2348:
739:
I found myself before a problem that I solved and for which I discovered a great many solutions; looking deeper for its solutions, I obtained two thousand six hundred and seventy-six correct ones. My astonishment about that was great, but I found out that, when I recounted this discovery, those who
950:
is superior in the accuracy of its principle and the exactness of its argumentation. It thus behooves us, the community of mathematicians, to recognize his priority and to admit his knowledge and his superiority, as in writing his book on algebra he was an initiator and the discoverer of its
1531:
Hesitating progress-the slow development toward algebraic symbolization in abbacus-and related manuscripts, c. 1300 to c. 1550: Contribution to the conference" Philosophical
Aspects of Symbolic Reasoning in Early Modern Science and Mathematics", Ghent, 27–29 August
945:
I have studied with great attention the writings of the mathematicians, examined their assertions, and scrutinized what they explain in their works; I thus observed that the book by Muḥammad ibn Mūsā al-Khwārizmī known as
740:
did not know me were arrogant, shocked, and suspicious of me. I thus decided to write a book on this kind of calculations, with the purpose of facilitating its treatment and making it more accessible.
424:
1155:
526:
999:
758:
for non-mathematicians, like land surveyors and other government officials, which presents a set of rules for calculating the volume and surface area of solids (mainly rectangular
610:. A partial translation to Latin was done in the 14th century by William of Luna, and in the 15th century the whole work also appeared in a Hebrew translation by Mordekhai Finzi.
699:
2367:
595:
A number of
Islamic mathematicians wrote commentaries on this work, including al-Iṣṭakhrī al-Ḥāsib and ʿAli ibn Aḥmad al-ʿImrānī (d. 955-6), but both commentaries are now lost.
476:
334:
525:
The first chapter teaches algebra by solving problems of application to geometry, often involving an unknown variable and square roots. The second chapter deals with the
744:
According to
Jacques Sesiano, Abu Kamil remained seemingly unparalleled throughout the Middle Ages in trying to find all the possible solutions to some of his problems.
2666:
2356:
554:
365:
279:
252:
2636:
911:
and other works. Unmistakable borrowings, but without Abu Kamil being explicitly mentioned and perhaps mediated by lost treatises, are also found in
Fibonacci's
735:. The title is derived from a type of problems known in the east which involve the purchase of different species of birds. Abu Kamil wrote in the introduction:
574:
2631:
2402:
1771:
17:
2641:
907:, and as such had a lasting impact on the development of algebra. Many of his examples and algebraic techniques were later copied by Fibonacci in his
2063:
1754:
1432:
1801:
1472:
2661:
2488:
1763:
1346:
Robert of
Chester's Latin Translation of the Algebra of Al-Khowarizmi, with an Introduction, Critical Notes and an English Version
1602:
1058:
1399:
Tradition, transmission, transformation: proceedings of two conferences on pre-modern science held at the
University of Oklahoma
2409:
2550:
2241:
1557:
1406:
1328:
1294:
1229:
1167:
977:
2626:
2347:
2621:
2328:
2292:
2145:
1573:
1129:
628:. It is also the earliest known Arabic work where solutions are sought to the type of indeterminate equations found in
580:
as solutions and coefficients. The fourth chapter shows how these irrationalities are used to solve problems involving
2267:
1796:
1747:
1716:
1582:
1441:
1381:
1196:
1138:
1098:
1019:
839:
2287:
2210:
370:
2571:
340:
beside those of integers. For example, he uses the Arabic expression "māl māl shayʾ" ("square-square-thing") for
2246:
2205:
2190:
482:
was geared towards the general public, Abu Kamil was addressing other mathematicians, or readers familiar with
1621:
Yadegari, Mohammad (1978-06-01). "The Use of
Mathematical Induction by Abū Kāmil Shujā' Ibn Aslam (850-930)".
588:, problems of application in realistic situations, and problems involving unrealistic situations intended for
2381:
933:, defending him against Ibn Barza who attributed the authority and precedent in algebra to his grandfather,
2068:
2058:
2002:
1740:
1786:
934:
2503:
655:
2473:
2452:
2200:
2170:
1947:
1861:
1550:
An introduction to the history of algebra: solving equations from
Mesopotamian times to the Renaissance
1321:
An introduction to the history of algebra: solving equations from
Mesopotamian times to the Renaissance
652:
In this treatise algebraic methods are used to solve geometrical problems. Abu Kamil uses the equation
1826:
292:
2155:
1907:
577:
471:
is perhaps Abu Kamil's most influential work, which he intended to supersede and expand upon that of
167:
1007:
426:). One notable feature of his works was enumerating all the possible solutions to a given equation.
2226:
2185:
2053:
1937:
1607:
1597:
1063:
1053:
589:
1912:
576:
and accompanied with geometrical illustrations and proofs. The third chapter contains examples of
2595:
2590:
2580:
1887:
1882:
1424:
Issues in the Origin and
Development of Hisab al-Khata'ayn (Calculation by Double False Position)
448:
Almost nothing is known about the life and career of Abu Kamil except that he was a successor of
2519:
2195:
2180:
2114:
2043:
1221:
1215:
1089:
625:
585:
286:
282:
613:
2333:
2160:
2124:
843:
337:
224:
1732:
1705:
1429:
2651:
2646:
2498:
2447:
2323:
2302:
2175:
2083:
532:
343:
257:
230:
8:
2656:
2468:
2395:
1917:
1821:
1593:
1279:
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
1264:
Encyclopaedia of the history of science, technology, and medicine in non-western cultures
1211:
1189:
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
1049:
1856:
1373:
1366:
2600:
2555:
2529:
2478:
2119:
1997:
1932:
1691:
1654:
1646:
1511:
559:
519:
503:
193:
93:
1568:
1124:
430:
2545:
2524:
1962:
1851:
1712:
1683:
1658:
1638:
1578:
1553:
1503:
1466:
1402:
1377:
1324:
1290:
1225:
1192:
1163:
1134:
1094:
1015:
973:
197:
98:
1534:. Preprints. Vol. 390. Berlin: Max Planck Institute for the History of Science.
645:
2423:
2297:
2272:
1977:
1957:
1866:
1846:
1831:
1675:
1630:
1495:
1286:
1282:
763:
1426:. Eighth North African Meeting on the History of Arab Mathematics. Radès, Tunisia.
638:. However, Abu Kamil explains certain methods not found in any extant copy of the
2584:
2576:
2483:
2236:
2099:
2018:
1902:
1436:
786:, and other parameters for different types of triangles, rectangles and squares.
771:
603:
175:
2416:
2388:
2129:
2028:
2023:
1972:
1841:
1811:
799:
767:
759:
495:
747:
433:
2615:
2231:
2150:
1791:
1687:
1642:
1507:
1184:
1003:
821:
728:
602:, and some sections were incorporated and improved upon in the Latin work of
436:
classified Abū Kāmil as the second greatest algebraist chronologically after
2104:
1160:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
196:. He is considered the first mathematician to systematically use and accept
2262:
2078:
1836:
926:
850:
706:
615:
Book of Rare Things in the Art of Calculation (Kitāb al-ṭarā’if fi’l-ḥisāb)
472:
449:
437:
201:
78:
1448:
2374:
2318:
2073:
2038:
1967:
1093:. Vol. 1 (2nd ed.). Brill Academic Publishers. pp. 132–3.
913:
634:
515:
507:
188:—lit. "The Egyptian Calculator") (c. 850 – c. 930) was a prominent
2282:
2109:
1982:
1952:
1927:
1922:
1695:
1515:
629:
336:. He wrote all problems rhetorically, and some of his books lacked any
1650:
1396:
208:, thus allowing Abu Kamil an important part in introducing algebra to
2277:
2165:
2033:
1992:
1942:
1892:
1816:
904:
900:
783:
710:
599:
598:
In Europe, similar material to this book is found in the writings of
529:
found in Al-Khwarizmi's book, but some of which, especially those of
499:
289:. He illustrated the rules of signs for expanding the multiplication
205:
189:
151:
147:
1679:
1499:
642:. He also describes one problem for which he found 2,678 solutions.
460:
136:
Use of irrational numbers as solutions and coefficients to equations
2048:
1987:
1806:
1634:
1012:
Mathematics Across Cultures: The History of Non-Western Mathematics
779:
755:
732:
702:
621:
581:
511:
491:
220:
113:
1577:. Vol. 1. New York: Charles Scribner's Sons. pp. 30–32.
1133:. Vol. 1. New York: Charles Scribner's Sons. pp. 30–32.
620:
Abu Kamil describes a number of systematic procedures for finding
2493:
1183:
Mat Rofa Bin Ismail (2008), "Algebra in Islamic Mathematics", in
930:
855:
701:
to calculate a numerical approximation for the side of a regular
647:
On the Pentagon and Decagon (Kitāb al-mukhammas wa’al-mu‘ashshar)
216:
109:
227:
to work easily with algebraic equations with powers higher than
204:
to equations. His mathematical techniques were later adopted by
2368:
The Compendious Book on Calculation by Completion and Balancing
483:
209:
925:
Abu Kamil was one of the earliest mathematicians to recognize
1762:
899:
The works of Abu Kamil influenced other mathematicians, like
713:
knew about this treatise and made extensive use of it in his
1707:
A Mathematical History of Division in Extreme and Mean Ratio
1210:
774:). The first few chapters contain rules for determining the
556:, were now worked out directly instead of first solving for
1666:
Karpinski, L. C. (1914-02-01). "The Algebra of Abu Kamil".
1486:
Karpinski, L. C. (1914-02-01). "The Algebra of Abu Kamil".
775:
749:
On Measurement and Geometry (Kitāb al-misāḥa wa al-handasa)
1397:
Ragep, F. J.; Sally P. Ragep; Steven John Livesey (1996).
2430:
1430:
http://facstaff.uindy.edu/~oaks/Biblio/COMHISMA8paper.doc
1343:
2403:
Book on the Measurement of Plane and Spherical Figures
838:), which contains algebraic solutions for problems of
584:. The rest of the book contains solutions for sets of
1191:, vol. 1 (2nd ed.), Springer, p. 114,
727:
A small treatise teaching how to solve indeterminate
658:
562:
535:
373:
346:
295:
260:
233:
1569:"Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad ibn Shujāʿ"
1125:"Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad ibn Shujāʿ"
27:
Egyptian mathematician of Abbasid era (c. 850 – 930)
1182:
967:
1704:
1365:
693:
568:
548:
418:
359:
328:
273:
246:
164:Abū Kāmil Shujāʿ ibn Aslam ibn Muḥammad Ibn Shujāʿ
1591:
1162:. Princeton University Press. pp. 518, 550.
1047:
462:Book of Algebra (Kitāb fī al-jabr wa al-muqābala)
2667:Mathematicians who worked on Islamic inheritance
2613:
720:
820:), which gained more attention after historian
2637:10th-century people from the Abbasid Caliphate
1729:: Entretiens avec Jean Rosmorduc. Seuil (2001)
2632:9th-century people from the Abbasid Caliphate
1748:
1702:
970:Encyclopedia of the history of Arabic science
937:. Abu Kamil wrote in the introduction of his
705:in a circle of diameter 10. He also uses the
419:{\displaystyle x^{5}=x^{2}\cdot x^{2}\cdot x}
1314:
1312:
1310:
1308:
1306:
1262:Sesiano, Jacques (1997-07-31). "Abū Kāmil".
490:. In this book Abu Kamil solves systems of
1118:
1116:
1114:
1112:
1110:
1755:
1741:
1043:
1041:
1039:
1037:
1035:
1033:
1031:
215:Abu Kamil made important contributions to
2642:Mathematicians from the Abbasid Caliphate
2489:Constantinople observatory of Taqi ad-Din
1764:Mathematics in the medieval Islamic world
1665:
1485:
1303:
1087:Hartner, W. (1960). "ABŪ KĀMIL SHUDJĀʿ".
993:
991:
989:
836:Kitāb al-waṣāyā bi al-jabr wa al-muqābala
1620:
1421:
1359:
1357:
1355:
1153:
1107:
859:listed the following additional titles:
824:linked it with an anonymous Latin work,
794:Some of Abu Kamil's lost works include:
1603:MacTutor History of Mathematics Archive
1547:
1318:
1276:
1261:
1217:The beginnings and evolution of algebra
1147:
1086:
1059:MacTutor History of Mathematics Archive
1028:
997:
972:. Vol. 2. Routledge. p. 240.
14:
2614:
2410:Encyclopedia of the Brethren of Purity
1528:
1471:: CS1 maint: archived copy as title (
1277:Sesiano, Jacques (2008). "Abū Kāmil".
1257:
1255:
1253:
1251:
1249:
1247:
1245:
1243:
1241:
1220:. Cambridge University Press. p.
986:
968:Rāshid, Rushdī; Régis Morelon (1996).
1736:
1566:
1363:
1352:
1176:
1122:
1082:
1080:
1078:
1076:
1074:
1072:
180:أبو كامل شجاع بن أسلم بن محمد بن شجاع
842:and discusses the opinions of known
832:Book of Estate Sharing using Algebra
1238:
1214:; Galina S. Smirnova (2000-01-15).
814:Book on Augmentation and Diminution
694:{\displaystyle x^{4}+3125=125x^{2}}
179:
24:
1703:Herz-Fischler, Roger (June 1987).
1614:
1574:Dictionary of Scientific Biography
1130:Dictionary of Scientific Biography
1069:
920:
25:
2678:
1668:The American Mathematical Monthly
1488:The American Mathematical Monthly
281:), and solved sets of non-linear
2662:Medieval Egyptian mathematicians
2346:
1727:Une histoire de la science arabe
1344:Louis Charles Karpinski (1915).
1212:Bashmakova, Izabella Grigorʹevna
798:A treatise on the use of double
452:, whom he never personally met.
329:{\displaystyle (a\pm b)(c\pm d)}
1548:Sesiano, Jacques (2009-07-09).
1522:
1479:
1415:
1390:
1372:. New York: Broadway. pp.
1337:
1319:Sesiano, Jacques (2009-07-09).
1270:
1156:"Mathematics in Medieval Islam"
1287:10.1007/978-1-4020-4425-0_9198
1204:
961:
826:Liber augmenti et diminutionis
323:
311:
308:
296:
13:
1:
2382:Principles of Hindu Reckoning
1541:
1281:. Springer Netherlands: 7–8.
1154:Berggren, J. Lennart (2007).
789:
722:Book of Birds (Kitāb al-ṭair)
709:in some of his calculations.
7:
2627:10th-century mathematicians
2572:Hindu–Arabic numeral system
2504:University of al-Qarawiyyin
1711:. Wilfrid Laurier Univ Pr.
10:
2683:
2622:9th-century mathematicians
2474:Al-Mustansiriya University
2453:Islamic geometric patterns
2201:Shams al-Din al-Samarqandi
869:Book of the Key to Fortune
818:Kitāb al-jamʿ wa al-tafrīq
18:Abū Kāmil Shujāʿ ibn Aslam
2564:
2538:
2512:
2461:
2440:
2355:
2344:
2311:
2255:
2219:
2138:
2092:
2011:
1875:
1779:
1770:
1266:. Springer. pp. 4–5.
1014:. Springer. p. 148.
998:Sesiano, Jacques (2000).
894:
578:quadratic irrationalities
192:mathematician during the
157:
143:
129:
119:
105:
89:
84:
74:
69:
65:
57:
49:
41:
32:
2227:Nizam al-Din al-Nisapuri
2186:Muhyi al-Din al-Maghribi
1608:University of St Andrews
1064:University of St Andrews
955:
590:recreational mathematics
455:
2596:History of trigonometry
2591:Trigonometric functions
2585:Western Arabic numerals
2581:Eastern Arabic numerals
2146:Ibn al‐Ha'im al‐Ishbili
1422:Schwartz, R. K (2004).
626:indeterminate equations
586:indeterminate equations
443:
2520:Babylonian mathematics
2211:Kamāl al-Dīn al-Fārisī
2196:Qutb al-Din al-Shirazi
2191:al-Hasan al-Marrakushi
2115:Al-Samawal al-Maghribi
2044:Abu Mansur al-Baghdadi
1787:'Abd al-Hamīd ibn Turk
1567:Levey, Martin (1970).
1428:Available online at:
1123:Levey, Martin (1970).
1090:Encyclopaedia of Islam
953:
935:'Abd al-Hamīd ibn Turk
804:Book of the Two Errors
742:
695:
570:
550:
420:
361:
330:
283:simultaneous equations
275:
248:
2546:Byzantine mathematics
2334:Ibn Hamza al-Maghribi
2161:Alam al-Din al-Hanafi
2125:Sharaf al-Din al-Tusi
1401:. BRILL. p. 48.
1364:Livio, Mario (2003).
1000:"Islamic mathematics"
943:
873:Kitāb miftāḥ al-falāḥ
737:
696:
571:
551:
549:{\displaystyle x^{2}}
527:six types of problems
421:
362:
360:{\displaystyle x^{5}}
338:mathematical notation
331:
276:
274:{\displaystyle x^{8}}
249:
247:{\displaystyle x^{2}}
225:Islamic mathematician
2551:European mathematics
2499:Maragheh observatory
2324:Muhammad Baqir Yazdi
2303:Ibn Ghazi al-Miknasi
2176:Nasir al-Din al-Tusi
2084:Muhammad al-Baghdadi
1594:Robertson, Edmund F.
1050:Robertson, Edmund F.
1008:D'Ambrosio, Ubiratàn
929:'s contributions to
877:Book of the Adequate
656:
560:
533:
494:whose solutions are
371:
344:
293:
258:
231:
2469:Al-Azhar University
2396:The Book of Healing
1802:Al-Ḥajjāj ibn Yūsuf
1592:O'Connor, John J.;
1529:Høyrup, J. (2009).
1048:O'Connor, John J.;
909:Practica geometriae
840:Islamic inheritance
715:Practica geometriae
520:quadratic equations
514:) as solutions and
285:with three unknown
223:. He was the first
124:The Book of Algebra
70:Academic background
2601:History of algebra
2556:Indian mathematics
2530:Indian mathematics
2479:House of Knowledge
1933:Brethren of Purity
1827:Banū Mūsā brothers
1435:2011-09-15 at the
885:Book of the Kernel
808:Kitāb al-khaṭaʾayn
733:integral solutions
691:
622:integral solutions
566:
546:
506:(in the form of a
504:irrational numbers
416:
357:
326:
271:
244:
198:irrational numbers
194:Islamic Golden Age
99:Middle Abbasid era
94:Islamic Golden Age
2609:
2608:
2525:Greek mathematics
2448:Alhazen's problem
2342:
2341:
1963:Ibrahim ibn Sinan
1913:Sinān ibn al-Fatḥ
1559:978-0-8218-4473-1
1552:. AMS Bookstore.
1408:978-90-04-10119-7
1330:978-0-8218-4473-1
1323:. AMS Bookstore.
1296:978-1-4020-4559-2
1231:978-0-88385-329-0
1169:978-0-691-11485-9
979:978-0-415-12411-9
762:, right circular
569:{\displaystyle x}
200:as solutions and
185:Al-ḥāsib al-miṣrī
161:
160:
61:Al-ḥāsib al-miṣrī
16:(Redirected from
2674:
2424:Tabula Rogeriana
2350:
2298:Sibt al-Maridini
1958:Sinan ibn Thabit
1867:Abu Said Gorgani
1857:Thābit ibn Qurra
1847:Ishaq ibn Hunayn
1832:Hunayn ibn Ishaq
1777:
1776:
1757:
1750:
1743:
1734:
1733:
1725:Djebbar, Ahmed.
1722:
1710:
1699:
1662:
1610:
1588:
1563:
1536:
1535:
1526:
1520:
1519:
1483:
1477:
1476:
1470:
1462:
1460:
1459:
1453:
1447:. Archived from
1446:
1427:
1419:
1413:
1412:
1394:
1388:
1387:
1371:
1368:The Golden Ratio
1361:
1350:
1349:
1341:
1335:
1334:
1316:
1301:
1300:
1274:
1268:
1267:
1259:
1236:
1235:
1208:
1202:
1201:
1180:
1174:
1173:
1151:
1145:
1144:
1120:
1105:
1104:
1084:
1067:
1066:
1045:
1026:
1025:
995:
984:
983:
965:
700:
698:
697:
692:
690:
689:
668:
667:
608:Liber mahameleth
575:
573:
572:
567:
555:
553:
552:
547:
545:
544:
425:
423:
422:
417:
409:
408:
396:
395:
383:
382:
366:
364:
363:
358:
356:
355:
335:
333:
332:
327:
280:
278:
277:
272:
270:
269:
253:
251:
250:
245:
243:
242:
182:, also known as
181:
58:Other names
30:
29:
21:
2682:
2681:
2677:
2676:
2675:
2673:
2672:
2671:
2612:
2611:
2610:
2605:
2577:Arabic numerals
2560:
2534:
2508:
2484:House of Wisdom
2457:
2436:
2358:
2351:
2338:
2307:
2251:
2237:Ibn al-Durayhim
2215:
2134:
2100:Jabir ibn Aflah
2088:
2019:Abu Nasr Mansur
2007:
1903:Ahmad ibn Yusuf
1871:
1766:
1761:
1719:
1680:10.2307/2972073
1617:
1615:Further reading
1585:
1560:
1544:
1539:
1527:
1523:
1500:10.2307/2972073
1484:
1480:
1464:
1463:
1457:
1455:
1451:
1444:
1442:"Archived copy"
1440:
1437:Wayback Machine
1420:
1416:
1409:
1395:
1391:
1384:
1362:
1353:
1348:. Macmillan Co.
1342:
1338:
1331:
1317:
1304:
1297:
1275:
1271:
1260:
1239:
1232:
1209:
1205:
1199:
1181:
1177:
1170:
1152:
1148:
1141:
1121:
1108:
1101:
1085:
1070:
1046:
1029:
1022:
996:
987:
980:
966:
962:
958:
951:principles, ...
923:
921:On al-Khwarizmi
897:
881:Kitāb al-kifāya
861:Book of Fortune
802:, known as the
792:
770:, and circular
768:square pyramids
760:parallelepipeds
752:
725:
685:
681:
663:
659:
657:
654:
653:
650:
618:
604:John of Seville
561:
558:
557:
540:
536:
534:
531:
530:
502:, and accepted
480:of al-Khwarizmi
465:
458:
446:
404:
400:
391:
387:
378:
374:
372:
369:
368:
351:
347:
345:
342:
341:
294:
291:
290:
265:
261:
259:
256:
255:
238:
234:
232:
229:
228:
139:
96:
37:
35:
28:
23:
22:
15:
12:
11:
5:
2680:
2670:
2669:
2664:
2659:
2654:
2649:
2644:
2639:
2634:
2629:
2624:
2607:
2606:
2604:
2603:
2598:
2593:
2588:
2574:
2568:
2566:
2562:
2561:
2559:
2558:
2553:
2548:
2542:
2540:
2536:
2535:
2533:
2532:
2527:
2522:
2516:
2514:
2510:
2509:
2507:
2506:
2501:
2496:
2491:
2486:
2481:
2476:
2471:
2465:
2463:
2459:
2458:
2456:
2455:
2450:
2444:
2442:
2438:
2437:
2435:
2434:
2427:
2420:
2417:Toledan Tables
2413:
2406:
2399:
2392:
2389:Book of Optics
2385:
2378:
2371:
2363:
2361:
2353:
2352:
2345:
2343:
2340:
2339:
2337:
2336:
2331:
2326:
2321:
2315:
2313:
2309:
2308:
2306:
2305:
2300:
2295:
2290:
2285:
2280:
2275:
2270:
2265:
2259:
2257:
2253:
2252:
2250:
2249:
2244:
2239:
2234:
2229:
2223:
2221:
2217:
2216:
2214:
2213:
2208:
2203:
2198:
2193:
2188:
2183:
2178:
2173:
2168:
2163:
2158:
2153:
2148:
2142:
2140:
2136:
2135:
2133:
2132:
2130:Ibn al-Yasamin
2127:
2122:
2117:
2112:
2107:
2102:
2096:
2094:
2090:
2089:
2087:
2086:
2081:
2076:
2071:
2066:
2061:
2056:
2051:
2046:
2041:
2036:
2031:
2029:Kushyar Gilani
2026:
2021:
2015:
2013:
2009:
2008:
2006:
2005:
2000:
1995:
1990:
1985:
1980:
1975:
1973:Nazif ibn Yumn
1970:
1965:
1960:
1955:
1950:
1945:
1940:
1935:
1930:
1925:
1920:
1915:
1910:
1905:
1900:
1895:
1890:
1885:
1879:
1877:
1873:
1872:
1870:
1869:
1864:
1859:
1854:
1852:Na'im ibn Musa
1849:
1844:
1842:Yusuf al-Khuri
1839:
1834:
1829:
1824:
1819:
1814:
1812:Qusta ibn Luqa
1809:
1804:
1799:
1794:
1789:
1783:
1781:
1774:
1772:Mathematicians
1768:
1767:
1760:
1759:
1752:
1745:
1737:
1731:
1730:
1723:
1717:
1700:
1663:
1635:10.1086/352009
1629:(2): 259–262.
1616:
1613:
1612:
1611:
1589:
1583:
1564:
1558:
1543:
1540:
1538:
1537:
1521:
1478:
1414:
1407:
1389:
1382:
1351:
1336:
1329:
1302:
1295:
1269:
1237:
1230:
1203:
1197:
1175:
1168:
1146:
1139:
1106:
1099:
1068:
1027:
1020:
1004:Selin, Helaine
985:
978:
959:
957:
954:
922:
919:
896:
893:
889:Kitāb al-ʿasīr
865:Kitāb al-falāḥ
848:
847:
829:
811:
800:false position
791:
788:
751:
746:
731:with positive
729:linear systems
724:
719:
688:
684:
680:
677:
674:
671:
666:
662:
649:
644:
617:
612:
565:
543:
539:
475:. Whereas the
464:
459:
457:
454:
445:
442:
415:
412:
407:
403:
399:
394:
390:
386:
381:
377:
354:
350:
325:
322:
319:
316:
313:
310:
307:
304:
301:
298:
268:
264:
241:
237:
159:
158:
155:
154:
145:
141:
140:
138:
137:
133:
131:
127:
126:
121:
117:
116:
107:
106:Main interests
103:
102:
91:
87:
86:
82:
81:
76:
72:
71:
67:
66:
63:
62:
59:
55:
54:
51:
47:
46:
43:
39:
38:
33:
26:
9:
6:
4:
3:
2:
2679:
2668:
2665:
2663:
2660:
2658:
2655:
2653:
2650:
2648:
2645:
2643:
2640:
2638:
2635:
2633:
2630:
2628:
2625:
2623:
2620:
2619:
2617:
2602:
2599:
2597:
2594:
2592:
2589:
2586:
2582:
2578:
2575:
2573:
2570:
2569:
2567:
2563:
2557:
2554:
2552:
2549:
2547:
2544:
2543:
2541:
2537:
2531:
2528:
2526:
2523:
2521:
2518:
2517:
2515:
2511:
2505:
2502:
2500:
2497:
2495:
2492:
2490:
2487:
2485:
2482:
2480:
2477:
2475:
2472:
2470:
2467:
2466:
2464:
2460:
2454:
2451:
2449:
2446:
2445:
2443:
2439:
2433:
2432:
2428:
2426:
2425:
2421:
2419:
2418:
2414:
2412:
2411:
2407:
2405:
2404:
2400:
2398:
2397:
2393:
2391:
2390:
2386:
2384:
2383:
2379:
2377:
2376:
2372:
2370:
2369:
2365:
2364:
2362:
2360:
2354:
2349:
2335:
2332:
2330:
2327:
2325:
2322:
2320:
2317:
2316:
2314:
2310:
2304:
2301:
2299:
2296:
2294:
2291:
2289:
2286:
2284:
2281:
2279:
2276:
2274:
2271:
2269:
2266:
2264:
2261:
2260:
2258:
2254:
2248:
2245:
2243:
2240:
2238:
2235:
2233:
2232:Ibn al-Shatir
2230:
2228:
2225:
2224:
2222:
2218:
2212:
2209:
2207:
2206:Ibn al-Banna'
2204:
2202:
2199:
2197:
2194:
2192:
2189:
2187:
2184:
2182:
2179:
2177:
2174:
2172:
2169:
2167:
2164:
2162:
2159:
2157:
2154:
2152:
2151:Ahmad al-Buni
2149:
2147:
2144:
2143:
2141:
2137:
2131:
2128:
2126:
2123:
2121:
2118:
2116:
2113:
2111:
2108:
2106:
2103:
2101:
2098:
2097:
2095:
2091:
2085:
2082:
2080:
2077:
2075:
2072:
2070:
2067:
2065:
2062:
2060:
2057:
2055:
2052:
2050:
2047:
2045:
2042:
2040:
2037:
2035:
2032:
2030:
2027:
2025:
2022:
2020:
2017:
2016:
2014:
2010:
2004:
2001:
1999:
1996:
1994:
1991:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1956:
1954:
1951:
1949:
1946:
1944:
1941:
1939:
1936:
1934:
1931:
1929:
1926:
1924:
1921:
1919:
1916:
1914:
1911:
1909:
1906:
1904:
1901:
1899:
1896:
1894:
1891:
1889:
1886:
1884:
1881:
1880:
1878:
1874:
1868:
1865:
1863:
1860:
1858:
1855:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1818:
1815:
1813:
1810:
1808:
1805:
1803:
1800:
1798:
1795:
1793:
1792:Sanad ibn Ali
1790:
1788:
1785:
1784:
1782:
1778:
1775:
1773:
1769:
1765:
1758:
1753:
1751:
1746:
1744:
1739:
1738:
1735:
1728:
1724:
1720:
1718:0-88920-152-8
1714:
1709:
1708:
1701:
1697:
1693:
1689:
1685:
1681:
1677:
1673:
1669:
1664:
1660:
1656:
1652:
1648:
1644:
1640:
1636:
1632:
1628:
1624:
1619:
1618:
1609:
1605:
1604:
1599:
1595:
1590:
1586:
1584:0-684-10114-9
1580:
1576:
1575:
1570:
1565:
1561:
1555:
1551:
1546:
1545:
1533:
1525:
1517:
1513:
1509:
1505:
1501:
1497:
1493:
1489:
1482:
1474:
1468:
1454:on 2014-05-16
1450:
1443:
1438:
1434:
1431:
1425:
1418:
1410:
1404:
1400:
1393:
1385:
1383:0-7679-0816-3
1379:
1375:
1374:89–90, 92, 96
1370:
1369:
1360:
1358:
1356:
1347:
1340:
1332:
1326:
1322:
1315:
1313:
1311:
1309:
1307:
1298:
1292:
1288:
1284:
1280:
1273:
1265:
1258:
1256:
1254:
1252:
1250:
1248:
1246:
1244:
1242:
1233:
1227:
1223:
1219:
1218:
1213:
1207:
1200:
1198:9781402045592
1194:
1190:
1186:
1185:Helaine Selin
1179:
1171:
1165:
1161:
1157:
1150:
1142:
1140:0-684-10114-9
1136:
1132:
1131:
1126:
1119:
1117:
1115:
1113:
1111:
1102:
1100:90-04-08114-3
1096:
1092:
1091:
1083:
1081:
1079:
1077:
1075:
1073:
1065:
1061:
1060:
1055:
1051:
1044:
1042:
1040:
1038:
1036:
1034:
1032:
1023:
1021:1-4020-0260-2
1017:
1013:
1009:
1005:
1001:
994:
992:
990:
981:
975:
971:
964:
960:
952:
949:
942:
940:
936:
932:
928:
918:
916:
915:
910:
906:
902:
892:
890:
886:
882:
878:
874:
870:
866:
862:
858:
857:
852:
845:
841:
837:
833:
830:
827:
823:
822:Franz Woepcke
819:
815:
812:
809:
805:
801:
797:
796:
795:
787:
785:
781:
777:
773:
769:
765:
761:
757:
750:
745:
741:
736:
734:
730:
723:
718:
716:
712:
708:
704:
686:
682:
678:
675:
672:
669:
664:
660:
648:
643:
641:
637:
636:
631:
627:
623:
616:
611:
609:
605:
601:
596:
593:
591:
587:
583:
579:
563:
541:
537:
528:
523:
521:
517:
513:
509:
505:
501:
497:
496:whole numbers
493:
489:
485:
481:
479:
474:
470:
463:
453:
451:
441:
439:
435:
432:
431:encyclopedist
427:
413:
410:
405:
401:
397:
392:
388:
384:
379:
375:
352:
348:
339:
320:
317:
314:
305:
302:
299:
288:
284:
266:
262:
239:
235:
226:
222:
218:
213:
211:
207:
203:
199:
195:
191:
187:
186:
177:
173:
169:
165:
156:
153:
149:
146:
142:
135:
134:
132:
130:Notable ideas
128:
125:
122:
120:Notable works
118:
115:
111:
108:
104:
100:
95:
92:
88:
85:Academic work
83:
80:
77:
73:
68:
64:
60:
56:
52:
48:
44:
40:
31:
19:
2429:
2422:
2415:
2408:
2401:
2394:
2387:
2380:
2373:
2366:
2357:Mathematical
2312:16th century
2263:Ibn al-Majdi
2256:15th century
2220:14th century
2139:13th century
2093:12th century
2079:Omar Khayyam
2012:11th century
1908:Aṣ-Ṣaidanānī
1897:
1876:10th century
1837:Al-Khwarizmi
1726:
1706:
1674:(2): 37–48.
1671:
1667:
1626:
1622:
1601:
1572:
1549:
1530:
1524:
1494:(2): 37–48.
1491:
1487:
1481:
1456:. Retrieved
1449:the original
1423:
1417:
1398:
1392:
1367:
1345:
1339:
1320:
1278:
1272:
1263:
1216:
1206:
1188:
1178:
1159:
1149:
1128:
1088:
1057:
1011:
969:
963:
947:
944:
938:
927:al-Khwarizmi
924:
912:
908:
898:
888:
884:
880:
876:
872:
868:
864:
860:
854:
851:Ibn al-Nadim
849:
835:
831:
825:
817:
813:
807:
803:
793:
754:A manual of
753:
748:
743:
738:
726:
721:
714:
707:golden ratio
651:
646:
639:
633:
619:
614:
607:
597:
594:
524:
516:coefficients
487:
477:
473:Al-Khwarizmi
468:
466:
461:
450:al-Khwarizmi
447:
438:al-Khwarizmi
428:
214:
202:coefficients
184:
183:
171:
163:
162:
123:
79:Al-Khwarizmi
2652:850s births
2647:Algebraists
2375:De Gradibus
2329:Taqi ad-Din
2319:Al-Birjandi
2293:al-Qalaṣādī
2074:Al-Isfizari
2039:Ibn al-Samh
1968:Al-Isfahani
1948:al-Uqlidisi
1918:al-Khojandi
1883:Abu al-Wafa
1822:al-Dinawari
1780:9th century
1598:"Abu Kamil"
1054:"Abu Kamil"
914:Liber Abaci
640:Arithmetica
635:Arithmetica
512:fourth root
508:square root
434:Ibn Khaldūn
429:The Muslim
2657:930 deaths
2616:Categories
2539:Influenced
2513:Influences
2283:Ali Qushji
2242:Al-Khalili
2110:Al-Khazini
2105:Al-Kharaqī
2064:al-Zarqālī
2054:al-Jayyānī
1998:al-Majriti
1983:Abu al-Jud
1953:Al-Battani
1928:Al-Saghani
1923:Al-Nayrizi
1862:al-Marwazi
1797:al-Jawharī
1542:References
1458:2012-06-08
790:Lost works
630:Diophantus
144:Influenced
75:Influences
34:Abu Kamil
2288:al-Wafa'i
2278:Ulugh Beg
2181:al-Abhari
2166:Ibn Adlan
2156:Ibn Munim
2120:al-Hassar
2059:al-Nasawī
2034:Al-Biruni
2003:al-Jabali
1993:Al-Karaji
1943:Ibn Yunus
1898:Abu Kamil
1893:Al-Qabisi
1888:al-Khazin
1817:Al-Mahani
1688:0002-9890
1659:144112534
1643:0021-1753
1508:0002-9890
905:Fibonacci
901:al-Karaji
784:perimeter
711:Fibonacci
600:Fibonacci
500:fractions
492:equations
411:⋅
398:⋅
318:±
303:±
287:variables
206:Fibonacci
172:Auoquamel
168:Latinized
152:Fibonacci
148:Al-Karaji
2441:Concepts
2273:al-Kāshī
2247:al-Umawi
2049:Avicenna
1988:Al-Sijzi
1938:Ibn Sahl
1807:Al-Kindi
1467:cite web
1433:Archived
1010:(eds.).
780:diagonal
756:geometry
703:pentagon
582:polygons
488:Elements
221:geometry
190:Egyptian
114:geometry
36:أبو كامل
2565:Related
2494:Madrasa
2462:Centers
2268:al-Rūmī
2171:al-Urdi
2069:ibn Hud
2024:Alhazen
1978:al-Qūhī
1696:2972073
1516:2972073
1187:(ed.),
948:Algebra
939:Algebra
931:algebra
883:), and
856:Fihrist
853:in his
844:jurists
478:Algebra
469:Algebra
254:(up to
217:algebra
110:Algebra
1715:
1694:
1686:
1657:
1651:230435
1649:
1641:
1581:
1556:
1514:
1506:
1405:
1380:
1327:
1293:
1228:
1195:
1166:
1137:
1097:
1018:
976:
895:Legacy
764:prisms
484:Euclid
210:Europe
176:Arabic
53:c. 930
45:c. 850
2359:works
1692:JSTOR
1655:S2CID
1647:JSTOR
1512:JSTOR
1452:(PDF)
1445:(PDF)
1002:. In
956:Notes
772:cones
456:Works
1713:ISBN
1684:ISSN
1639:ISSN
1623:Isis
1579:ISBN
1554:ISBN
1532:2009
1504:ISSN
1473:link
1439:and
1403:ISBN
1378:ISBN
1325:ISBN
1291:ISBN
1226:ISBN
1193:ISBN
1164:ISBN
1135:ISBN
1095:ISBN
1016:ISBN
974:ISBN
903:and
776:area
673:3125
624:for
498:and
467:The
444:Life
367:(as
219:and
50:Died
42:Born
2431:Zij
1676:doi
1631:doi
1496:doi
1283:doi
891:).
875:),
867:),
679:125
632:'s
518:to
510:or
486:'s
170:as
90:Era
2618::
2583:,
1690:.
1682:.
1672:21
1670:.
1653:.
1645:.
1637:.
1627:69
1625:.
1606:,
1600:,
1596:,
1571:.
1510:.
1502:.
1492:21
1490:.
1469:}}
1465:{{
1376:.
1354:^
1305:^
1289:.
1240:^
1224:.
1222:52
1158:.
1127:.
1109:^
1071:^
1062:,
1056:,
1052:,
1030:^
1006:;
988:^
941::
917:.
810:).
782:,
778:,
766:,
717:.
606:,
592:.
522:.
440:.
212:.
178::
174:,
150:,
112:,
2587:)
2579:(
1756:e
1749:t
1742:v
1721:.
1698:.
1678::
1661:.
1633::
1587:.
1562:.
1518:.
1498::
1475:)
1461:.
1411:.
1386:.
1333:.
1299:.
1285::
1234:.
1172:.
1143:.
1103:.
1024:.
982:.
887:(
879:(
871:(
863:(
846:.
834:(
828:.
816:(
806:(
687:2
683:x
676:=
670:+
665:4
661:x
564:x
542:2
538:x
414:x
406:2
402:x
393:2
389:x
385:=
380:5
376:x
353:5
349:x
324:)
321:d
315:c
312:(
309:)
306:b
300:a
297:(
267:8
263:x
240:2
236:x
166:(
101:)
97:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.