For each Arabic word, we give references to the text, and thus also to the translation. References to explanations of the word or concept in our commentary are preceded by a “C”. For words that were used in both technical and non-technical ways, we include references to both. The listing follows the alphabetical order of the roots of the words.
| ا | |
 |
āḥād: units, 65.2, 65.8, 68.19, 69.3,16. C65.2. |
 |
uss: 1. index, 70.15, 71.12, 101.19, 107.12. C68.18. |
| 2. power, 225.1,8, 226.3, 227.15, 229.19. C68.18. | |
 |
illā: less, 76.19, 86.11, 140.2, 173.18, 219.5. C141.7, C173.10, C219.4. |
 |
imām: denominator, 94.12, 120.1, 135.12, 138.1, 170.10, 206.6. C93.6. |
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awwal: prime, 66.7. C66.7. |
| ب | |
 |
basaṭa: to numerate, 93.3, 134.1, 138.5, 145.9. C93.10. |
|
basṭ: numerator, 93.17, 137.13, 139.10, 142.8, 170.10. C93.10. |
 |
mabsūṭ: numerator, 144.6, 145.3, 151.2, 158.7. C93.10. |
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basīṭ (and related forms): simple, 66.9, 67.17, 69.15, 134.2, 217.8. C66.7. |
 |
mubʿʿiḍ: portioned, 137.1, 139.10. |
 |
baqiya: to leave, remain, 72.2, 85.5, 88.10, 113.4, 165.1, 229.19. C83.1. |
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bāqī: remainder, 72.7, 84.12, 90.9, 141.6, 176.2, 201.4, 216.2, 220.2, 231.6. C83.1. |
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baqiya: residue, 89.2, 90.5, 91.13, 92.6. C83.1. |
 |
bāqiya: residual, 92.1,12, 93.12. C83.1. |
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mutabāyna: 1. different (i.e., relatively prime), 122.13, 123.11. C122.2. |
| 2. incommensurable, 180.11, 182.5. C173.10. | |
| ث | |
 |
mustathnā (and related forms): excluded, 137.12, 140.1, 142.11, 183.17, 220.5, 230.1. C140.1, C173.10, C219.4. |
 |
mustathnā minhu (and related forms): diminished, 140.14, 141.3, 230.1. C140.1, C173.10, C219.4. |
| ج | |
 |
jabara: to restore, 129.6, 154.7, 217.3, 223.9. C129.1, C211.2, C219.4, C223.1. |
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majbūr: number to be restored, 129.8, 154.2. |
 |
majbūr ilayhi: restored number, 129.8, 154.2. |
 |
al-jabr: 1. restoration, 129.1, 154.1, 211.1,2, 217.5, 220.11. C129.1, C211.1, C220.5. |
| 2. algebra, 183.19, 189.3, 211.8. C191.1, C211.1. | |
 |
al-jabr wa l-muqābala: algebra, 191.4, 209.2. C191.1, C211.1, C223.1. |
 |
jadhr: 1. root (square root), 66.18, 68.12, 163.5, 173.5, 180.7, 187.11, 213.8,11, 214.12, 216.22. C213.7. |
| 2. root (unknown in algebra), 211.9,15, 212.8, 214.14, 215.12, 216.20. C213.7. | |
 |
majdhūr: has a root, 66.17, 164.2. C66.13. |
 |
majdhūra: has a root, 163.14, 166.14. C66.13. |
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jazaʾa: to partition, 184.10, 186.8. C65.2, C179.1, C186.8. |
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juzʾ: 1. part, 61.9, 94.11, 95.8, 117.2, 121.1, 127.2, 131.1, 134.6, 152.6, 172.2. C131.1. See also ajzāʾ ṣumm and ajzāʾ muḥāṣṣa. |
| 2. portion, 198.5, 199.4, 200.5, 202.1, 203.5. | |
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ajzāʾ: parts (from Euclid |
 |
jamaʿa: to add, 74.9, 86.15, 100.2, 134.8, 179.2, 201.11, 219.5. C73.2. |
|
jamʿ: addition, 73.1, 74.1, 80.20, 147.4, 176.11, 219.1. |
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majmūʿ: 1. sum, 71.20, 80.15, 100.3, 173.8, 198.17, 226.10. C73.2. |
| 2. addend, 74.18, 75.15, 76.5, 91.9, 179.11, 180.7. | |
 |
majmūʿ ilayhi: augend, 74.18, 91.9, 147.6, 180.7. |
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jumla: sum, 79.6, 109.8. C73.2. |
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jins: species, 104.16, 105.4, 219.2, 220.1, 221.16; type, 117.9, 134.6; kind, 195.14, 211.3,6. C68.18. |
| ح | |
 |
ḥarf: 1. letter, 88.12, 89.1,6. C68.18. |
| 2. particle, 142.2, 173.16, 182.5, 220.1. C68.18. | |
| 3. conjunction, 142.10, 173.14, 180.11, 181.2. C68.18. | |
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maḥsūsa: sensible, 133.6. C133.3. |
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muḥāṣṣa: apportionment, 120.20. C120.20. |
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ajzāʾ muḥāṣṣa: apportioned parts, 121.1, 122.2. C120.20. |
 |
ḥaṭṭa: to reduce, 129.7, 155.13, 217.1. C129.1, C217.1. |
|
ḥaṭṭ: reduction, 129.1, 154.1, 217.5. C129.1, C217.1. |
 |
maḥṭūṭ: number to be reduced, 129.12, 154.4, 155.14. |
 |
maḥṭūṭ ilayhi: reduced number, 129.12, 154.2, 155.14. |
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ḥalla: to decompose, 68.15, 117.16, 120.1, 123.4. C68.11. |
|
ḥall: decomposition, 68.15, 117.2, 122.9. |
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ḥamala: to add, 71.18, 84.17, 108.10, 167.12, 200.4, 214.7, 216.11. C73.2. |
| خ | |
 |
mukhtalif: distinct, 136.8, 137.12, 139.1, 142.7, 145.14. C93.15, C136.8, C139.1. |
 |
mukhtalifa: difference, 73.20. |
| د | |
 |
dirham: 1. dirham (unit of currency), 95.10, 117.16, 158.2, 207.7. C211.8. |
| 2. dirham (unit in arithmetic/algebra), 219.3, 220.3, 221.13, 223.7, 228.3. C211.8. | |
 |
adaqq: finer, 94.11, 135.8, 136.7, 158.10. |
| ر | |
 |
rabaʿa: to square, 80.5, 112.17, 113.14, 214.7, 215.8, 232.3. |
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murabbaʿ: square, 66.17, 112.17, 164.17, 173.4, 211.10. C66.17. |
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tarbīʿ: squaring, 79.18, 80.10, 112.16. |
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martaba: rank, 65.1, 68.18, 74.22, 174.2, 180.6, 230.14. C68.18, C174.1. |
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radda: transform, 143.1, 180.1,6, 184.9, 188.2, 228.8. C179.20. |
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rakiba: 1. to compose (numbers), 122.13, 123.5. C66.7, C68.11. |
| 2. to combine (a proportion), 121.23, 196.17, 204.2. C196.16. | |
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murakkaba (and related forms): 1. composed; composite; composition (numbers), 66.12,16, 68.1, 120.1, 127.4,12, 128.2. C66.7. |
| 2. composite (equations), 211.14, 212.6, 217.1. C211.13, C219.4. | |
| ز | |
 |
zawj: even, 65.6. |
 |
zawj al-zawj: evenly-even, 65.12. C65.10. |
 |
zawj al-fard: evenly-odd, 65.17. C65.10. |
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zawj al-zawj wa l-fard: evenly-evenly-odd, 66.1. C65.10. |
 |
zāda: 1. to add, 71.13, 110.2, 113.17, 175.7, 204.19, 220.10. C73.2. |
| 2. to exceed, 77.6, 108.9, 169.12. C73.2. | |
 |
zāʾid: 1. appended, 87.11, 183.19, 189.3, 211.5, 228.9. C219.4. |
| 2. exceeds, 198.15, 200.6, 201.9, 203.5. C219.4. | |
 |
ziyāda: added; additional; excess, 77.7, 108.13, 115.5, 200.6. |
| س | |
 |
musaṭṭaḥ: 1. surface (in arithmetic), 67.3, 80.10, 182.5, 225.6, 231.14. C66.17. |
| 2. surface (in geometry), 133.7. C66.17. | |
 |
saqaṭa: to drop, 76.13, 109.17, 123.4, 140.11, 166.17, 175.13, 199.4, 216.18, 231.4. C83.1. |
 |
ism: 1. name, 59.1, 66.13, 67.16, 69.15, 71.6, 134.1, 157.9, 229.5. C68.18. |
| 2. term, 173.5, 174.5, 176.1, 211.12, 217.2, 225.1, 229.15. | |
 |
dhū l-ismīn: binomial (lit., “two unified names”), 173.13, 175.11, 180.13, 188.18. C173.10. |
 |
sammā: to denominate, 94.1, 108.9, 121.15, 166.9, 181.16, 187.1. C93.6. |
 |
tasmiya: denomination, 93.6, 109.7, 118.15, 151.1. C118.14. |
 |
musammā: denominated number, 94.3, 124.8, 153.5. C93.6. |
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musammā minhu: denominating number, 93.6, 123.18, 153.5, 181.18. C93.6. |
| ش | |
 |
ishtirāk: common divisor, 122.4, 146.3, 153.10, 230.11. C122.2. |
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shayʾ: thing, 211.8, 213.7, 219.10, 225.2, 227.20. C211.8. |
| ص | |
 |
ṣaḥīḥ: 1. whole; whole number, 61.10, 65.2, 92.15, 149.2, 154.10, 163.1, 207.10. |
| 2. posited number, 198.14, 199.14, 200.10, 201.10. See footnote in translation at 198.14. | |
 |
ṣarafa: to convert, 157.10, 158.9. C157.1. |
|
ṣarf: conversion, 95.8. |
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masrūf: fraction to be converted, 158.7,12, 159.1. |
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masrūf ilayhi: converted fraction, 158.1,8,12. |
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taṣfīr: voiding, 114.7. C74.17. |
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ṣifr: zero, 69.9, 75.5, 84.1, 98.22, 112.8, 114.4, 119.13, 170.8. C74.17. |
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aṣamm: deaf (i.e., prime), 127.5,14, 128.12. C66.7, C134.2. |
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ajzāʾ ṣumm: deaf parts (i.e., prime), 66.9, 126.2, 127.9, 128.12. C134.2. |
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ṣanf: kind, 207.8, 208.8. C68.18. |
| ض | |
 |
ḍaraba: to multiply, 71.13, 95.10, 96.3, 129.3, 183.2, 211.11, 226.9. |
|
ḍarb: 1. multiplication, 92.8, 95.1, 98.4, 103.18, 157.11, 225.1, 227.6. C95.2, C149.2, C183.4, C225.1. |
| 2. variety, 65.6, 66.15, 67.17; type, 73.3,10, 83.2, 170.14, 211.1,14, 214.3, 223.6; kind, 95.15, 98.4. C68.18. | |
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maḍrūb: 1. multiplicand, 92.12, 95.4, 96.4, 99.17, 102.4, 149.4, 226.9. |
| 2. multiplication, 93.3, 98.9. | |
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maḍrūb fīhi: multiplier, 92.12, 95.4, 96.4, 101.1, 103.4, 149.4, 226.9. |
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ḍaʿafa: to duplicate, 149.5, 186.1. |
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taḍʿīf: duplication; duplicating, 95.2,5, 114.7, 149.2, 184.10, 186.1. C74.17, C95.2, C149.2, C179.1, C186.1. |
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ḍilʿ: side, 66.18, 67.2,13, 68.9,12. C66.17. |
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ḍāfa: 1. to add, 97.15, 102.6, 105.3, 110.10, 215.18. C73.2. |
| 2. to attach, 124.5, 135.1, 144.4. | |
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muḍāf: combined, 137.14. C137.13. |
| ط | |
 |
ṭaraḥa: 1. to subtract, 76.4, 83.7, 84.2, 147.1, 179.1, 211.3, 220.1, 221.1. C83.1. |
| 2. to cast out, 87.18, 88.1, 91.2, 125.16. | |
|
ṭarḥ: 1. subtraction, 83.1, 91.12, 147.3, 176.11, 211.7, 219.1. C83.1,2, C219.4. |
| 2. modulus, 91.13, 125.6, 126.3, 127.1. | |
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maṭrūḥ: subtrahend, 83.6, 86.15, 148.1, 182.1, 220.13. |
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maṭrūḥ minhu: minuend, 83.6, 86.4, 91.12, 148.1, 220.10. |
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munṭariḥa (and related forms): cast out entirely, 87.22, 88.6, 125.8,9, 126.1, 127.1. |
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maṭlūb: required number, 76.14, 101.14, 147.12, 171.3, 198.18, 220.17, 228.13, 231.12. |
| ع | |
 |
ʿadda: to count, 66.8, 127.11, 128.1,12, 166.1. C127.9. |
 |
ʿadad: number, 61.9, 65.2, 68.18, 69.15, 71.13, 73.2, 133.1, 163.3, 170.7, 173.13, 211.8. C65.2, C219.1. |
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ʿidda: number, 79.1,3,10. |
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ʿadala: to equal, 211.13,15, 216.13, 223.2, 227.14, 227.16, 228.1. C211.13, C213.7. |
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muʿādala: 1. equation, 217.2,4, 227.16,18, 228.2. C213.7. |
| 2. equalization, 211.5, 220.11, 221.8. C213.7. | |
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mutaʿādilān: two sides of [the] equation, 220.8, 223.1. |
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ʿaqd: power of ten (lit., “bent finger-joint”), 87.17, 109.19, 110.7, 111.3. C110.5. |
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maʿqūl: intelligible, 133.6. C133.3. |
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ʿilla: cause, 87.11. |
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ʿalā: to surpass, 121.6. C73.2. |
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maʿnā: meaning, 68.12, 94.12, 95.5,9,11,13, 113.2, 117.9, 211.1, 213.8. C95.3. |
| ف | |
 |
fard: odd, 65.6. |
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mufrad (and related forms): simple, 109.20, 137.13, 211.14, 213.2. C137.13, C211.13. |
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munfaṣila: detached, 141.9, 142.8,13. C141.7. |
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munfaṣil: 1. apotome, 173.4, 173.16, 176.4,18, 182.9, 188.18. C173.10. |
| 2. discrete, 117.4, 133.8. C117.2, C133.3. | |
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faḍala: to exceed, 78.1,7. C73.2. |
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faḍl mā bayna: difference between (sometimes just mā bayna or faḍl bayna), 78.2, 111.21, 173.9, 197.1, 201.1, 204.14, 229.5. |
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tafāḍul (and related forms): disparity, 73.7,15, 76.7, 79.1. |
| ق | |
 |
qabila: 1. to confront, 198.10, 199.5, 207.3, 217.7, 221.19, 223.9. C223.1. |
| 2. to match, 99.18. | |
 |
muqābala: confrontation, 199.6,12, 211.3, 221.8. C211.1, C220.5. |
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qadr: size (of a ratio), 124.6. |
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taqrīb: approximation, 166.12, 168.6, 169.1, 173.2. |
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qasama: to divide, 61.10, 65.2, 72.1, 93.10, 117.16, 118.1, 119.18, 151.4, 187.2, 189.1, 229.2,12,16, 230.13. C117.2. |
|
qism: 1. kind, 65.2, 73.6; type, 82.1, 95.3, 157.11; variety, 163.2. C68.18. |
| 2. part, 118.8, 139.1, 144.8, 202.4,10. | |
 |
qisma: division, 72.1, 117.2, 118.14,15, 120.20, 151.4, 188.18, 229.6. C68.18, C95.2, C117.2,9, C118.14, C230.11. |
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maqsūm: dividend, 93.14, 117.8, 119.2, 151.5, 152.14, 187.3, 229.2,14. C93.6. |
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maqsūm ʿalayhi: divisor, 93.6, 117.2, 118.4,18, 119.7, 151.5, 181.15, 188.7, 229.3,18. C93.6. |
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munqaṭiʿ: disconnected, 140.1,18, 143.1. C140.1. |
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qānūn: basic rule, 170.7, 191.1. |
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quwwa: area (lit., “power”), 177.8,14. C163.4, C177.5. See also munṭaq fī l-quwwa below. |
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maqām: denominator, 122.15, 171.2. C93.6. |
 |
qiyās: rule, 175.18, 183.10, 184.7, 187.18. |
| ك | |
 |
kasr: fraction, 65.2, 93.15, 133.4, 134.1, 135.10, 143.5, 154.6, 157.4, 170.10. C65.2, C131.1, C133.3, C134.2. |
 |
mukaʿʿab: cube, 67.12,15, 68.14,15, 74.1, 80.2. C67.12, C211.8. |
 |
kaʿb: 1. cube root, 67.13,16, 68.9,12. C67.12. |
| 2. cube (the third power in algebra), 221.1, 225.2,13, 226.7, 227.10, 229.8. C67.12, C211.8. | |
 |
kamm (and kammīya): quantity, 73.17, 93.5. C73.17, C92.17. |
 |
kayf (and kaifīya): quality, 73.7, 93.5. C73.17, C92.17. |
| م | |
 |
māl: 1. quantity, 199.1,19, 200.1, 201.1, 203.13, 213.8,14, 215.7. C211.8. |
| 2. māl (the second power in algebra), 211.8,15, 213.7, 214.9, 215.12, 225.4,8, 226.1. C211.8. | |
| ن | |
 |
nazala: to remove, 114.8, 123.1, 142.2, 146.3, 221.5. C83.1. |
 |
manzila: place, 69.1,17, 71.8,19, 76.18, 83.10, 90.4, 112.6, 164.1. C68.18. |
 |
nisba: 1. ratio, 73.8, 78.4, 108.10, 113.10, 117.5, 123.21, 124.6, 133.3, 163.3, 195.7. C131.1, C133.3, C193.1. |
| 2. proportion, 121.23, 191.4, 195.2. C193.1, C195.2. | |
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nisba ʿadadiyya: arithmetic progression, 73.17, 74.5. |
 |
nisba handasiyya: geometric progression, 73.7, 78.13. C73.17. |
 |
muntasib: related, 135.10, 138.1, 139.4. C135.1,10. |
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munṭaq: rational (lit., “expressible” in speech), 163.2, 167.9, 172.10, 174.2, 177.8, 183.10. C134.2. |
 |
ghayr munṭaq: surd (lit., “inexpressible”), 163.2,4,6. C163.2. |
 |
munṭaq fī l-quwwa: rational in square (lit., “expressible in power”), 163.7, 180.7, 188.7. C163.4. |
 |
naqaṣa: to subtract, 112.9, 168.14, 173.6, 183.16, 204.10, 215.4, 232.8. C83.1. |
 |
nāqiṣ: 1. deleted, 87.11, 189.3, 211.5, 220.10, 228.9. C219.4. |
| 2. falls short, 198.12, 199.7, 202.7, 205.19. C219.4. | |
 |
tanqīl (and related forms): shifting, 95.16, 97.3, 98.8, 99.14, 157.7. |
 |
muntahā ilayhi: upper extreme, 79.13, 80.5,20, 81.2, 82.2. |
 |
nāfa: excess, 108.9. |
 |
nawʿ: species, 65.10, 66.7, 71.13, 211.3,8, 220.5, 226.9; kind, 66.16, 67.18, 157.2, 158.1, 195.2; type, 92.15, 97.1, 99.14, 118.14, 207.9. C68.18. |
| و | |
 |
wa: and, C219.1. |
 |
muwassaṭ (and mutawassit): medial, 163.8, 176.14, 180.8, 187.10, 188.7. C163.4. |
 |
muwassaṭayn: bimedial, 176.13,18, 177.14. C176.10. |
 |
waṣala: to join (i.e., form a binomial), 174.15, 175.1,3,5,7,9. C173.10. |
 |
muttaṣil: 1. continuous, 117.6. C117.2, C133.3. |
| 2. connected, 140.14,16, 141.9, 143.1. C140.14. | |
| 3. joining, 177.9,15. C173.10. | |
| 4. binomial (lit., “joining”), 188.19,20, 189.12,14. C173.10. | |
 |
muttaṣila: connected, 142.2,8,11. C140.14. |
 |
mawdhiʿ: place, 108.12, 109.5. C68.18. |
 |
wafiqa: to reconcile (i.e., cancel common factors), 120.3,17, 123.1,5. C119.18. |
 |
ʿalā tawālī: consecutive; consecutively, 79.13,15, 80.2,5, 81.16, 89.6. |