them. Multiply one quotient by the other, then by itself, it is equal to 204. (p. 153r)
AKH68 One says that [the product of the quotients is] multiplied by itself to give 30.Then the root of 30 is the product of one quotient [by the other]. (p. 153r)
AKH69 One says that 10 is divided into two parts, each of the latter is divided into 40. The quotients when added and then the sum mul­tiplied by itself gives 625. (p. 153v)
AKK23 If one says to you that there are 3 roots of an amount, then 4 roots of what remains of this from the amount is equal to the amount of the difference plus 4. (p. 124v)