The achievements of Muslims in the area of mathematics is very remarkable. This is the study of science, like all other science, the beginning of the second Abbasi Caliph, Al-Mansour; the second half of the eighth century AD In the meantime, the work of mathematics to do something to stimulate entirely from India and Greece Muslims.1 works , and then translated into 'Arabic. Investigation, and at the end of the fifth century AH / 11th century, almost all of the original and creative work of Muslims, and even sent a letter to all non-Muslims in the Arabic mathematical works. In the 12th century, Christians and Jews started the work of translation from the Arabic and Hebrew to Latin America, but also started research in this area. But at the end of the 13th century the work of mathematics not the Muslims like Christians or Jews can do.

The number of Muslims, including the zero word count of the amount of writing, or counting the letters. Therefore, there is no simple arithmetic applied to daily life issues in trade and commerce and the distribution of land and cultural heritage. Zero of the algorithm is very important. Non-zero, this is not possible as the country tens of thousands of elements, a few, such as If you do not use the zero, it is necessary to use a table (known as the abacus) and out of units, tens of thousands, hundreds, and so on against each of the place. 2 the use of Muslims a century ago it was known as the West. Latin word Arab ciphra zero; in Arabic is sifr, or zero which means that space.

West, the use of lessons learned from the Arabs, so called for «Arabic numerals" 0.3 Arabs themselves as Hindi numbers>> (Al-Hindi A'dad aluminum). India, the Indian word translation of some writers, because that these figures are of Indian origin. However, the Hindi translation of the word does not seem correct, because sometimes written in place of Hindi words Handasi, that means the terms of Handasah works of art and geometry. Accordingly, the figures may only be referred to as Hindi means that the «mathematical characters». Few such circumstances, India can be considered as an alternative word Handasi who graduated from the circle in astronomy Dä'ira known as e-commerce can be translated into Hindi <<math (geometry) circle ' 0.4

Arabic numerals in the spread of Christianity in Europe is very slow. Christian mathematician, or the use of the old Roman numerals and the abacus, or the use of Arabic numerals, the old system. This is after the 12th century, the Muslims to acquire knowledge of Western scholars to have some literature on the digital system, and out, and is complemented by Leonardo of Pisa zero.5, who in his travel, the Muslim lands Arabic numerals and research system, the publication of a work, is mainly responsible for the introduction in Europe. The system is known as the algorithm (or algorithm), in which authors from Latin America, the father of aluminum from Khwärizmi (a native of Khwarizm) who is well-known Muslim mathematician, astronomer and geographer of the 9th century AD in the prosperous development of the Caliph Al – Ma 'Road. The full name is Abu Abdullah Muhammad ibn Musa Al-Khawàrizmi. The name of the popularity of so many has been included in multi-language world. To the 18th century, the number of science (1, 2, 3, etc.) requested by the Latin American writer algorithm, because it is in Spain, the so-called Guorismo. English poet, Chaucer as the so-called zero-augrim.6

Progress has been made of Muslim arithmetic. He wrote the books of the day-to-day use of the arithmetic. In addition, he wrote commercial arithmetic. Algebra they are an exact science. Aluminum Khwärizmi appeal, to deal with this problem Jabr Al-Kitab Wa'l Muqabalah (property of this book and compare). Jabr is the meaning of the word «property». This is something other specific amount or by multiplying the equivalent to another. The meaning of the word is compared Muqábalah. The term applied to compare the two sides, so that the equation 1 + b = 5, it seems the word Al-Jabr was originally used for such a simple action that is in addition and multiplication, but means that the whole theme. 7

Muslims in the establishment of analytic geometry and triangular and global level. Early in the development of the past is considered as part of Astronomy, as an independent branch of mathematics in the 13th century became quite advanced. Under the Caliph Al-Mansour, the center moved to the Syrian Muslim Caliphate Persia. The new capital of Baghdad, which is by the famous minister Khalid Ibn Barmak Baghdad to build the initial measurement. Persian astronomers and engineers, Naubakht, and an astronomer named Martha God has established for this purpose. In order for a book玛莎安拉is involved in the prices of these items, this is the existing Arabic. This is the first project of its kind in the Arab literature.8 a book on astrology decision, written by Kitariko Ahkam Al Naubakht.9

Caliph gathered around him some lessons in the courts of men. Court mathematician, Mohammed Ibn Ibrahim Tariq Fazari and Ya'qub Hinduism this is the first Arab mathematics and mathematical astronomy in India through the work, Siddhanta.10 sometimes ibn Yusuf Hajjaj flourish between 786 and 833 in Baghdad, the possibility of all. Is the first Arabic to EucZid E.emento. This work is translated twice, first under the Caliph Harun Rashid and his son al-mamu Academy again. The second text translated into Arabic Abu Latin.11 Conseil – Darir aluminum Jurfani (4 845), who is Muslim astronomers, mathematicians, write a paper geometric problems.12

Muslim mathematician, astronomer and geographer, Abu Abdullah Muhammad ibn Musa Al-Khwãrizmi (4 850) compiled in the Greek and Hindu knowledge and, through algorithm (later translated into Latin), Muslims and Europeans to enter the Indian figures. The impact of thinking in mathematics is more than any other medieval writer. He wrote Encyclopedia of the work of dealing with arithmetic, geometry, music and astronomy. In his books deal with the source of the problem numerals.13

In his book on algebra, Al Khwãrizmi first issue, the two equations. After introducing multiplication and division. It involves the measurement of the surface. Part of the hook to deal with the question of succession. First degree equation numerical example proves that. Authors distinguish between the following six boxes of second-degree equation. Equivalent to the root of the square, ax2 = bx value? Square equal to number, ax2 = C's? Roots equal to numbers of Ax = C? Number equal to the square and the grass-roots level, ax2 + bx value = C's? Equal to the square and the number of grass-roots ç = ax2 + bx value? Equivalent to the grass roots and the number of squares, Benxi Iron and Steel + ç = ax2. The author gives the analytical solution of linear and quadratic equations. Equation therapy thinking positive and negative points, it seems that only. The author also gives geometric solutions, figures show that of the quadratic equation x2 + l0x = 30. These equations are repeated after writers.14

In his book, the program list of six cases of Leonardo of Pisa quadratic equations such as Al – Khwärizmi do. I will comment on, the Arab method is superior to methods Pythagorus.15 three brothers, Mohammed and Ahmed Hasan, the so-called巴努穆萨(Moussa's son), in which period of vigorous development of the Al – mamu Academy of Sciences, write a lot of mathematics, mechanical engineering and astronomy. Ahmed is very interested in mechanics and Hasan in geometry. The third brother, Mohammed Abu Ja'far, who is also a student of logic and Euclid and the Almagest, is perhaps the most important thing. One of the most important projects, the rest of these papers (Frastün or Qarastun), measuring the extent and angle trisection and determine the average ratio between the two countries, given the number (and then translated into Latin America). Banu small description of the kinematic angle trisection and the lack of built gardener (with a string connected to the family) 0.16

The Encyclopedia of the scholars and philosophers of the Arabs, Abu Yusuf Ya'qüb Iraq Isäq, known as Jin Di (Latinized the Al – Kindus) belonging to the tribe, because Kindah), he wrote: 270 projects, of which involving mathematics. He wrote four books of the use of Hindi numbers. The writings of Al-Kindi Al Khwärizmi and some of the main channel system are well known West.17

Second, the cessation of the 9th century AD, in some significant increase in the Muslim mathematicians. Some of whom specialize in arithmetic, geometry, as well as in some other person, who is of particular interest to astronomers also showed Triangle. During this period, the number used by the public. This is because at the time of the trade to flourish in the Muslim world. Keen to speed up the trade figures all over the world. The date of the first Muslim documents bearing the number 874 and 888 AC18

The great astronomers and mathematicians of the century was Abu Abdullah Muhammad ibn Isa Al Mahãni its Mahan, Kerman, Persia (4 844 AC) He wrote a few reviews in the European and Archimedes was to improve the translation of Menelaus Ishak's Hunain Gay Spherics. His attempt to solve a problem, Archimedes is a sphere divided into two parts is a specific reason. This has led to three equation X3 + C2b = cx2, the so-called al-Mahani's equation. This problem has been the classical Muslim problem.19

Al Hilal Himsi translated the first four books in Arabic Ahmed Apollonius, of which three sons banana. Ahmed Ibn Yü'suf who is the Secretary of Tulunis, the rulers of Egypt from 868-905, wrote a book as a model, a commentary of Ptolemy Centiloquium, OH and the ratio of a book. The latter is particularly important, because the idea of the impact of the Middle Ages, and aware of the Western mathematicians. Theorem Menelaou (triangular horizontal cut) 0.20

Iraq Al德勒哈蒂姆this Nairizi (Latin Anaritius), which flourish under the base Mu'tadid (4 922) Ptolemy and Euclid written comments, which translated into Latin. Tangent as the use of real triangular element.21萨比特伊Qurrah (note 901) improved. Theory and friendly (if P = 3.2n – 1? G = 3.2n – 1 – 1? R = 9.22n – 1 -1? If P, Q and R together with the Prime Minister for the 2n paraquat are friendly and digital 2nr). Count, and paraboloids parabola is very valuable. 22

Al-Battani (4 929) The third chapter is dedicated to the work of the astronomical triangle. Sines is considered more than the use of the English string. Completion of the introduction of functions, and vice versa umbra umbra extension (we cotangents and tangent, which is the basic elements of triangle), and give the table cotangents degrees. To cross-strait relations and the perspective of the spherical trigonometry formula that 1 = cosine cosine b cosc + b, Wong Tai Sin, Wong Tai Sin, cosine ç A.23

In the 10th century AD, all the creative work of mathematics entirely Muslim, and all documents have been prepared in Arabic. The end of this century greatly increased the number of math.阿布卡米尔, who was one of the leading mathematicians in this period, work to improve algebra Khwãrizmi base. This is the square root of the establishment and a strong two equations. In particular, he studies, the Pentagon and the decagon and the treatment of algebra, as well as the increase and the elimination of free radicals, which is equivalent to the formula; 1 ±; = B's; (a + b ±; 2ab). He said that the proliferation and the Secretary of the Al – algebraic number. We solve the equations up to five strangers. The project is to study and extensive use of aluminum and Leonardo Karkhi the Pisa.24

Muslim doctors and Ya'qüb mathematician Ibn Said阿布奥斯曼in Baghdad Dimashqi the rapid development of politics and religion under the Muqtadir (295-320/908-932) is being translated into Arabic the work of Aristotle , Euclid, and Galen and pulse, such as temperament, the most important translation of the book of the tenth Euclid, together with Papus "comment" at this. He is a police hospital in Baghdad, Mecca and Madinah.25

Astronomer and mathematician, IHN Sinan Ibrahim Hage阿布伊斯written comments of the first book of the second curve and Almagest. Many documents, geometry and astronomy disciplines (for example, in sundial) is responsible for himself. In the squaring of the parabola is much simpler than Archimedes. In fact, this is the simplest inventions ever before, points calculus.26 Sinan Ibrahim's father is also an astronomer and mathematician. They all accepted Islam. Muslim mathematician and astronomer,阿里艾Ahmed ibn Imrãni (4 955) wrote a comment on阿布卡米尔algebra.27

Ja'far Abu – Khàzin (4 961) wrote a comment »Euclid tenth book. Other books in mathematics and astronomy, but also attributed to him. We solve the cone of the three equations known as the aluminum Mãhãni aluminum Mãhãni he can not solve the equation. 28, base Kühi, who is the author of a number of mathematics and astronomy projects, the survey result of Archimedes and Apollo higher than the second equation. We have solved these equations and discuss the terms of solvency. These surveys are the best made for the geometric Muslims.29

Abu mathematician for the 'id Ahmed Sijzi (951-1024) made a special study of the cross and the circle of conical part. This movement to replace the old one angle trisection of a purely geometric solution. (Intersection of a circle and an equilateral exaggeration) 0.30 "aluminum Sãghàni (4 990) is also a research trisections angle.31

Muhammad Abu'l Wafa Büzjani, who is one of the greatest astronomers and mathematicians of the Muslims, to flourish, he died in Baghdad, 997 or 998. This is the last Arabic translators and commentators of Greek works. He wrote reviews of Euclid, Diophantos, and Al – Khwãrizmi, and the actual value, entitled Kitab Al-Kamil (the complete book). A book, using the so-called geometric effect is also attributed to Al-Handasah him; his problem to the geometric compass move, introduced the other the size of the construction of a square, and about the construction of the regular heptagon (taking the side of one half of a side of equilateral triangle in the same cycle). This is a polyhedron is described, and gives the parable of the building points. He built the solution to the geometric X4 = 1 + ax3 and X4 = Bay

Abu'l – Wafa contributed to the development of the triangle is significant. He is the first of the Sine Theorem showed that the generality of the relative spherical triangle. It provides a new method of constructing sine tables, the value of 300, Wong Tai Sin, to correct a small number of eight. He knows that the relationship between Wong Tai Sin (1 ± b) the relationship and also the equivalent of 2sin2; / 2 = 1 – Certificate of Origin; crimes; = 2sin; / 2 power factor; / 2. We introduced the secant and cosecant six key elements, such as Triangle. He studied the tangent and the tangent table. Knowledge, this is a simple relationship between the triangular line 6, which is the most commonly used definition of them.32

Mahmoud Abu Hamid al-CD Khujandi. Exchange 1000) show that the sum of negative numbers can not be two cubic meters cubic meters of numbers. It can be seen as a discoverer of the Sine Theorem triangles.33阿布奈斯尔spherical Mansour Ben Ali, a teacher than Rooney is three, and the discovery of this theorem funding. Introduced a improved version of Menelaos spherics. He is the author of many astronomical triangle, and Ahmad ibn works.34 Maslamah commercial arithmetic wrote a book entitled Al Muâmalât. He spoke about the power of friendship and sex numbers.35

We discussed the progress of mathematics in the 11th century. Account the development of air this branch of science in Latin America and the Muslim world, George Leighton said: "The small stream of mathematical thought can be found in the Latin American literature, flow will gradually increase, but not really important until the 13th century, when the a sufficient number of the water will flow from the Arabic. He also wrote: «Let us enter Islam. It is almost like a shadow from the world's open Sunday from sleeping in a highly active," the work of 0.36 in the east, mathematics is In Egypt, West Africa and in Spain, Morocco, Tunisia and elsewhere.

Ibn Yunus (41,009), introduced the first formula is necessary before the invention of a few, that is the equivalent of the Office; of Origin; = ½ [Cosine Cosine (?-?) + (?+?)] . to some value sin10 = (1 / 3) * (8 / 9) * Wong Tai Sin (September 0 + (2 / 3) * (16/15) * crime (15/16) 0,37 Apostolos Labbän Lebanon Küshyar mathematician has made valuable contributions to the development triangle. He began to continue to investigate the Abu Ja'far tangent and Table tangents.38

Abu Ja'far Muhammad ibn Hussein to write a curriculum vitae (translated from French) and reasonable right-angle triangle, and to determine the meaning of the two sides between the two lines of proportionals geometric methods, the kinematic method that is what the so-called aluminum Handsah Thabit al-Muslim, "a fixed geometry." solution to his equation x2 + 1 = Y2.39

Abu Bakr Muhammad ibn Hasan (or Hussein)哈西卜aluminum aluminum Karkhi, and prosperity in Baghdad, the level加利卜阿布Mohammed Fakhr Ibn Khalaf Al-Mulk (4 1016). This is one of the greatest Muslim mathematicians. He wrote a book value of the name of Al-Kafi fi'l – Hisâb (sufficient basis). This book is primarily on the basis of Greek knowledge. Rather than the use of figures, author's name to write the number. He wrote a book entitled Algebraic aluminum specialized Minister Fakhri. His evidence to solve quadratic equations, and to reduce the equation of the type of C + ax2p = bxp to quadratic equations .. also introduced another and eliminate the root causes; 8 +; = 18; 50; 3; 54 – 3; 2 = 3; 16 and add the line:; 1N iodine = (; 1N a) (for 2n +1) / 3

? 1N iodine = (; 1N a) 2 (geometric proof). His solution to the Diophantine equation, including in 2005 the issue of the existence of Diophantos.40

Persian mathematician Abu'l Hasan 'Ali Nasawi, which flourished in the Sudan Buwayhid, aluminum majdal Dawlah (4. 1029) and his successor, wrote the algorithm in the Persian Gulf practice, this translated into the Arab text. Known as the Al-Mu and numerical – fi'l – Hisäb Al Hindi, the scores of the Secretary and the extraction of square and cube roots. Hexadecimal from decimal to replace is remarkable, for example, 17 ° = 1 / 100? L70.0000 = (1/l00) 4120 = 40 7'12;. 41

Ibn Haitham studied the issue have catoptrics Alhaji set. As follows: "Draw lines from the two cycles to meet the needs of the surrounding of a point, so that the point of view of equality of points and normal." Equation of the problem led to the fourth degree. Ibn Haitham to resolve with the help of a circle cross-exaggerated. Also solved the Mãhãni aluminum (cubic) equation in the same way.42

The encyclopedist Raihãn Ahmad ibn Muhammad Abu Biruni (4 in 1045) was a mathematician, astronomer, philosopher, traveler and geographer, made a good contribution to mathematics. This is a one of the greatest scientists. He spent a lot of time in India. We translated some Sanskrit works translated into Arabic, and the dissemination of knowledge of the Muslim people of India. Many works in a variety of scientific subjects attributed to him. He gave a very clear to the Arabic numerals and methods of angle trisection. It solves many problems (and later was appointed as a base Birunic issues), it can not alone.43 ruler and compass

Now we come to the mathematical work «Bin Ibrahim Omar Khayyam is one of the greatest Muslim mathematicians and astronomers of the Middle Ages. Algebra as an important work in progress, the Greeks and the Al Khwarizmi and other Muslim algebraists, and shows an advanced stage of development of this science. Although Al-Khwarizmi only quadratics, Omar Al-Khayyam mainly cubic equation. Make a good basis for the classification of equations, the complex equation, that is, contains some of the provisions. From the early 17th century modern classification is based on the equation to some extent. However, it should be pointed out that the higher the level of equations, are more likely to have different terms. The author of cubic equation is divided into 27 categories divided into four categories. The scope of efforts to address and discuss solutions. Provides a partial solution to the geometry, some of them. Euclid also investigated and summarized the recommendations. Algebra of Omar Al-Khayyam editing and translation into French of the floor Woepeke held in Paris in 1857. 44

Base of the great astronomers Zarqàli (Latin Arzachel) to explain the construction of this triangle tables.45 Jaber Aflah, in his book on astronomy Kitdb of the so-called Al-isra Al Hai'ah or write Majisti introduced an important triangle. Given the equivalent of type: Origin of B = Cosine 1, Wong Tai Sin B recangu1ar in the spherical triangle C.46 Ibn Yâsmini wrote a poem of a short-term algebra, and Muhammad al – Hassär, vigorous development in the 12th or the 13th century, wrote a paper arithmetic and algebra, it has been translated into Hebrew in 1271.47

'Abd Al Malik al-Shirazi Apollonius abreviated papers, and Fakhr al – Din of Ratsiraka, scholars and philosophers, Euclid wrote the proposal. Mohammed Abdullah Ibn Hassär composition with the help of an article entitled Ibn Yunus Al Birkàr Tamam Al Risãlah, (a theory of perfect compass). The «perfect compass>> is a tool, it can be any cone drawn.48西穆斯林mathematician, the Badr Lebanon, including the collection of algebra, known as Al-Jabr Ikhtisar valley – Muqäbalah. This series includes the theoretical and numerical examples. It involves quadratic equations, surds, polynomial multiplication, numerical theory prort.1on, indefinite system of linear equations and similar problems.49

The encyclopedist Kamal al – Din Ibn Yunus of (4 in 1242) wrote a paper arithmetic, algebra, square numbers, and the regular heptagon and similar problems. One of the problems it solves, asked the Emperor Frederick, which is made of aluminum Ayyübi Kamil, (King of Egypt from 1218 to 1238, and Damascus from 1234 to 1235). This issue has been resolved is how the size of the construction of a circular section. Evidence to address given by one of his students, al-Umar Al-Mufaddal the 'Abhari, who wrote an article for it.50

Morocco astronomer, mathematician and geographer Al-Hassan Marakãshi, who until florished. Kok in 1262, wrote several works of astronomy. Project's main mosque, called "base Mabadi wa'l – Ghäyãt (or acceded to the beginnings and ends; In other words, the principles and results) is a good compilation of practical knowledge of the astronomical instruments and methods, triangular sundial. In this work, not only show that the necessary experts and sine wave (Sam arrow), but also what is the so-called complementary sine wave (Jaib Tamam) Wong Tai Sin (90 ° – 1) = COS and over, Wong Tai Sin (jaib Federer), Wong Tai Sin (1 – 90 °) =- Sines cosine table form every six months and the experience of Sines and the arc sines.51

Morocco, another astronomer and mathematician, 13th century, Abu'l – 'Abbãs Ahmed Ben Mohamed is a very popular Muslim writers. He is the author of 74 works, most of them eat in the mathematics and astronomy. The most popular works is his book Al-Tälkhis' a base Hisab. The purpose of this book is at least two centuries, many reviews written. It is an appreciation of Ibn Khaldun. A French translation appeared in 164. This is a numerical summary of the report contains many interesting features; to improve the treatment site; continue to use Hindi numbers, the Western form of packages (ghubar). It also includes a summary of the square and cube; Casting 99.999, eight and seven; the rule of law, the position of a double error. ; (Highway A2 + R); 1 + (r/2a), one of R?字母a

? (A + by R / (2 +1)) when R "1

In addition to the author's thesis Talkhis four terms, respectively, with integer, fraction, and proportion of the root. Also wrote a paper that is the amount of binomials and the form of epitomes ±; or b; 1 ±? Group B; heritage issues, and geometry. Introduction he wrote on the measurement of R and the surface of Euclid. A book, algebra is also attributed to him.52

Now we come to the mathematical work Nasir al – Din Al-Tusi was the Persian philosopher, mathematician, astronomer, doctors and scientists. In his Arabic and Persian. This is one of the greatest Muslim mathematicians and scientists. Born in 1201 in the Turkish, Khorasan. In the "Abbasi Caliph in 1258, he became minister of Hulagu. 64 multidisciplinary books, he is responsible. He wrote a number of papers or comments on the geometry and algebra of typhoid fever. A number of numerical works are also attributed to him. He wrote letter to the heritage and prove that the sum of the two papers odd square meters can not. We have proved that if a circle involving another cycle, double the diameter of the circle of the two series or even a roll-call in the opposite direction, the rest of the tangential speed of 2 times greater than in other countries, then the initial point of contact along the small circle diameter of the circle will be greater.

Nasir al – Din of the major achievements of the high triangle. He proposed a translation of Menelaos spherics he wrote a paper in a separate request Shakl aluminum Qatta »means the percentage of the industry. This refers to Menelaus Theorem to reduce the lateral triangle; Catalan words or phrases in Latin America in Latin America or adjust catta FIGURA Catalan catta aluminum Shakl the Qatta "corruption in the Arabic Al Qatta ».'s five aluminum Shakl book Qattä 'books 3 and 4 for the plane and spherical trigonometry, respectively. This is the first book in the triangle which was seen as a separate branch of science and astronomy research, no matter. This is the biggest project of its kind in the Middle Ages. It contains the first clear formulation of the law there are two aircraft necessary evidence of the triangle. It also includes six basic types, to address the global right-angle triangle. It also provides the solution to replace the other triangle, if necessary, review from the perspective of both sides, and vice versa, with the polar triangle. 53

After Qattä of Shakl Nasir Al al – Din, and a book bearing the same title, the author is Muhiyy al – Din Al-Maghribi was the Hispano Muslim mathematician, astronomer industry. The latter part is based on the first, but the initial development of great; for example, provide two necessary and appropriate proof of the theorem of spherical triangle slope. Evidence is different from the one given to Nasir al – Din's. This theorem, and then extended to other triangles. He is also the Greek version of the classic elements of Euclid, Apollonios the Conies, a brief preface, the Menelaos and Odosios' Spherics arid other works.54

Test

1. Sutton, George, introduced the history of science, Washington, in 1953, a first volume 521

2. Arnold and Guillaume, the legacy of Islam, Oxford, 1974, p. 385.

3. Ibid. , No. 384.

4. Ibid. , Pp. 384-385.

5. Ibid. , No. 386.

6. Al-Khawarizmi, Mohammed Ibn Musa Al-Jabr effect wa'l Muqabalah, Cairo, 1939, with foreword and banana Mustafa Muhammad Ali, p. 13.

7. Arnold & Guillaume, op. Before. , No. 382.

8. Sutton, op. Before. , Vol. I, para 531.

9. Ibid.

10. Ibid. , No. 530.

11. Ibid. No. 562.

12. Ibid.

13. The Nadeem, Al Fihrist, Cairo, p. 383. Sutton, op. Before. , No. 563.

14. Al-Khawarizmi, with the former. Before. Page. 15-66, 67-106.

15. Arnold & Guillaume, op. Before. , No. 384.

16. Lebanon Nadim, op. Before. Page. 378-379. Sutton, op. Before. , P. 561.

17. Ibid. , No. 357.

18. Sutton, op. Continuous infusion. , No. 585.

19. Ibid. , No. 597.

20. Ibid. , P. 598.

21. Aluminum Qifti. , Tarikh Al Hukamä, Leipzig, 1903, No. 254

22. Ibid. 599.

23. Ibid. , No. 602.

24. Ibid. , No. 630.

25. Ibid. , No. 631.

26. Ibid. ; Aluminum Qifti », op. Before. , P. 57.

27. Aluminum Qifti, ibid. , P. 233.

28. Sutton, op. Before. , No. 664.

29. Aluminum Qifti, with the former. Before. , P. 351.

30. Sutton, op. Before. , 665.

31. Ibid. , 666.

32. Ibid. , 666. ; The Nadeem paragraph. , P. 394.

33. Ibid. , No. 667.

34. Ibid. , No. 668.

35. Ibid.

36. Ibid. , No. 695.

37. Ibid. , No. 716. ; Cell A1 – Qifti, with the former. Before. , P. 230

38. Al-Baghdadi, Ismail Basha, Hadiyyat aluminum 'Arifin, Istanbul, vol. I, 1951, No. 838.

39. Sutton, op. Before. , 666.

40. Ibid. , No. 718.

41. Ibid. , No. 719.

42. Al-Baghdadi, op. Before. , Vol. II, p. 66. ; Sutton, op. Before. , No. 721.

43. Sutton, ibid. , 707.

44. Ibid. , No. 759.

45. Ibid. , No. 758.

46. Ibid. , Volume II, part I, p. 206.

47. Ibid. , No. 400

48. Ibid. , No. 401

49. Ibid. II, Part II, Section 622.

50. Ibid. , No. 600.

51. Ibid. , No. 621; Al-Baghdadi, op. Before. , Vol. 1, p. 286.

52.Sarton, ibid. , No. 998.

53. Ibid. By 1001. ; Al-Baghdadi, op. Before. , Vol. II, p. 131.

54. Sutton, op. Before. , No. 1051. ; Al-Baghdadi, op. Before. , No. 516.