1713:
4385:
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1446:(1114–1187) played a key role in translating and disseminating these works, thus making them accessible to a wider audience. Cremona is said to have translated into Latin "no fewer than 90 complete Arabic texts." European mathematicians, building on the foundations laid by Islamic scholars, further developed practical trigonometry for applications in navigation, cartography, and celestial navigation, thus pushing forward the age of discovery and scientific revolution. The practical applications of trigonometry for navigation and astronomy became increasingly important during the Age of Exploration.
197:. He developed a new vocabulary for algebra, distinguishing between purely algebraic terms and those shared with arithmetic. Al-Khwārizmī noticed that the representation of numbers is crucial in daily life. Thus, he wanted to find or summarize a way to simplify the mathematical operation, so-called later, the algebra. His algebra was initially focused on linear and quadratic equations and the elementary arithmetic of binomials and trinomials. This approach, which involved solving equations using radicals and related algebraic calculations, influenced mathematical thinking long after his death.
1794:: "A complete history of mathematics of medieval Islam cannot yet be written, since so many of these Arabic manuscripts lie unstudied... Still, the general outline... is known. In particular, Islamic mathematicians fully developed the decimal place-value number system to include decimal fractions, systematised the study of algebra and began to consider the relationship between algebra and geometry, studied and made advances on the major Greek geometrical treatises of Euclid, Archimedes, and Apollonius, and made significant improvements in plane and spherical geometry."
30:
1481:(Kitāb fī al-jabr wa al-muqābala) is "essentially a commentary on and elaboration of al-Khwārizmī's work; in part for that reason and in part for its own merit, the book enjoyed widespread popularity in the Muslim world". It contains 69 problems, which is more than al-Khwārizmī who had 40 in his book. Abū Kāmil's Algebra plays a significant role in shaping the trajectory of Western mathematics, particularly in its impact on the works of the Italian mathematician Leonardo of Pisa, widely recognized as Fibonacci. In his
1729:
144:, spanning from the 8th to the 14th century, marked a period of considerable advancements in various scientific disciplines, attracting scholars from medieval Europe seeking access to this knowledge. Trade routes and cultural interactions played a crucial role in introducing Arabic mathematical ideas to the West. The translation of Arabic mathematical texts, along with Greek and Roman works, during the 14th to 17th century, played a pivotal role in shaping the intellectual landscape of the
308:
3755:
1800:, Vol. 1, Chapter VII.4: "In a general way it may be said that the Golden Age of Arabian mathematics was confined largely to the 9th and 10th centuries; that the world owes a great debt to Arab scholars for preserving and transmitting to posterity the classics of Greek mathematics; and that their work was chiefly that of transmission, although they developed considerable originality in algebra and showed some genius in their work in trigonometry."
1523:, "Arabic science only reproduced the teachings received from Greek science". Besides being considered as merely some insignificant additions or reflections to the great tradition of Greek classical science, math works from Arabic mathematicians are also blamed for lacking rigor and too focused on practical applications and calculations, and this is why Western historians argued they could never reach the level of Greek mathematicians. As
205:
developed in the
Western world. Al-Khwārizmī's method, which involved completing the square, not only provided a practical solution for equations of this type but also introduced an abstract and generalized approach to mathematical problems. His work, encapsulated in his seminal text "Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala" (The Compendious Book on Calculation by Completion and Balancing), was translated into
1459:(1048–1131) was a Persian mathematician, astronomer, and poet, known for his work on algebra and geometry, particularly his investigations into the solutions of cubic equations. He was "the first in history to elaborate a geometrical theory of equations with degrees ≤ 3", and has great influence on the work of Descartes, a French mathematician who is often regarded as the founder of analytical geometry. Indeed, "to read
413:, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for the future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before."
1313:—is negative, and by a negative number is positive. If we subtract a negative number from a higher negative number, the remainder is their negative difference. The difference remains positive if we subtract a negative number from a lower negative number. If we subtract a negative number from a positive number, the remainder is their positive sum. If we subtract a positive number from an empty power (
1610:
history of mathematics necessitates acknowledging the interconnectedness of diverse mathematical traditions and dispelling the notion of a uniquely
European mathematical heritage. The contributions of Arab mathematicians, marked by practical applications and theoretical innovations, form an integral part of the rich tapestry of mathematical history, and deserves recognition.
405:"Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed
187:," marking it as a distinct discipline. He regarded his work as "a short work on Calculation by (the rules of) Completion and Reduction, confining it to what is easiest and most useful in arithmetic". Later, people commented his work was not just a theoretical treatise but also practical, aimed at solving problems in areas like commerce and land measurement.
1452:
is one of the islamic mathematicians who made great contributions to the development of trigonometry. He "innovated new trigonometric functions, created a table of cotangents, and made some formulas in spherical trigonometry." These discoveries, together with his astronomical works which are praised
286:
connected
Western Europeans with the Islamic world. While the primary purpose of the Crusades was military, there was also cultural exchange and exposure to Islamic knowledge, including mathematics. European scholars who traveled to the Holy Land and other parts of the Islamic world gained access to
1536:
and the origin of algebraic geometry is traced back to
Descartes, while Arabic mathematicians' contributions are ignored deliberately. In Rashed's words: "To justify the exclusion of science written in Arabic from the history of science, one invokes its absence of rigor, its calculatory appearance
385:
Al-Khwarizmi's algebra was rhetorical, which means that the equations were written out in full sentences. This was unlike the algebraic work of
Diophantus, which was syncopated, meaning that some symbolism is used. The transition to symbolic algebra, where only symbols are used, can be seen in the
1527:
wrote, Arabic math "in no way superseded the level attained by
Diophantus". On the other hand, they perceived that Western mathematicians went into a very different way both in its method employed and ultimate purpose, "the hallmark of Western science in its Greek origins as well as in its modern
1609:
views, sometimes marginalized these achievements. The East lacking rationality and scientific spirit perpetuated a biased perspective, hindering the recognition of the significant role played by Arabic mathematics in the development of algebra and other mathematical disciplines. Reevaluating the
237:
Arabic mathematics, epitomized by al-Khwārizmī's work, was crucial in shaping the mathematical landscape. Its spread to the West was driven by its practical applications, the expansion of mathematical concepts by his successors, and the translation and adaptation of these ideas into the
Western
233:
Al-Khwārizmī's algebra was an autonomous discipline with its historical perspective, eventually leading to the "arithmetization of algebra". His successors expanded on his work, adapting it to new theoretical and technical challenges and reorienting it towards a more arithmetical direction for
1502:
and math were unique phenomena of the West. Even though some math contributions from Arab mathematicians are occasionally acknowledged, they are considered to be "outside history or only integrated in so far as it contributed to science, which is essentially
European", and just some technical
204:
of the form (ax^2 + bx = c), commonly referred to as "squares plus roots equal numbers," was a monumental achievement in the history of algebra. This breakthrough laid the groundwork for the systematic approach to solving quadratic equations, which became a fundamental aspect of algebra as it
213:
The spread of Arabic mathematics to the West was facilitated by several factors. The practicality and general applicability of al-Khwārizmī's methods were significant. They were designed to convert numerical or geometrical problems into equations in normal form, leading to canonical solution
209:
in the 12th century. This translation played a pivotal role in the transmission of algebraic knowledge to Europe, significantly influencing mathematicians during the
Renaissance and shaping the evolution of modern mathematics. Al-Khwārizmī's contributions, especially his proof for quadratic
124:
expanded on his work, contributing to advancements in various mathematical domains. The practicality and broad applicability of these mathematical methods facilitated the dissemination of Arabic mathematics to the West, contributing substantially to the evolution of
Western mathematics.
1081:
slowly removed the distinction between magnitude and number, allowing irrational quantities to appear as coefficients in equations and to be solutions of algebraic equations. They worked freely with irrationals as mathematical objects, but they did not examine closely their nature.
1073:. In the Greek view, magnitudes varied continuously and could be used for entities such as line segments, whereas numbers were discrete. Hence, irrationals could only be handled geometrically; and indeed Greek mathematics was mainly geometrical. Islamic mathematicians including
1564:
in that period was one of the main reasons why Arabic mathematicians were often ignored for their contributions, as people outside the West were considered to be lacking the necessary rationality and scientific spirit to made significant contributions to math and science.
1417:
during the translation movement. "The Moors (western Mohammedans from that part of North Africa once known as Mauritania) crossed over into Spain early in the seventh century, bringing with them the cultural resources of the Arab world". In the 13th century, King
1463:' s Géométrie is to look upstream towards al-Khayyām and al-Ṭūsī; and downstream towards Newton, Leibniz, Cramer, Bézout and the Bernoulli brothers". Numerous problems that appear in "La Géométrie" (Geometry) have foundations that date back to al-Khayyām.
1537:
and its practical aims. Furthermore, strictly dependent on Greek science and, lastly, incapable of introducing experimental norms, scientists of that time were relegated to the role of conscientious guardians of the Hellenistic museum."
1836:"The Islamic mathematicians exercised a prolific influence on the development of science in Europe, enriched as much by their own discoveries as those they had inherited by the Greeks, the Indians, the Syrians, the Babylonians, etc."
546:– 1213/4) developed a novel approach to the investigation of cubic equations—an approach which entailed finding the point at which a cubic polynomial obtains its maximum value. For example, to solve the equation
281:
became centers of learning and attracted scholars from different cultural backgrounds.Therefore, mathematical knowledge from the Islamic world found its way to Europe through various channels. Meanwhile, the
1408:
The influence of medieval Arab-Islamic mathematics to the rest of the world is wide and profound, in both the realm of science and mathematics. The knowledge of the Arabs went into the western world through
1712:
1497:
Despite the fundamental works Arabic mathematicians have done on the development of Algebra and algebraic geometry, Western historians in the 18th and early 19th century still regarded it as a fact that
1218:
In the 9th century, Islamic mathematicians were familiar with negative numbers from the works of Indian mathematicians, but the recognition and use of negative numbers during this period remained timid.
679:
265:. As a result, the intellectual achievements of Islamic scholars attracted the attention of scholars in medieval Europe who sought to access this wealth of knowledge. Trade routes, such as the
495:, and a vertical line through the intersection point. The solution is given by the length of the horizontal line segment from the origin to the intersection of the vertical line and the
685:. His surviving works give no indication of how he discovered his formulae for the maxima of these curves. Various conjectures have been proposed to account for his discovery of them.
1605:, extended their influence beyond their time. Despite the foundational contributions of Arab mathematicians, Western historians in the 18th and early 19th centuries, influenced by
681:, and that the equation would have no solutions, one solution or two solutions, depending on whether the height of the curve at that point was less than, equal to, or greater than
4404:
363:
35:
1272:
3039:
642:
589:
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1376:("reckoning by two errors"). It was used for centuries to solve practical problems such as commercial and juridical questions (estate partitions according to rules of
4393:
2573:"Biomedical ethics, 7th edition David DeGrazia, Thomas A. Mappes, Jeffrey Brand-Ballard: 2010, Softcover, 732pp, ISBN-9780073407456 £171.15 McGraw-Hill Incorporated"
2475:"Biomedical ethics, 7th edition David DeGrazia, Thomas A. Mappes, Jeffrey Brand-Ballard: 2010, Softcover, 732pp, ISBN-9780073407456 £171.15 McGraw-Hill Incorporated"
1560:" movement emerged in the 19th century was interpreted as "against Rationalism" and a return to a more "spiritual and harmonious" lifestyle. Thus, the prevailing
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136:'s methods. This dissemination was influenced not only by economic and political factors but also by cultural exchanges, exemplified by events such as the
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Europe, he was considered the original inventor of algebra, although it is now known that his work is based on older Indian or Greek sources. He revised
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1094:
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wrote a book of algebra accompanied with geometrical illustrations and proofs. He also enumerated all the possible solutions to some of his problems.
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to exclude the Arabic period when he retraced the evolution of algebra. And instead, the history of classical algebra is written as the work of the
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17:
1317:), the remainder is the same negative, and if we subtract a negative number from an empty power, the remainder is the same positive number.
238:
context. This spread was a complex process involving economics, politics, and cultural exchange, greatly influencing Western mathematics.
5054:
2449:
877:
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Arabic manuscripts and mathematical treatises. During the 14th to 17th century, the translation of Arabic mathematical texts, along with
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renaissance, is its conformity to rigorous standards". Thus, the perceived non-rigorous proof in Arabic mathematicians' book authorizes
299:, who studied in North Africa and the Middle East, helped introduce and popularize Arabic numerals and mathematical concepts in Europe.
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40:
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equations, are a testament to the rich mathematical heritage of the Islamic world and its enduring impact on Western mathematics.
5022:
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1581:, facilitated by cultural exchanges and translations, left a lasting impact on Western mathematical thought. Mathematicians like
1473:, also known as Al-ḥāsib al-miṣrī—lit. "The Egyptian Calculator") (c. 850 – c. 930), was studied algebra following the author of
897:
852:
418:
314:'s "Cubic equations and intersections of conic sections" the first page of the two-chaptered manuscript kept in Tehran University
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Berggren, J. Lennart; Al-Tūsī, Sharaf Al-Dīn; Rashed, Roshdi (1990). "Innovation and Tradition in Sharaf al-Dīn al-Ṭūsī's
183:) work between AD 813 and 833 in Baghdad was a turning point. He introduced the term "algebra" in the title of his book, "
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532:. This method had been used by the Greeks, but they did not generalize the method to cover all equations with positive
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193:'s approach was groundbreaking in that it did not arise from any previous "arithmetical" tradition, including that of
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in the 11th century introduced the general law of sines. The plane law of sines was described in the 13th century by
834:
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539:
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4324:
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3555:
1895:"Extending al-Karaji's Work on Sums of Odd Powers of Integers - Introduction | Mathematical Association of America"
970:
737:
3263:. Abhandlungen zur Geschichte der Mathematischen Wissenschaften Mit Einschluss Ihrer Anwendungen, X Heft. Leipzig.
1577:'s algebraic innovations serving as a cornerstone. The dissemination of Arabic mathematics to the West during the
1485:(1202), Fibonacci extensively incorporated ideas from Arabic mathematicians, using approximately 29 problems from
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suggests that al-Khwarizmi's original work was not based on Ptolemy but on a derivative world map, presumably in
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view was "East and West oppose each other not as geographical but as historical positivities", which labeled "
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of al-Khwārizmī. Khayyám obtained the solutions of these equations by finding the intersection points of two
438:
116:'s approach, departing from earlier arithmetical traditions, laid the groundwork for the arithmetization of
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4105:
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By the 12th century, al-Karaji's successors were to state the general rules of signs and use them to solve
3823:
1918:
1619:
453:
5147:
5027:
4977:
4960:
4917:
4912:
4816:
4768:
4540:
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1923:
720:
4860:
4715:
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4207:
3984:
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3218:. 1.–2. Band, 1.–3. Supplementband. Berlin: Emil Fischer, 1898, 1902; Leiden: Brill, 1937, 1938, 1942.
1230:
112:
played a key role in this transformation, introducing algebra as a distinct field in the 9th century.
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3944:
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2199:
1573:
The medieval Arab-Islamic world played a crucial role in shaping the trajectory of mathematics, with
960:
2323:
4950:
4656:
4263:
4222:
4090:
3974:
3492:
3356:
2450:"Issues in the Origin and Development of Hisab al-Khata'ayn (Calculation by Double False Position)"
2333:
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2063:
2035:
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295:
ones, played a crucial role in shaping the intellectual landscape of the Renaissance. Figures like
3949:
2025:
1719:
1697:
1661:
1442:, which helps European mathematicians and astronomers in their studies. European scholars such as
602:
549:
4632:
4627:
4617:
3924:
3919:
3526:
3514:
3485:
3411:
2432:. Eighth North African Meeting on the History of Arab Mathematics. Radès, Tunisia. Archived from
2426:
Issues in the Origin and Development of Hisab al-Khata'ayn (Calculation by Double False Position)
1204:, he stated the law of sines for plane and spherical triangles and provided proofs for this law.
1185:
1163:
379:
269:, facilitated the movement of goods, ideas, and knowledge between the East and West. Cities like
245:(8th to 14th century) was characterized by significant advancements in various fields, including
1996:
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4232:
4217:
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heritage rather than open up a completely new branch of mathematics. In the French philosopher
1034:
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1941:
1380:), as well as purely recreational problems. The algorithm was often memorized with the aid of
425:
Several other mathematicians during this time period expanded on the algebra of Al-Khwarizmi.
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3502:
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1955:
1821:
1327:
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1492:
1372:. Within the tradition of Golden Age Muslim mathematics, double false position was known as
4922:
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8:
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2401:
Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures
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Lumpkin, Beatrice; Zitler, Siham (1992). "Cairo: Science Academy of the Middle Ages". In
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1016:(c. 300 BCE). The first explicit formulation of the principle of induction was given by
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Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". In Victor J. Katz (ed.).
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1989:
1685:
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382:, and unlike Diophantus, also gives general solutions for the equations he deals with.
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A Book on What Is Necessary from the Science of Arithmetic for Scribes and Businessmen
1065:, but were not happy with them and only able to cope by drawing a distinction between
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for their accuracy, greatly advanced astronomical calculations and instruments.
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334:
165:
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3372:
List of Inventions and Discoveries in Mathematics During the Islamic Golden Age
3333:
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3256:
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did not use negative numbers or negative coefficients. But within fifty years,
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288:
2636:
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1850:
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2596:
2498:
2396:
2272:
2158:
1430:, where scholars translated numerous scientific and philosophical works from
1109:
1017:
941:
529:
219:
156:
Arabic mathematics, particularly algebra, developed significantly during the
4141:
2664:
The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook
1340:
wrote a now-lost treatise on the use of double false position, known as the
337:
word meaning completion or "reunion of broken parts", flourished during the
53:, especially during the 9th and 10th centuries, was built upon syntheses of
5104:
4299:
4115:
3873:
2844:; Berggren, J. L. (1988). "Episodes in the Mathematics of Medieval Islam".
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1984:
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laid the foundation for advances in various mathematical fields, including
190:
161:
133:
120:, influencing mathematical thought for an extended period. Successors like
113:
109:
98:
3000:
Sowjetische Beiträge zur Geschichte der Naturwissenschaft pp. 62–160.
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that "negative quantities must be counted as terms". In the 10th century,
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2734:(in Italian), vol. V, Rome: Istituto per l'Oriente, pp. 458–532
1606:
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Western historians' perception of the contribution of Arab mathematicians
1349:
1125:
888:
445:. Omar Khayyam found the general geometric solution of a cubic equation.
250:
246:
145:
128:
Arabic mathematical knowledge spread through various channels during the
78:
46:
2730:(1939), "Al-Ḥuwārismī e il suo rifacimento della Geografia di Tolomeo",
1883:(Report). Washington, DC: The MAA Mathematical Sciences Digital Library.
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was discovered in the 10th century: it has been attributed variously to
307:
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3989:
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2688:(1991), "Greek Trigonometry and Mensuration, and The Arabic Hegemony",
2625:"The Development of Arabic Mathematics: Between Arithmetic and Algebra"
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1008:
The earliest implicit traces of mathematical induction can be found in
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The Development of Arabic Mathematics: Between Arithmetic and Algebra
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The Development of Arabic Mathematics: Between Arithmetic and Algebra
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1466:
1389:
1381:
1337:
1333:
1275:
1224:
1038:
543:
296:
266:
254:
215:
121:
74:
3157:
2859:
4085:
4024:
3843:
2893:
2163:
Mathematics Across Cultures: The History of Non-Western Mathematics
2132:
1602:
1516:
473:
283:
258:
137:
94:
4648:
1348:). The oldest surviving writing on double false position from the
249:. Scholars in the Islamic world made substantial contributions to
5087:
4905:
4900:
4530:
2395:
Mat Rofa Bin Ismail (2008), "Algebra in Islamic Mathematics", in
1598:
1541:
1365:
1361:
1129:
1102:
350:
330:
270:
262:
184:
117:
90:
81:). Important developments of the period include extension of the
3191:“The Formation of «Islamic Mathematics»: Sources and Conditions”
2976:
1227:
illustrated the rules of signs for expanding the multiplication
151:
5109:
5097:
5092:
4856:
4763:
4405:
The Compendious Book on Calculation by Completion and Balancing
1700:(c. 1380–1429) (decimals and estimation of the circle constant)
1557:
1545:
1512:
1504:
1431:
1414:
1009:
777:
767:
484:
364:
The Compendious Book on Calculation by Completion and Balancing
58:
36:
The Compendious Book on Calculation by Completion and Balancing
3334:"Bibliography of Mathematics in Medieval Islamic Civilization"
4965:
4895:
4878:
3799:
1435:
1410:
1086:
274:
206:
3033:(Cambridge UP, 2013), chapters 2 and 3 mathematics in Islam.
3031:
The Cambridge History of Science. Volume 2: Medieval Science
2577:
Graefe's Archive for Clinical and Experimental Ophthalmology
2479:
Graefe's Archive for Clinical and Experimental Ophthalmology
599:
positive, he would note that the maximum point of the curve
4890:
4873:
4793:
4788:
3141:
The Crest of the Peacock: Non-European Roots of Mathematics
3121:
The Crest of the Peacock: Non-European Roots of Mathematics
2086:
2084:
1357:
1114:
Compendious Book on Calculation by Completion and Balancing
789:
513:
3227:
Biografías de Matemáticos Árabes que florecieron en España
3195:
Filosofi og Videnskabsteori på Roskilde Universitetscenter
3008:. translated by M. Cazenave and K. Jaouiche. Paris: Vrin.
4467:
3314:
3298:
3261:
Die Mathematiker und Astronomen der Araber und ihre Werke
1754:
Indian influence on Islamic mathematics in medieval Islam
2938:
The Cambridge Illustrated History of the World's Science
2081:
2339:
1774:
Timeline of science and engineering in the Muslim world
4440:
Book on the Measurement of Plane and Spherical Figures
2694:(2nd ed.), New York City: John Wiley & Sons,
1881:
Mathematical Treasures: Mesopotamian Accounting Tokens
657:
3406:
3340:
3138:
Katz, Victor J.; Joseph, George Gheverghese (1992). "
2403:, vol. 1 (2nd ed.), Springer, p. 115,
2253:
2114:
1556:" as the essence of the West, while the "Call of the
1438:. The translations included Islamic contributions to
1233:
650:
605:
552:
397:
On the work done by Al-Khwarizmi, J. J. O'Connor and
2542:
Classical Mathematics from Al-Khwarizmi to Descartes
2096:
2069:
2982:
Die Mathematik der Länder des Ostens im Mittelalter
2394:
2311:
2299:
2157:Sesiano, Jacques (2000). "Islamic Mathematics". In
1957:
Learning Activities from the History of Mathematics
674:{\displaystyle x=\textstyle {\sqrt {\frac {b}{3}}}}
214:formulae. His work and that of his successors like
108:underwent significant developments in mathematics.
2786:
2285:. Vol. 7. New York: Charles Scribner's Sons.
1988:
1266:
673:
636:
583:
374:of first and second-degree (linear and quadratic)
3152:(1). Mathematical Association of America: 82–84.
2875:
2317:
2193:
2047:
2019:
5134:
2566:
2564:
2562:
2468:
2466:
1511:'s work, Arabic math is merely "a reflection of
518:Treatise on Demonstration of Problems of Algebra
367:, Al-Khwarizmi deals with ways to solve for the
3072:Studies in the exact sciences in medieval Islam
3070:Daffa, Ali Abdullah al-; Stroyls, J.J. (1984).
2854:(6). Mathematical Association of America: 567.
1844:
1842:
1138:and wrote on astronomy and astrology. However,
3291:(presenter) (2008). "The Genius of the East".
2962:. Translated by A. F. W. Armstrong. Springer.
2840:
2618:
2616:
2614:
2612:
2610:
2608:
2606:
2534:
2532:
361:, known as the father of algebra. In his book
353:was the founder of algebra, is along with the
4664:
3785:
3392:
3221:
3173:
3003:
2878:Episodes in the Mathematics of Medieval Islam
2823:Episodes in the Mathematics of Medieval Islam
2559:
2463:
2324:"Abu Abd Allah Muhammad ibn Muadh Al-Jayyani"
1809:
978:
200:Al-Khwārizmī's proof of the rule for solving
152:Origin and spread of Arab-Islamic mathematics
3124:(2nd ed.). Princeton University Press.
3069:
2876:Hogendijk, Jan P.; Berggren, J. L. (1989). "
2277:"Al-Khwārizmī, Abu Ja'far Muḥammad ibn Mūsā"
1874:
1872:
1839:
1021:
3347:"Arabic mathematics: forgotten brilliance?"
2629:Boston Studies in the Philosophy of Science
2603:
2529:
2054:"Arabic mathematics: forgotten brilliance?"
1116:presented the first systematic solution of
1014:proof that the number of primes is infinite
4671:
4657:
3792:
3778:
3399:
3385:
3273:: CS1 maint: location missing publisher (
3178:. Leipzig: BG Teubner Verlagsgesellschaft.
3137:
3045:The History of Mathematics: A Brief Course
2994:: CS1 maint: location missing publisher (
2910:
2165:. Springer Netherlands. pp. 137–165.
2152:
2150:
1979:
1977:
1368:. He justified the technique by a formal,
985:
971:
132:, driven by the practical applications of
5143:Mathematics in the medieval Islamic world
4526:Constantinople observatory of Taqi ad-Din
3801:Mathematics in the medieval Islamic world
3328:
3006:Les mathématiques arabes: VIII–XV siècles
2888:(4). American Oriental Society: 697–698.
2793:(4th rev. ed.), Dover Publications,
2710:A History of Mathematics: An Introduction
2390:
2388:
2362:
2360:
2358:
2356:
2354:
2241:
1869:
1722:'s perfect compass to draw conic sections
1519:and Indian influences". And according to
1153:
3241:(in German). Brill Academic Publishers.
2882:Journal of the American Oriental Society
2820:
2661:
2422:
2345:
2279:. In Gillispie, Charles Coulston (ed.).
2121:Journal of the American Oriental Society
1983:
1848:
1388:and balance-scale diagrams explained by
1332:Between the 9th and 10th centuries, the
1321:
1286:considered debts as negative numbers in
452:
333:, the name of which is derived from the
306:
28:
3352:MacTutor History of Mathematics Archive
3184:Journal articles on Islamic mathematics
3088:
2726:
2666:(2nd ed.). Princeton, New Jersey:
2570:
2472:
2329:MacTutor History of Mathematics Archive
2305:
2205:MacTutor History of Mathematics Archive
2156:
2147:
2059:MacTutor History of Mathematics Archive
2031:MacTutor History of Mathematics Archive
1974:
1045:, who used it for special cases of the
419:MacTutor History of Mathematics archive
14:
5135:
4447:Encyclopedia of the Brethren of Purity
3233:
3176:Gesichte der Mathematik im Mittelalter
3117:
3029:Lindberg, D.C., and M. H. Shank, eds.
2954:
2916:The Muslim contribution to mathematics
2781:
2622:
2538:
2517:Contributions to Non-Standard Analysis
2385:
2366:
2351:
2271:
2247:
2102:
2075:
1991:Mathematics: From the Birth of Numbers
1613:
520:containing the systematic solution of
4652:
3773:
3380:
3255:
3239:Geschichte Des Arabischen Schrifttums
3094:Studies in the Islamic Exact Sciences
3038:
2932:
2759:
2738:
2684:
2259:
2221:
2090:
1953:
1937:
1878:
1797:
1769:Science in the medieval Islamic world
1471:أبو كامل شجاع بن أسلم بن محمد بن شجاع
1056:
1004:Mathematical induction § History
3216:Geschichte der Arabischen Litteratur
3024:Book chapters on Islamic mathematics
2712:. HarperCollins college publishers.
2707:
1791:
1194:The book of unknown arcs of a sphere
4678:
3118:Joseph, George Gheverghese (2000).
3112:Books on the history of mathematics
2732:Raccolta di scritti editi e inediti
1470:
1207:
457:To solve the third-degree equation
169:
24:
2808:
2282:Dictionary of Scientific Biography
2200:"Abu Mansur ibn Tahir Al-Baghdadi"
1820:. Transaction Publishers. p.
1664:(c. 940–1000) (centres of gravity)
1396:, who were each mathematicians of
448:
140:and the translation movement. The
25:
5159:
3322:
1849:ben Musa, Mohammed (2013-03-28).
1817:Golden age of the Moor, Volume 11
1305:the product of a negative number—
441:, found several solutions of the
392:Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī
4847:Reception in early modern Europe
4842:Contributions to Medieval Europe
4383:
3754:
3753:
3174:Youschkevitch, Adolf P. (1964).
3004:Youschkevitch, Adolf P. (1976).
2789:A Concise History of Mathematics
2742:The Algebra of Mohammed Ben Musa
2571:Masters, Barry R. (2011-06-08).
2473:Masters, Barry R. (2011-06-08).
1960:. Walch Publishing. p. 26.
1852:The Algebra of Mohammed ben Musa
1727:
1711:
1384:, such as a verse attributed to
1267:{\displaystyle (a\pm b)(c\pm d)}
234:abstract algebraic calculation.
3146:The College Mathematics Journal
3144:by George Gheverghese Joseph".
3042:(1997). "Islamic Mathematics".
2505:
2416:
2265:
2215:
2187:
2108:
2041:
2013:
1370:Euclidean-style geometric proof
1023:Traité du triangle arithmétique
3206:Bibliographies and biographies
2980:; Rozenfeld, Boris A. (1960).
2940:. Cambridge University Press.
2519:, Elsevier, pp. iii, 1972
1947:
1911:
1887:
1879:Swetz, Frank J. (2012-08-15).
1855:. Cambridge University Press.
1803:
1785:
1593:, with their contributions to
1261:
1249:
1246:
1234:
522:cubic or third-order equations
378:. He introduces the method of
343:Muhammad ibn Musa al-Khwarizmi
162:Muhammad ibn Musa al-Khwārizmī
110:Muhammad ibn Musa al-Khwārizmī
13:
1:
4419:Principles of Hindu Reckoning
3229:. Madrid: Estanislao Maestre.
2847:American Mathematical Monthly
2825:. New York: Springer-Verlag.
2821:Berggren, J. Lennart (1986).
2539:Rashed, Roshdi (2014-08-21).
2295:– via Encyclopedia.com.
1779:
1568:
1403:
228:rational Diophantine analysis
173:
18:Mathematics in medieval Islam
5083:Arab Agricultural Revolution
3365:Rediscovering Arabic Science
2815:Books on Islamic mathematics
2371:. Springer. pp. 36–37.
2026:"al-Marrakushi ibn Al-Banna"
1424:Toledo School of Translators
997:
637:{\displaystyle \ y=bx-x^{3}}
584:{\displaystyle \ x^{3}+a=bx}
185:Kitab al-jabr wa al-muqabala
89:, the systematised study of
7:
4609:Hindu–Arabic numeral system
4541:University of al-Qarawiyyin
2171:10.1007/978-94-011-4301-1_9
1924:Online Etymology Dictionary
1742:
1041:(c. 1000) and continued by
388:Ibn al-Banna' al-Marrakushi
345:, a Persian scholar in the
302:
10:
5164:
4511:Al-Mustansiriya University
4490:Islamic geometric patterns
4238:Shams al-Din al-Samarqandi
3367:, 2007, Saudi Aramco World
2668:Princeton University Press
2654:
2229:. Texas A&M University
1704:
1489:with scarce modification.
1325:
1211:
1157:
1075:Abū Kāmil Shujāʿ ibn Aslam
1061:The Greeks had discovered
1001:
502:
322:
318:
5075:
5035:Geography and cartography
5003:
4941:
4855:
4807:
4749:
4741:Influences on Western art
4686:
4601:
4575:
4549:
4498:
4477:
4392:
4381:
4348:
4292:
4256:
4175:
4129:
4048:
3912:
3816:
3807:
3749:
3711:
3680:
3639:
3613:
3419:
2880:by J. Lennart Berggren".
2637:10.1007/978-94-017-3274-1
2589:10.1007/s00417-011-1640-x
2491:10.1007/s00417-011-1640-x
2367:Rashed, R. (1994-06-30).
2224:"The History of Infinity"
2222:Allen, G. Donald (n.d.).
1676:(973–1048) (trigonometry)
961:Islamization of knowledge
844:Science in medieval times
4264:Nizam al-Din al-Nisapuri
4223:Muhyi al-Din al-Maghribi
3357:University of St Andrews
3283:Television documentaries
3064:Books on Islamic science
2912:Daffa', Ali Abdullah al-
2745:. Kessinger Publishing.
2739:Rosen, Fredrick (1831).
2708:Katz, Victor J. (1993).
2691:A History of Mathematics
2423:Schwartz, R. K. (2004).
2334:University of St Andrews
2210:University of St Andrews
2064:University of St Andrews
2036:University of St Andrews
1995:. W. W. Norton. p.
1954:Swetz, Frank J. (1993).
1106:positional number system
1085:In the twelfth century,
472:Khayyám constructed the
241:The period known as the
4633:History of trigonometry
4628:Trigonometric functions
4622:Western Arabic numerals
4618:Eastern Arabic numerals
4183:Ibn al‐Ha'im al‐Ishbili
3096:. Syracuse Univ Press.
2978:Youschkevitch, Adolf P.
2623:Rashed, Roshdi (1994).
1674:Abū al-Rayḥān al-Bīrūnī
1656:'Abd al-'Aziz al-Qabisi
1650:Abu'l-Hasan al-Uqlidisi
1284:Abū al-Wafā' al-Būzjānī
1164:History of trigonometry
4557:Babylonian mathematics
4248:Kamāl al-Dīn al-Fārisī
4233:Qutb al-Din al-Shirazi
4228:al-Hasan al-Marrakushi
4152:Al-Samawal al-Maghribi
4081:Abu Mansur al-Baghdadi
3824:'Abd al-Hamīd ibn Turk
3672:Medieval Islamic world
3408:History of mathematics
3223:Sánchez Pérez, José A.
3048:. Wiley-Interscience.
2918:. London: Croom Helm.
2767:. Dover Publications.
2765:History of Mathematics
1736:theorem of Ibn Haytham
1652:(fl. 952) (arithmetic)
1622:(fl. 830) (quadratics)
1620:'Abd al-Hamīd ibn Turk
1342:Book of the Two Errors
1319:
1309:—by a positive number—
1268:
1154:Spherical trigonometry
1022:
675:
638:
585:
500:
423:
315:
170:محمد بن موسى الخوارزمي
106:medieval Islamic world
43:
5018:Alchemy and chemistry
4583:Byzantine mathematics
4371:Ibn Hamza al-Maghribi
4198:Alam al-Din al-Hanafi
4162:Sharaf al-Din al-Tusi
3741:Future of mathematics
3718:Women in mathematics
3199:Preprints og Reprints
1328:False position method
1326:Further information:
1322:Double false position
1303:
1269:
1212:Further information:
1190:Ibn Muʿādh al-Jayyānī
1158:Further information:
1079:Ibn Tahir al-Baghdadi
1029:In between, implicit
676:
639:
586:
540:Sharaf al-Dīn al-Ṭūsī
516:– 1123/24) wrote the
503:Further information:
456:
439:Sharaf al-Dīn al-Tūsī
403:
323:Further information:
310:
32:
4588:European mathematics
4536:Maragheh observatory
4361:Muhammad Baqir Yazdi
4340:Ibn Ghazi al-Miknasi
4213:Nasir al-Din al-Tusi
4121:Muhammad al-Baghdadi
3693:Over Cantor's theory
3343:Robertson, Edmund F.
3307:(presenter) (2010).
2320:Robertson, Edmund F.
2196:Robertson, Edmund F.
2050:Robertson, Edmund F.
2022:Robertson, Edmund F.
1477:, al-Khwārizmī. His
1420:Alfonso X of Castile
1295:polynomial divisions
1231:
1202:On the Sector Figure
1198:Nasīr al-Dīn al-Tūsī
1186:Abu al-Wafa' Buzjani
1178:Nasir al-Din al-Tusi
1035:arithmetic sequences
772:(Islamic monotheism)
738:Early social changes
733:Early historiography
648:
603:
550:
376:polynomial equations
4928:Early social change
4827:Early social change
4506:Al-Azhar University
4433:The Book of Healing
3839:Al-Ḥajjāj ibn Yūsuf
3729:Approximations of π
3640:By ancient cultures
3363:Richard Covington,
3341:O'Connor, John J.;
3074:. New York: Wiley.
2318:O'Connor, John J.;
2194:O'Connor, John J.;
2093:, pp. 241–242.
2048:O'Connor, John J.;
2020:O'Connor, John J.;
1764:History of geometry
1759:History of calculus
1614:Other major figures
1503:innovations to the
1378:Quranic inheritance
1360:mathematician from
1356:(10th century), an
1174:Abu-Mahmud Khojandi
1122:quadratic equations
524:, going beyond the
399:Edmund F. Robertson
202:quadratic equations
51:Golden Age of Islam
5148:Islamic Golden Age
4638:History of algebra
4593:Indian mathematics
4567:Indian mathematics
4516:House of Knowledge
3970:Brethren of Purity
3864:Banū Mūsā brothers
3532:Information theory
3294:The Story of Maths
1640:(before 858 – 929)
1579:Islamic Golden Age
1428:Kingdom of Castile
1374:hisāb al-khaṭāʾayn
1346:Kitāb al-khaṭāʾayn
1278:wrote in his book
1264:
1188:as a contributor.
1063:irrational numbers
1057:Irrational numbers
1049:and properties of
1037:was introduced by
671:
670:
634:
581:
501:
411:irrational numbers
339:Islamic golden age
325:History of algebra
316:
243:Islamic Golden Age
224:numerical analysis
142:Islamic Golden Age
83:place-value system
71:Indian mathematics
44:
5130:
5129:
5098:elementary school
4716:Geometric pattern
4646:
4645:
4562:Greek mathematics
4485:Alhazen's problem
4379:
4378:
4000:Ibrahim ibn Sinan
3950:Sinān ibn al-Fatḥ
3767:
3766:
3603:Separation axioms
3330:Hogendijk, Jan P.
3310:Science and Islam
3212:Brockelmann, Carl
3015:978-2-7116-0734-1
2842:Toomer, Gerald J.
2677:978-0-691-11485-9
2552:978-1-317-62239-0
2180:978-94-011-4301-1
1967:978-0-8251-2264-4
1862:978-1-108-05507-9
1812:Van Sertima, Ivan
1646:(c. 850 – c. 930)
1548:, the prevailing
1500:Classical science
1444:Gerard of Cremona
1051:Pascal's triangle
1033:by induction for
995:
994:
747:Modern philosophy
668:
667:
608:
555:
87:decimal fractions
55:Greek mathematics
16:(Redirected from
5155:
5005:Medieval science
4673:
4666:
4659:
4650:
4649:
4461:Tabula Rogeriana
4387:
4335:Sibt al-Maridini
3995:Sinan ibn Thabit
3904:Abu Said Gorgani
3894:Thābit ibn Qurra
3884:Ishaq ibn Hunayn
3869:Hunayn ibn Ishaq
3814:
3813:
3794:
3787:
3780:
3771:
3770:
3757:
3756:
3477:Category theory
3401:
3394:
3387:
3378:
3377:
3359:
3337:
3332:(January 1999).
3289:Marcus du Sautoy
3278:
3272:
3264:
3252:
3230:
3179:
3169:
3135:
3107:
3085:
3059:
3019:
2999:
2993:
2985:
2973:
2951:
2929:
2905:
2871:
2836:
2803:
2792:
2778:
2756:
2735:
2723:
2704:
2681:
2649:
2648:
2620:
2601:
2600:
2568:
2557:
2556:
2536:
2527:
2526:
2525:
2524:
2509:
2503:
2502:
2470:
2461:
2460:
2458:
2452:. Archived from
2447:
2445:
2444:
2438:
2431:
2420:
2414:
2413:
2392:
2383:
2382:
2364:
2349:
2343:
2337:
2336:
2315:
2309:
2303:
2297:
2296:
2269:
2263:
2257:
2251:
2245:
2239:
2238:
2236:
2234:
2228:
2219:
2213:
2212:
2191:
2185:
2184:
2154:
2145:
2144:
2112:
2106:
2100:
2094:
2088:
2079:
2073:
2067:
2066:
2045:
2039:
2038:
2017:
2011:
2010:
1994:
1981:
1972:
1971:
1951:
1945:
1935:
1929:
1928:
1915:
1909:
1908:
1906:
1905:
1891:
1885:
1884:
1876:
1867:
1866:
1846:
1837:
1835:
1807:
1801:
1789:
1731:
1720:Abū Sahl al-Qūhī
1715:
1698:Jamshīd al-Kāshī
1692:Ismail al-Jazari
1662:Abū Sahl al-Qūhī
1632:Thabit ibn Qurra
1540:In 18th century
1515:, combined with
1472:
1422:established the
1315:martaba khāliyya
1273:
1271:
1270:
1265:
1214:Negative numbers
1208:Negative numbers
1089:translations of
1047:binomial theorem
1025:
987:
980:
973:
932:
925:
923:Classical Arabic
781:
773:
688:
687:
680:
678:
677:
672:
669:
660:
659:
643:
641:
640:
635:
633:
632:
606:
590:
588:
587:
582:
565:
564:
553:
427:Abu Kamil Shuja'
421:
407:rational numbers
182:
178:
175:
171:
93:and advances in
21:
5163:
5162:
5158:
5157:
5156:
5154:
5153:
5152:
5133:
5132:
5131:
5126:
5071:
4999:
4988:Early sociology
4937:
4901:decision-making
4851:
4832:Early conquests
4803:
4745:
4682:
4680:Islamic studies
4677:
4647:
4642:
4614:Arabic numerals
4597:
4571:
4545:
4521:House of Wisdom
4494:
4473:
4395:
4388:
4375:
4344:
4288:
4274:Ibn al-Durayhim
4252:
4171:
4137:Jabir ibn Aflah
4125:
4056:Abu Nasr Mansur
4044:
3940:Ahmad ibn Yusuf
3908:
3803:
3798:
3768:
3763:
3745:
3707:
3688:Brouwer–Hilbert
3676:
3635:
3614:Numeral systems
3609:
3471:Grandi's series
3415:
3405:
3325:
3320:
3266:
3265:
3257:Suter, Heinrich
3249:
3158:10.2307/2686206
3132:
3104:
3082:
3056:
3016:
2987:
2986:
2970:
2948:
2934:Ronan, Colin A.
2926:
2860:10.2307/2322777
2833:
2811:
2809:Further reading
2806:
2801:
2783:Struik, Dirk J.
2775:
2761:Smith, David E.
2753:
2720:
2702:
2678:
2657:
2652:
2621:
2604:
2569:
2560:
2553:
2537:
2530:
2522:
2520:
2511:
2510:
2506:
2471:
2464:
2456:
2448:
2442:
2440:
2436:
2429:
2421:
2417:
2411:
2393:
2386:
2379:
2365:
2352:
2344:
2340:
2316:
2312:
2304:
2300:
2293:
2270:
2266:
2262:, p. v–vi.
2258:
2254:
2246:
2242:
2232:
2230:
2226:
2220:
2216:
2192:
2188:
2181:
2155:
2148:
2113:
2109:
2101:
2097:
2089:
2082:
2074:
2070:
2046:
2042:
2018:
2014:
2007:
1982:
1975:
1968:
1952:
1948:
1936:
1932:
1917:
1916:
1912:
1903:
1901:
1893:
1892:
1888:
1877:
1870:
1863:
1847:
1840:
1832:
1808:
1804:
1795:
1790:
1786:
1782:
1749:Arabic numerals
1745:
1738:
1732:
1723:
1716:
1707:
1616:
1571:
1495:
1487:Book of Algebra
1479:Book of Algebra
1406:
1330:
1324:
1232:
1229:
1228:
1216:
1210:
1182:Abu Nasr Mansur
1166:
1156:
1101:introduced the
1099:Indian numerals
1059:
1006:
1000:
991:
936:
935:
928:
921:
881:
875:
828:
779:
771:
764:
725:
701:Islamic studies
658:
649:
646:
645:
628:
624:
604:
601:
600:
560:
556:
551:
548:
547:
512:(c. 1038/48 in
507:
451:
449:Cubic equations
422:
417:
347:House of Wisdom
327:
321:
305:
180:
176:
158:medieval period
154:
23:
22:
15:
12:
11:
5:
5161:
5151:
5150:
5145:
5128:
5127:
5125:
5124:
5123:
5122:
5117:
5112:
5102:
5101:
5100:
5095:
5085:
5079:
5077:
5073:
5072:
5070:
5069:
5064:
5059:
5058:
5057:
5047:
5042:
5037:
5032:
5031:
5030:
5020:
5015:
5009:
5007:
5001:
5000:
4998:
4997:
4996:
4995:
4985:
4980:
4975:
4970:
4969:
4968:
4958:
4953:
4947:
4945:
4939:
4938:
4936:
4935:
4930:
4925:
4920:
4915:
4910:
4909:
4908:
4903:
4898:
4896:use of analogy
4888:
4883:
4882:
4881:
4876:
4865:
4863:
4853:
4852:
4850:
4849:
4844:
4839:
4834:
4829:
4824:
4822:Historiography
4819:
4813:
4811:
4805:
4804:
4802:
4801:
4796:
4791:
4786:
4781:
4776:
4771:
4766:
4761:
4755:
4753:
4747:
4746:
4744:
4743:
4738:
4733:
4728:
4723:
4718:
4713:
4708:
4703:
4698:
4692:
4690:
4684:
4683:
4676:
4675:
4668:
4661:
4653:
4644:
4643:
4641:
4640:
4635:
4630:
4625:
4611:
4605:
4603:
4599:
4598:
4596:
4595:
4590:
4585:
4579:
4577:
4573:
4572:
4570:
4569:
4564:
4559:
4553:
4551:
4547:
4546:
4544:
4543:
4538:
4533:
4528:
4523:
4518:
4513:
4508:
4502:
4500:
4496:
4495:
4493:
4492:
4487:
4481:
4479:
4475:
4474:
4472:
4471:
4464:
4457:
4454:Toledan Tables
4450:
4443:
4436:
4429:
4426:Book of Optics
4422:
4415:
4408:
4400:
4398:
4390:
4389:
4382:
4380:
4377:
4376:
4374:
4373:
4368:
4363:
4358:
4352:
4350:
4346:
4345:
4343:
4342:
4337:
4332:
4327:
4322:
4317:
4312:
4307:
4302:
4296:
4294:
4290:
4289:
4287:
4286:
4281:
4276:
4271:
4266:
4260:
4258:
4254:
4253:
4251:
4250:
4245:
4240:
4235:
4230:
4225:
4220:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4179:
4177:
4173:
4172:
4170:
4169:
4167:Ibn al-Yasamin
4164:
4159:
4154:
4149:
4144:
4139:
4133:
4131:
4127:
4126:
4124:
4123:
4118:
4113:
4108:
4103:
4098:
4093:
4088:
4083:
4078:
4073:
4068:
4066:Kushyar Gilani
4063:
4058:
4052:
4050:
4046:
4045:
4043:
4042:
4037:
4032:
4027:
4022:
4017:
4012:
4010:Nazif ibn Yumn
4007:
4002:
3997:
3992:
3987:
3982:
3977:
3972:
3967:
3962:
3957:
3952:
3947:
3942:
3937:
3932:
3927:
3922:
3916:
3914:
3910:
3909:
3907:
3906:
3901:
3896:
3891:
3889:Na'im ibn Musa
3886:
3881:
3879:Yusuf al-Khuri
3876:
3871:
3866:
3861:
3856:
3851:
3849:Qusta ibn Luqa
3846:
3841:
3836:
3831:
3826:
3820:
3818:
3811:
3809:Mathematicians
3805:
3804:
3797:
3796:
3789:
3782:
3774:
3765:
3764:
3762:
3761:
3750:
3747:
3746:
3744:
3743:
3738:
3737:
3736:
3726:
3725:
3724:
3715:
3713:
3709:
3708:
3706:
3705:
3700:
3698:Leibniz–Newton
3695:
3690:
3684:
3682:
3678:
3677:
3675:
3674:
3669:
3664:
3659:
3657:Ancient Greece
3654:
3649:
3643:
3641:
3637:
3636:
3634:
3633:
3628:
3623:
3617:
3615:
3611:
3610:
3608:
3607:
3606:
3605:
3600:
3599:
3598:
3585:
3584:
3583:
3578:
3568:
3567:
3566:
3560:Number theory
3558:
3553:
3552:
3551:
3541:
3540:
3539:
3529:
3524:
3523:
3522:
3517:
3507:
3506:
3505:
3495:
3490:
3489:
3488:
3483:
3475:
3474:
3473:
3468:
3458:
3457:
3456:
3446:
3445:
3444:
3436:
3435:
3434:
3423:
3421:
3417:
3416:
3404:
3403:
3396:
3389:
3381:
3375:
3374:
3369:
3360:
3338:
3324:
3323:External links
3321:
3319:
3318:
3305:Jim Al-Khalili
3302:
3285:
3284:
3280:
3279:
3253:
3247:
3231:
3219:
3208:
3207:
3203:
3202:
3189:Høyrup, Jens.
3186:
3185:
3181:
3180:
3171:
3130:
3114:
3113:
3109:
3108:
3102:
3090:Kennedy, E. S.
3086:
3080:
3066:
3065:
3061:
3060:
3054:
3035:
3034:
3026:
3025:
3021:
3020:
3014:
3001:
2974:
2968:
2956:Rashed, Roshdi
2952:
2946:
2930:
2924:
2908:
2907:
2906:
2894:10.2307/604119
2872:
2831:
2817:
2816:
2812:
2810:
2807:
2805:
2804:
2799:
2779:
2773:
2757:
2751:
2736:
2724:
2718:
2705:
2700:
2686:Boyer, Carl B.
2682:
2676:
2658:
2656:
2653:
2651:
2650:
2602:
2583:(1): 159–160.
2558:
2551:
2528:
2504:
2485:(1): 159–160.
2462:
2459:on 2011-09-15.
2415:
2409:
2384:
2377:
2350:
2348:, p. 518.
2338:
2310:
2298:
2291:
2273:Toomer, Gerald
2264:
2252:
2240:
2214:
2186:
2179:
2159:Selin, Helaine
2146:
2133:10.2307/604533
2127:(2): 304–309.
2107:
2095:
2080:
2068:
2040:
2012:
2005:
1973:
1966:
1946:
1930:
1910:
1886:
1868:
1861:
1838:
1830:
1802:
1783:
1781:
1778:
1777:
1776:
1771:
1766:
1761:
1756:
1751:
1744:
1741:
1740:
1739:
1733:
1726:
1724:
1717:
1710:
1706:
1703:
1702:
1701:
1695:
1689:
1688:(c. 1116–1196)
1683:
1677:
1671:
1668:Ibn al-Haytham
1665:
1659:
1653:
1647:
1641:
1635:
1629:
1628:(d. after 864)
1623:
1615:
1612:
1570:
1567:
1494:
1491:
1405:
1402:
1386:Ibn al-Yasamin
1354:Qusta ibn Luqa
1336:mathematician
1323:
1320:
1263:
1260:
1257:
1254:
1251:
1248:
1245:
1242:
1239:
1236:
1209:
1206:
1168:The spherical
1155:
1152:
1058:
1055:
999:
996:
993:
992:
990:
989:
982:
975:
967:
964:
963:
957:
956:
952:
951:
950:
949:
944:
938:
937:
934:
933:
926:
918:
914:
911:
910:
905:
900:
892:
891:
885:
884:
883:
882:
871:
868:
867:
861:
860:
855:
847:
846:
840:
839:
838:
837:
832:
826:
821:
816:
811:
806:
801:
793:
792:
786:
785:
784:
783:
775:
765:
763:
762:
760:Concept of God
757:
751:
749:
740:
735:
727:
726:
724:
723:
718:
713:
707:
704:
703:
697:
696:
666:
663:
656:
653:
631:
627:
623:
620:
617:
614:
611:
580:
577:
574:
571:
568:
563:
559:
530:conic sections
505:Cubic equation
487:with diameter
450:
447:
443:cubic equation
415:
357:mathematician
320:
317:
304:
301:
153:
150:
9:
6:
4:
3:
2:
5160:
5149:
5146:
5144:
5141:
5140:
5138:
5121:
5118:
5116:
5113:
5111:
5108:
5107:
5106:
5103:
5099:
5096:
5094:
5091:
5090:
5089:
5086:
5084:
5081:
5080:
5078:
5074:
5068:
5065:
5063:
5060:
5056:
5055:ophthalmology
5053:
5052:
5051:
5048:
5046:
5043:
5041:
5038:
5036:
5033:
5029:
5026:
5025:
5024:
5021:
5019:
5016:
5014:
5011:
5010:
5008:
5006:
5002:
4994:
4991:
4990:
4989:
4986:
4984:
4981:
4979:
4976:
4974:
4971:
4967:
4964:
4963:
4962:
4959:
4957:
4954:
4952:
4949:
4948:
4946:
4944:
4940:
4934:
4931:
4929:
4926:
4924:
4921:
4919:
4916:
4914:
4911:
4907:
4904:
4902:
4899:
4897:
4894:
4893:
4892:
4891:Jurisprudence
4889:
4887:
4884:
4880:
4877:
4875:
4872:
4871:
4870:
4867:
4866:
4864:
4862:
4858:
4854:
4848:
4845:
4843:
4840:
4838:
4835:
4833:
4830:
4828:
4825:
4823:
4820:
4818:
4815:
4814:
4812:
4810:
4806:
4800:
4797:
4795:
4792:
4790:
4787:
4785:
4782:
4780:
4777:
4775:
4772:
4770:
4767:
4765:
4762:
4760:
4757:
4756:
4754:
4752:
4748:
4742:
4739:
4737:
4734:
4732:
4729:
4727:
4724:
4722:
4719:
4717:
4714:
4712:
4709:
4707:
4704:
4702:
4699:
4697:
4694:
4693:
4691:
4689:
4685:
4681:
4674:
4669:
4667:
4662:
4660:
4655:
4654:
4651:
4639:
4636:
4634:
4631:
4629:
4626:
4623:
4619:
4615:
4612:
4610:
4607:
4606:
4604:
4600:
4594:
4591:
4589:
4586:
4584:
4581:
4580:
4578:
4574:
4568:
4565:
4563:
4560:
4558:
4555:
4554:
4552:
4548:
4542:
4539:
4537:
4534:
4532:
4529:
4527:
4524:
4522:
4519:
4517:
4514:
4512:
4509:
4507:
4504:
4503:
4501:
4497:
4491:
4488:
4486:
4483:
4482:
4480:
4476:
4470:
4469:
4465:
4463:
4462:
4458:
4456:
4455:
4451:
4449:
4448:
4444:
4442:
4441:
4437:
4435:
4434:
4430:
4428:
4427:
4423:
4421:
4420:
4416:
4414:
4413:
4409:
4407:
4406:
4402:
4401:
4399:
4397:
4391:
4386:
4372:
4369:
4367:
4364:
4362:
4359:
4357:
4354:
4353:
4351:
4347:
4341:
4338:
4336:
4333:
4331:
4328:
4326:
4323:
4321:
4318:
4316:
4313:
4311:
4308:
4306:
4303:
4301:
4298:
4297:
4295:
4291:
4285:
4282:
4280:
4277:
4275:
4272:
4270:
4269:Ibn al-Shatir
4267:
4265:
4262:
4261:
4259:
4255:
4249:
4246:
4244:
4243:Ibn al-Banna'
4241:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4188:Ahmad al-Buni
4186:
4184:
4181:
4180:
4178:
4174:
4168:
4165:
4163:
4160:
4158:
4155:
4153:
4150:
4148:
4145:
4143:
4140:
4138:
4135:
4134:
4132:
4128:
4122:
4119:
4117:
4114:
4112:
4109:
4107:
4104:
4102:
4099:
4097:
4094:
4092:
4089:
4087:
4084:
4082:
4079:
4077:
4074:
4072:
4069:
4067:
4064:
4062:
4059:
4057:
4054:
4053:
4051:
4047:
4041:
4038:
4036:
4033:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4013:
4011:
4008:
4006:
4003:
4001:
3998:
3996:
3993:
3991:
3988:
3986:
3983:
3981:
3978:
3976:
3973:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3917:
3915:
3911:
3905:
3902:
3900:
3897:
3895:
3892:
3890:
3887:
3885:
3882:
3880:
3877:
3875:
3872:
3870:
3867:
3865:
3862:
3860:
3857:
3855:
3852:
3850:
3847:
3845:
3842:
3840:
3837:
3835:
3832:
3830:
3829:Sanad ibn Ali
3827:
3825:
3822:
3821:
3819:
3815:
3812:
3810:
3806:
3802:
3795:
3790:
3788:
3783:
3781:
3776:
3775:
3772:
3760:
3752:
3751:
3748:
3742:
3739:
3735:
3732:
3731:
3730:
3727:
3723:
3720:
3719:
3717:
3716:
3714:
3710:
3704:
3703:Hobbes–Wallis
3701:
3699:
3696:
3694:
3691:
3689:
3686:
3685:
3683:
3681:Controversies
3679:
3673:
3670:
3668:
3665:
3663:
3660:
3658:
3655:
3653:
3652:Ancient Egypt
3650:
3648:
3645:
3644:
3642:
3638:
3632:
3629:
3627:
3624:
3622:
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3582:
3579:
3577:
3574:
3573:
3572:
3569:
3565:
3562:
3561:
3559:
3557:
3556:Math notation
3554:
3550:
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3538:
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3534:
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3516:
3513:
3512:
3511:
3508:
3504:
3501:
3500:
3499:
3496:
3494:
3493:Combinatorics
3491:
3487:
3484:
3482:
3479:
3478:
3476:
3472:
3469:
3467:
3464:
3463:
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3327:
3326:
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3306:
3303:
3300:
3296:
3295:
3290:
3287:
3286:
3282:
3281:
3276:
3270:
3262:
3258:
3254:
3250:
3248:90-04-02007-1
3244:
3240:
3236:
3232:
3228:
3224:
3220:
3217:
3213:
3210:
3209:
3205:
3204:
3200:
3196:
3192:
3188:
3187:
3183:
3182:
3177:
3172:
3167:
3163:
3159:
3155:
3151:
3147:
3143:
3142:
3133:
3131:0-691-00659-8
3127:
3123:
3122:
3116:
3115:
3111:
3110:
3105:
3103:0-8156-6067-7
3099:
3095:
3091:
3087:
3083:
3081:0-471-90320-5
3077:
3073:
3068:
3067:
3063:
3062:
3057:
3055:0-471-18082-3
3051:
3047:
3046:
3041:
3037:
3036:
3032:
3028:
3027:
3023:
3022:
3017:
3011:
3007:
3002:
2997:
2991:
2983:
2979:
2975:
2971:
2969:0-7923-2565-6
2965:
2961:
2957:
2953:
2949:
2947:0-521-25844-8
2943:
2939:
2935:
2931:
2927:
2925:0-85664-464-1
2921:
2917:
2913:
2909:
2903:
2899:
2895:
2891:
2887:
2883:
2879:
2873:
2869:
2865:
2861:
2857:
2853:
2849:
2848:
2843:
2838:
2837:
2834:
2832:0-387-96318-9
2828:
2824:
2819:
2818:
2814:
2813:
2802:
2800:0-486-60255-9
2796:
2791:
2790:
2784:
2780:
2776:
2774:0-486-20429-4
2770:
2766:
2762:
2758:
2754:
2752:1-4179-4914-7
2748:
2744:
2743:
2737:
2733:
2729:
2728:Nallino, C.A.
2725:
2721:
2719:0-673-38039-4
2715:
2711:
2706:
2703:
2701:0-471-54397-7
2697:
2693:
2692:
2687:
2683:
2679:
2673:
2669:
2665:
2660:
2659:
2646:
2642:
2638:
2634:
2630:
2626:
2619:
2617:
2615:
2613:
2611:
2609:
2607:
2598:
2594:
2590:
2586:
2582:
2578:
2574:
2567:
2565:
2563:
2554:
2548:
2545:. Routledge.
2544:
2543:
2535:
2533:
2518:
2514:
2508:
2500:
2496:
2492:
2488:
2484:
2480:
2476:
2469:
2467:
2455:
2451:
2439:on 2014-05-16
2435:
2428:
2427:
2419:
2412:
2410:9781402045592
2406:
2402:
2398:
2397:Helaine Selin
2391:
2389:
2380:
2378:9780792325659
2374:
2370:
2363:
2361:
2359:
2357:
2355:
2347:
2346:Berggren 2007
2342:
2335:
2331:
2330:
2325:
2321:
2314:
2307:
2302:
2294:
2292:0-684-16962-2
2288:
2284:
2283:
2278:
2274:
2268:
2261:
2256:
2249:
2244:
2225:
2218:
2211:
2207:
2206:
2201:
2197:
2190:
2182:
2176:
2172:
2168:
2164:
2160:
2153:
2151:
2142:
2138:
2134:
2130:
2126:
2122:
2118:
2111:
2105:, p. 97.
2104:
2099:
2092:
2087:
2085:
2078:, p. 96.
2077:
2072:
2065:
2061:
2060:
2055:
2051:
2044:
2037:
2033:
2032:
2027:
2023:
2016:
2008:
2006:0-393-04002-X
2002:
1998:
1993:
1992:
1986:
1985:Gullberg, Jan
1980:
1978:
1969:
1963:
1959:
1958:
1950:
1943:
1939:
1934:
1926:
1925:
1920:
1914:
1900:
1896:
1890:
1882:
1875:
1873:
1864:
1858:
1854:
1853:
1845:
1843:
1833:
1831:1-56000-581-5
1827:
1823:
1819:
1818:
1813:
1806:
1799:
1793:
1788:
1784:
1775:
1772:
1770:
1767:
1765:
1762:
1760:
1757:
1755:
1752:
1750:
1747:
1746:
1737:
1730:
1725:
1721:
1718:Engraving of
1714:
1709:
1708:
1699:
1696:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1670:(c. 965–1040)
1669:
1666:
1663:
1660:
1657:
1654:
1651:
1648:
1645:
1642:
1639:
1636:
1633:
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1621:
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1277:
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1226:
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1215:
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1199:
1195:
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1187:
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1179:
1175:
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1165:
1161:
1151:
1149:
1145:
1141:
1137:
1136:
1131:
1127:
1123:
1119:
1115:
1111:
1110:Western world
1107:
1104:
1100:
1096:
1092:
1088:
1083:
1080:
1076:
1072:
1068:
1064:
1054:
1052:
1048:
1044:
1040:
1036:
1032:
1027:
1024:
1019:
1015:
1011:
1005:
988:
983:
981:
976:
974:
969:
968:
966:
965:
962:
959:
958:
954:
953:
948:
945:
943:
940:
939:
931:
927:
924:
920:
919:
917:
913:
912:
909:
906:
904:
901:
899:
896:
895:
894:
893:
890:
887:
886:
879:
878:Ophthalmology
874:
870:
869:
866:
863:
862:
859:
856:
854:
851:
850:
849:
848:
845:
842:
841:
836:
833:
831:
827:
825:
822:
820:
817:
815:
812:
810:
807:
805:
802:
800:
797:
796:
795:
794:
791:
790:Jurisprudence
788:
787:
782:
776:
774:
770:
766:
761:
758:
756:
753:
752:
750:
748:
744:
741:
739:
736:
734:
731:
730:
729:
728:
722:
719:
717:
714:
712:
709:
708:
706:
705:
702:
699:
698:
694:
690:
689:
686:
684:
664:
661:
654:
651:
629:
625:
621:
618:
615:
612:
609:
598:
594:
578:
575:
572:
569:
566:
561:
557:
545:
541:
537:
535:
531:
527:
523:
519:
515:
511:
506:
498:
494:
490:
486:
482:
479: =
478:
475:
471:
468: =
467:
464:
461: +
460:
455:
446:
444:
440:
437:, along with
436:
432:
428:
420:
414:
412:
408:
402:
400:
395:
393:
389:
383:
381:
377:
373:
370:
366:
365:
360:
356:
352:
348:
344:
340:
336:
332:
329:The study of
326:
313:
309:
300:
298:
294:
290:
285:
280:
276:
272:
268:
264:
260:
256:
252:
248:
244:
239:
235:
231:
229:
225:
221:
220:number theory
217:
211:
208:
203:
198:
196:
192:
188:
186:
167:
163:
159:
149:
147:
143:
139:
135:
131:
126:
123:
119:
115:
111:
107:
102:
100:
96:
92:
88:
84:
80:
76:
72:
68:
64:
60:
56:
52:
48:
42:
38:
37:
31:
27:
19:
5105:Sufi studies
5076:Other fields
5044:
4956:Contemporary
4879:consultation
4701:Architecture
4466:
4459:
4452:
4445:
4438:
4431:
4424:
4417:
4410:
4403:
4394:Mathematical
4349:16th century
4300:Ibn al-Majdi
4293:15th century
4257:14th century
4176:13th century
4130:12th century
4116:Omar Khayyam
4049:11th century
3945:Aṣ-Ṣaidanānī
3913:10th century
3874:Al-Khwarizmi
3800:
3671:
3631:Hindu-Arabic
3527:Group theory
3515:Trigonometry
3486:Topos theory
3364:
3350:
3308:
3292:
3260:
3238:
3235:Sezgin, Fuat
3226:
3215:
3198:
3197:. 3. Række:
3194:
3175:
3149:
3145:
3139:
3120:
3093:
3071:
3044:
3040:Cooke, Roger
3030:
3005:
2981:
2959:
2937:
2915:
2885:
2881:
2877:
2851:
2845:
2822:
2788:
2764:
2741:
2731:
2709:
2690:
2663:
2628:
2580:
2576:
2541:
2521:, retrieved
2516:
2507:
2482:
2478:
2454:the original
2441:. Retrieved
2434:the original
2425:
2418:
2400:
2368:
2341:
2327:
2313:
2306:Nallino 1939
2301:
2280:
2267:
2255:
2250:, p. 93
2243:
2231:. Retrieved
2217:
2203:
2189:
2162:
2124:
2120:
2117:al-Muʿādalāt
2116:
2110:
2098:
2071:
2057:
2043:
2029:
2015:
1990:
1956:
1949:
1933:
1922:
1913:
1902:. Retrieved
1898:
1889:
1851:
1816:
1805:
1798:Smith (1958)
1787:
1626:Sind ibn Ali
1595:trigonometry
1575:al-Khwārizmī
1572:
1539:
1509:Ernest Renan
1496:
1486:
1482:
1478:
1474:
1465:
1455:
1448:
1440:trigonometry
1407:
1394:Ibn al-Banna
1373:
1345:
1341:
1331:
1314:
1310:
1306:
1304:
1292:
1287:
1279:
1221:Al-Khwarizmi
1217:
1201:
1193:
1170:law of sines
1167:
1160:Law of sines
1140:C.A. Nallino
1133:
1113:
1091:Al-Khwarizmi
1084:
1070:
1066:
1060:
1028:
1007:
955:Other topics
903:Architecture
864:
809:Etiquettical
768:
745: /
682:
596:
592:
538:
525:
517:
510:Omar Khayyam
508:
496:
492:
488:
480:
476:
469:
465:
462:
458:
435:Omar Khayyam
424:
404:
396:
384:
362:
328:
312:Omar Khayyám
261:, and other
240:
236:
232:
212:
199:
191:Al-Khwārizmī
189:
155:
134:al-Khwārizmī
130:medieval era
127:
114:Al-Khwārizmī
103:
99:trigonometry
45:
41:Al-Khwarizmi
34:
33:A page from
26:
5045:Mathematics
4706:Calligraphy
4412:De Gradibus
4366:Taqi ad-Din
4356:Al-Birjandi
4330:al-Qalaṣādī
4111:Al-Isfizari
4076:Ibn al-Samh
4005:Al-Isfahani
3985:al-Uqlidisi
3955:al-Khojandi
3920:Abu al-Wafa
3859:al-Dinawari
3817:9th century
3647:Mesopotamia
3621:Prehistoric
3581:Probability
3438:Algorithms
3201:1987 Nr. 1.
3136:(Reviewed:
2513:"Edited by"
2248:Struik 1987
2233:7 September
2103:Struik 1987
2076:Struik 1987
1792:Katz (1993)
1694:(1136–1206)
1682:(1048–1131)
1607:Orientalist
1562:Orientalism
1554:Rationalism
1550:Orientalist
1534:Renaissance
1483:Liber Abaci
1352:is that of
1350:Middle East
1299:al-Samaw'al
1126:Renaissance
1043:al-Samaw'al
908:Calligraphy
865:Mathematics
835:Theological
755:Eschatology
251:mathematics
247:mathematics
146:Renaissance
85:to include
79:Brahmagupta
49:during the
47:Mathematics
5137:Categories
5120:philosophy
5067:Psychology
5040:Inventions
4993:solidarity
4943:Philosophy
4923:Secularism
4837:Golden Age
4774:Capitalism
4721:Literature
4576:Influenced
4550:Influences
4320:Ali Qushji
4279:Al-Khalili
4147:Al-Khazini
4142:Al-Kharaqī
4101:al-Zarqālī
4091:al-Jayyānī
4035:al-Majriti
4020:Abu al-Jud
3990:Al-Battani
3965:Al-Saghani
3960:Al-Nayrizi
3899:al-Marwazi
3834:al-Jawharī
3571:Statistics
3503:Logarithms
3449:Arithmetic
2523:2023-12-15
2443:2012-06-08
2260:Rosen 1831
2091:Boyer 1991
1940:, p.
1938:Boyer 1991
1904:2023-12-15
1780:References
1680:Al-Khayyām
1638:Al-Battānī
1587:Al-Khayyām
1583:Al-Battānī
1569:Conclusion
1457:Al-Khayyām
1450:Al-Battānī
1404:Influences
1095:Arithmetic
1002:See also:
916:Literature
858:Inventions
814:Hygienical
778:Mysticism
716:Philosophy
644:occurs at
431:Abu al-Jud
359:Diophantus
195:Diophantus
181: 850
179: – c.
177: 780
67:Apollonius
63:Archimedes
5115:cosmology
5110:mysticism
5088:Education
5028:cosmology
5023:Astronomy
4983:Astrology
4966:dialectic
4874:consensus
4869:Democracy
4784:Socialism
4751:Economics
4696:Arabesque
4325:al-Wafa'i
4315:Ulugh Beg
4218:al-Abhari
4203:Ibn Adlan
4193:Ibn Munim
4157:al-Hassar
4096:al-Nasawī
4071:Al-Biruni
4040:al-Jabali
4030:Al-Karaji
3980:Ibn Yunus
3935:Abu Kamil
3930:Al-Qabisi
3925:al-Khazin
3854:Al-Mahani
3591:Manifolds
3587:Topology
3498:Functions
3269:cite book
2990:cite book
2984:. Berlin.
2645:0068-0346
2597:0721-832X
2499:0721-832X
1919:"algebra"
1686:Ibn Maḍāʾ
1644:Abū Kāmil
1634:(826–901)
1591:Abū Kāmil
1469:(Arabic:
1467:Abū Kāmil
1461:Descartes
1426:, in the
1390:al-Hassar
1382:mnemonics
1338:Abu Kamil
1280:al-Fakhrī
1276:Al-Karaji
1256:±
1241:±
1225:Abu Kamil
1200:. In his
1135:Geography
1067:magnitude
1039:al-Karaji
998:Induction
898:Astrology
853:Astronomy
830:Political
622:−
544:Tus, Iran
380:reduction
297:Fibonacci
267:Silk Road
255:astronomy
216:al-Karaji
122:al-Karaji
75:Aryabhata
5050:Medicine
5013:Timeline
4961:Theology
4918:Quietism
4886:Feminism
4861:politics
4817:Timeline
4478:Concepts
4310:al-Kāshī
4284:al-Umawi
4086:Avicenna
4025:Al-Sijzi
3975:Ibn Sahl
3844:Al-Kindi
3759:Category
3734:timeline
3722:timeline
3596:timeline
3576:timeline
3564:timeline
3549:timeline
3537:timeline
3520:timeline
3510:Geometry
3481:timeline
3466:timeline
3461:Calculus
3454:timeline
3442:timeline
3432:timeline
3420:By topic
3412:timeline
3345:(1999),
3259:(1900).
3237:(1997).
3225:(1921).
3092:(1984).
2958:(2001).
2936:(1983).
2914:(1977).
2874:Review:
2839:Review:
2785:(1987),
2763:(1958).
2275:(1990).
1987:(1997).
1743:See also
1658:(d. 967)
1603:geometry
1530:Bourbaki
1400:origin.
1398:Moroccan
1334:Egyptian
1311:al-zāʾid
1307:al-nāqiṣ
1301:writes:
1026:(1665).
873:Medicine
824:Military
804:Economic
799:Criminal
780:(Sufism)
721:Theology
693:a series
691:Part of
474:parabola
416:—
386:work of
369:positive
303:Concepts
284:Crusades
263:sciences
259:medicine
138:Crusades
95:geometry
5062:Physics
4906:schools
4809:History
4799:Welfare
4779:Poverty
4769:Banking
4759:History
4736:Pottery
4711:Gardens
4602:Related
4531:Madrasa
4499:Centers
4305:al-Rūmī
4208:al-Urdi
4106:ibn Hud
4061:Alhazen
4015:al-Qūhī
3626:Ancient
3427:Algebra
3166:2686206
2868:2322777
2655:Sources
2399:(ed.),
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