Scientica Islamica: 1201-1274 Nasir Al-Din Al-Tusi

Nasir Al-Din Al-Tusi

(1201-1274 C.E.)

Abu Jafar Muhammad Ibn Muhammad Ibn al-Hasan Nasir al-Din alTusi was born in Tus (Khurasan) in 1201 C.E. He learnt sciences and philosophy from Kamal al-Din Ibn Yunus and others. He was one of those who were kidnapped by Hasan Bin Sabah's agents and sent to

Almut, Hasan's stronghold. In 1256 when Almut was conquered by the Mongols, Nasir al-Din joined Halagu's service. Halagu Khan was deeply impressed by his knowledge, including his astrological competency; appointed him as one of his ministers, and, later on, as administrator of Auqaf. He was instrumental in the establishment and progress of the observatory at Maragha. In his last year of life he went to Baghdad and died there.

Although usually known as Nasir al-Din al-Tusi, his proper name was Muhammad ibn Muhammad ibn al-Hasan al-Tusi. In fact al-Tusi was known by a number of different names during his lifetime such as Muhaqqiq-i Tusi, Khwaja-yi Tusiand Khwaja

Nasir. Al-Tusi was born in Tus, which lies close to Meshed in northeastern Iran high up in the valley of the Kashaf River. He was born at the beginning of a century which would see conquests across the whole of the Islamic world from close to China in the east to Europe in the west. It was the era when the vast military power of the Mongols would sweep across the vast areas of the Islamic world displaying a bitter animosity towards Islam and cruelly massacring people. This was a period in which there would be little peace and tranquillity for great scholars to pursue their works, and al-Tusi was inevitably drawn into the conflict engulfing his country.

In Tus, al-Tusi's father was a jurist in the Twelfth Imam School. The Twelfth Imam was the main sect of Shi'ite Muslims and the school where al-Tusi was educated was mainly a religious establishment. However, while studying in Tus, al-Tusi was taught other topics by his uncle which would have an important influence on his intellectual development. These topics

included logic, physics and metaphysics while he also studied with other teachers learning mathematics, in particular algebra and geometry.

In 1214, when al-Tusi was 13 years old, Genghis Khan, who was the leader of the Mongols, turned away from his conquests in China and began his rapid advance towards the west. It would not be too long before al-Tusi would see the effects of these conquests on his own regions, but before that happened he was able to study more advanced topics. From Tus, al-Tusi went to Nishapur which is 75 km west of Tus. Nishapur was a good choice for al-Tusi to complete his education since it was an important centre of learning. There al-Tusi studied philosophy, medicine and mathematics. In particular he was taught mathematics by Kamal al-Din ibn Yunus, who himself had been a pupil of Sharaf al-Din al-Tusi. While in Nishapur al-Tusi began to acquire a reputation as an outstanding scholar and became well known throughout the area.

The Mongol invasion reached the area of Tus around 1220 and there was much destruction. Genghis Khan turned his attention again towards the east leaving his generals and sons in the west to continue his conquests. There was, amid the frequent fighting in the region, peaceful havens which attracted al-Tusi.

The Assassins, who practised an intellectual form of extremist Shi'ism, controlled the castle of Alamut in the Elburz Mountains, and other similar impregnable forts in the mountains. When invited by the Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim to join the service of the Assassins, al-Tusi accepted and became a highly regarded member of the Isma'ili Court. Whether he would have been able to leave, had he wished to, is not entirely clear.

However, al-Tusi did some of his best work while moving round the different strongholds, and during this period he wrote important works on logic, philosophy, mathematics and astronomy. The first of these works, Akhlaq-i nasiri, was written in 1232.

It was a work on ethics which al-Tusi dedicated to the Isma'ili ruler Nasir ad-Din 'Abd ar-Rahim.

In 1256 al-Tusi was in the castle of Alamut when it was attacked by the forces of the Mongol leader Hulegu, a grandson of Genghis Khan, who was at that time set on extending Mongol power in Islamic areas. Some claim that al-Tusi betrayed the defences of Alamut to the invading Mongols. Certainly Hulegu's forces destroyed Alamut and, Hulegu himself being himself interested in science, he treated al-Tusi with great respect. It may be that indeed al-Tusi felt that he was being held in Alamut against his will, for certainly he seemed enthusiastic in joining the victorious Mongols who appointed him as their scientific advisor. He was also put in charge of religious affairs and was with the Mongol forces under Hulegu when they attacked Baghdad in 1258.

Al-Musta'sim, the last Abbasid caliph in Baghdad, was a weak leader and he proved no match for Hulegu's Mongol forces when they attacked Baghdad. After having laid siege to the city, the Mongols entered it in February 1258 and al-Musta'sim together with 300 of his officials were murdered. Hulegu had little sympathy with a city after his armies had won a battle, so he burned and plundered the city and killed many of its inhabitants.

Certainly al-Tusi had made the right move as far as his own safety was concerned, and he would also profit scientifically by his change of allegiance. Hulegu was very pleased with his conquest of Baghdad and also pleased that such an eminent scholar as al-Tusi had joined him. So, when al-Tusi presented Hulegu with plans for the construction of a fine Observatory, Hulegu was happy to agree.

Hulegu had made Maragheh his capital . Maragheh was in the Azerbaijan region of northwestern Iran, and it was at Maragheh that the Observatory was to be built. Construction of the Observatory began in 1259 west of Maragheh, and traces of it can still be seen there today.

The observatory at Maragheh became operational in 1262. Interestingly the Persians were assisted by Chinese astronomers in the construction and operation of the observatory. It had various instruments such as a 4 metre wall quadrant made from copper and an azimuth quadrant which was the invention of Al-Tusi himself. Al-Tusi also designed other instruments for the

Observatory which was far more than a centre for astronomy. It possessed a fine library with books on a wide range of scientific topics, while work on science, mathematics and philosophy were vigorously pursued there.

Al-Tusi put his Observatory to good use, making very accurate tables of planetary movements. He published Zij-i ilkhani (the Ilkhanic Tables), written first in Persian and later translated into

Arabic, after making observations for 12 years. This work contains tables for computing the positions of the planets, and it also contains a star catalogue. This was not the only important work which al-Tusi produced in astronomy. It is fair to say that al-Tusi made the most significant development of Ptolemy's model of the planetary system up to the development of the heliocentric model in the time of Coper nicus. In al-Tusi's major astronomical treatise, al-Tadhkira fi'ilm al-hay'a(Memoir on astronomy) he:

... devised a new model of lunar motion, essentially different from Ptolemy's. Abolishing the eccentric and the centre of prosneusis, he founded it exclusively on the principle of eight uniformly rotating spheres and thereby succeeded in representing the irregularities of lunar motion with the same exactness as the "Almagest". His claim that the maximum difference in longitude between the two theories amounts to 10 proves perfectly true. In his model Nasir, for the first time in the history of astronomy, employed a theorem invented by himself which, 250 years later, occurred again in Copernicus, "De Revolutionibus", III 4. The theorem referred to in this quotation concerns the famous "Tusi-couple" which resolves linear motion into the sum of two circular motions. The aim of al-Tusi with this result was to remove all parts of Ptolemy's system that were not based on the principle of uniform circular motion. Many historians claim that the Tusi-couple result was used by Copernicus after he discovered it in Al-Tusi's work, but not all agree; see for example where it is claimed that Copernicus took the result from Proclus's Commentary on the first book of Euclid and not from al-Tusi.

Among numerous other contributions to astronomy, al-Tusi calculated the value of 51' for the precession of the equinoxes. He also wrote works on astronomical instruments, for example on constructing and using an astrolabe. In logic al-Tusi followed the teachings of ibn Sina (Avicenna).

He wrote five works on the subject, the most important of which is one on inference. Street describes this as follows:-

Tusi, a thirteenth century logician writing in Arabic, uses two logical connectives to build up molecular propositions: 'if-then', and 'either-or'. By referring to a dichotomous tree, Tusi shows how to choose the proper disjunction relative to the terms in the disjuncts.

He also discusses the disjunctive propositions which follow from a conditional proposition.

Al-Tusi wrote many commentaries on Greek texts. These included revised Arabic versions of works by Autolycus, Aristarchus, Euclid, Apollonius, Archimedes, Hypsicles, Theodosius, Menelaus and Ptolemy. In particular he wrote a commentary on Menelaus's Spherics, and Archimedes' On the sphere and cylinder. In the latter work al-Tusi discussed objections raised by earlier mathematicians to comparing lengths of

straight lines and of curved lines. Al-Tusi argues that comparisons are legitimate, despite the objections that, being different entities, they are incomparable.

Ptolemy's Almagestwas one of the works which Arabic scientists studied intently. In 1247 al-Tusi wrote Tahrir al-Majisti (Commentary on the Almagest) in which he introduced various trigonometrical techniques to calculate tables of sines. As in the Zij-i Ilkhahial-Tusi gave tables of sines with entries calculated to three sexagesimal places for each half degree of the argument.

One of al-Tusi's most important mathematical contributions was the creation of trigonometry as a mathematical discipline in its own right rather than as just a tool for astronomical applications. In Treatise on the quadrilateralal-Tusi gave the first extant

exposition of the whole system of plane and spherical trigonometry.

This work is really the first in history on trigonometry as an independent branch of pure mathematics and the first in which all six cases for a right-angled spherical triangle are set forth.

This work also contains the famous sine formula for plane triangles:

a/sin A=b/sin B =c/sin C

Another mathematical contribution was al-Tusi's manuscript, dated 1265, concerning the calculation of n-th roots of an integer. This work by al-Tusi is almost certainly not original but rather it is his version of methods developed by al-Karaji's school. In the manuscript al-Tusi determined the coefficients of the expansion of a binomial to any power giving the binomial formula and the Pascal triangle relations between binomial coefficients.

We should mention briefly other fields in which al-Tusi contributed. He wrote a famous work on minerals which contains an interesting theory of colour based on mixtures of black and white, and included chapters on jewels and perfumes. He also wrote on medicine, but his medical works are among his least important. Much more important were al-Tusi's contributions to philosophy and ethics. In particular in philosophy he asked important questions on the nature of space.

Al-Tusi had a number of pupils, one of the better known being Nizam al-a'Rajwho also wrote a commentary on the Almagest.Another of his pupils Qutb ad-Din ash-Shirazi gave the first satisfactory mathematical explanation of the rainbow. alTusi's influence, which continued through these pupils, is summed up as follows:-

Al-Tusi's influence, especially in eastern Islam, was immense. Probably, if we take all fields into account, he was more responsiblefor the revival of the Islamic sciences than any other individual. His bringing together so many competent scholars and scientists at Maragheh resulted not only in the revival of mathematics and astronomy but also in the renewal of Islamic philosophy and even theology.

He pioneered spherical trigonometry which includes six fundamental formulas for the solution of spherical right-angled triangles. One of his most important mathematical contributions was the treatment of trigonometry as a new mathematical discipline. He wrote on binomial coefficients which Pascal later introduced. (He can be called the "Father of Trigonometry".) He was also an astronomer philosopher, and medical scholar as well as a

Geometry

Trigonometry

Algebra

Hindu-Arabic Numerals and how they came into Europe as "Arabic numerals" are explained. See other links at the bottom of this site. Also see how "Hindu" numerals came to Persia and Arabia, and then how "Arabic" numbers came into Europe.

Read an overview of "Arab Contributions to Medieval mathematics". It includes the contributions of Al-Khwarizmi, Abu Kamil Shuja (al'Hasib), Abu'l-Wafa, al-Karkhi, Omar Khayyam, and Al-Kashi.

Several biographies of scientists and mathematicians are found on on the Muslim Scholars Homepage: Al-Khwarizmi, Al-Kindi, Omar Khayyam, Al-Biruni, Nasir al-Din, and others.

Learn about Mathematicians born in Iraq, including Al Khwarizmi.

Biographies of Mathematicians by Dr. Zahoor are listed. Choose three or four of the most famous: al-Khwarizmi (algebra) [al-Khwarizmi is also here], Omar Khyyam, al-Battani (trigonometry), al-Haitham (known as Alhazen in the West, developed analytical geometry by establishing linkage between algebra and geometry), al-Tusi (non-Euclidian geometry), and al-Biruni (who determined the circumference of the earth).

See a chart comparing modern Arabic numerals with the earlier Arabic numerals developed in the Middle Ages (and influenced by the Hindu numerals with the concept of place value and the "zero").

Al-Khwarizmi (father of algebra); read another biography of Al-Khwarizmi. Read about Al-Khwarizmi and see one of his famous works on completing the square (shown below).

Arabic Mathematics is a somewhat difficult, but important article about the contributions of the Arabs in the field of mathematics.

Within a century of Muhammad's conquest of Mecca, Islamic armies conquered lands from northern Africa, southern Europe, through the Middle East and east up to India. Within a century of that the Caliphate split up into several parts. The eastern segment, under the Abbasid caliphs, became a center of growth, of luxury, and of peace. In 766 the caliph al-Mansur founded his capitol in Baghdad and the caliph Harun al-Rashid, established a library. The stage was set for his successor, Al-Ma'mum.

In the 9 century Al-Ma'mum established Baghdad as the new center of wisdom and learning. He establihed a research institute, the Bayt al-Hikma (House of Wisdom), which would last more than 200 years. Al-Ma'mum was responsible for a large scale translation project of as many ancient works as could be found. Greek manuscripts were obtained through treaties. By the end of the century, the major works of the Greeks had been translated. In addition, they learned the mathematics of the Babylonnians and the Hindus.

What follows is a brief introduction to a few of the more prominent Arab mathematicians, and a sample of their work

impression of Nasir al-Tusi on an Iranian stamp.

Al-Khwarizmi's main concern was with quadratic equations possessing positive roots, which he noted can be encountered in one of three standard forms. These equations involve three kinds of quantities: simple numbers, the root (which is the unknown, x) and wealth, known as Mal in Arabic and is the square of the root. The labels indicate the real world motivation that often drove such enquiries within Muslim civilisation. Al-Khwarizmi then proceeded to describe in detail the numerical procedures that solve particular examples of equations drawn from one of the three standard types. The formula that is recorded is nothing more than a verbal description of the standard quadratic formula that we learnt at school. The distinguishing feature of Al-Khwarizmi's work, and indeed of his successors, is the proof that is provided for the validity of the numerical procedure using the axioms and theorems of geometry. Thabit bin Al-Qurra extended Al-Khwarizmi's contributions by demonstrating the validity of the formula for the unknown of general classes of quadratic equations. He undertook this by first stating basic theorems of geometry from Euclid; the various entities in the equations, including the unknowns are related to the corresponding geometric quantities, namely line segments and areas; finally using this geometric interpretation for the terms of the equation, Al-Qurra was able to show the correspondence between the geometric and algebraic solutions.

The full "arithmetisation of algebra" and extension of the study of equations to include higher order unknowns, was ushered in by Al-Karaji, who conducted his work in Baghdad around 1000 CE. It was Al-Karaji's view that unknowns need not be limited to roots and their squares, whether geometric magnitudes or absolute numbers. More generally, unknowns could appear as cubes, x3, mal mal, x4, mal cube, x5, and so on. Thus was he able to manipulate polynomial expressions, such as x4 + 4 x 3 – 6, employing rules based on the ordinary arithmetic rules for adding, subtracting, multiplying, dividing and extracting square roots. However, Al-Karaji did not quite complete the arithmetisation of algebra; the matter had to wait 70 years for another brilliant scholar, al-Samaw'al bin Yahya bin Yahuda al-Maghribi, to add the finishing touches. The remaining step rested on fully incorporating negative numbers into the theory. Although al-Karaji had managed to discover rules such as a – (– b) = a + b, he hadn't quite encountered the related identity, – a – (– b) = – (a + b). Such identities involving negative entities are not as trivial as they seem, particularly when they must be developed or discovered for the first time. As Berggren consoles:

"Students who have struggled with the law of signs may find comfort in learning that at one time the discovery of these rules taxed the ingenuity of the best mathematicians, and that the discovery of much of our elementary (pre-calculus) mathematics was a matter of considerable labor and many false starts".

A contemporary scholar, Ruth McNeill, reminisces on how such rules led her to abandon mathematics:

"What did me in was the idea that a negative number times a negative number comes out to a positive number. This seemed (and still seems) inherently unlikely – counterintuitive, as mathematicians say. I wrestled with the idea for what I imagine to be several weeks, trying to get a sensible explanation from my teacher, my classmates, my parents, anybody."

This, then, makes al-Samaw'al's statement of the missing relation all the more remarkable. The statement appears in his exotically entitled work, Al-Bahir fi'l – Hasib (The Shining Book on Calculation), which he wrote when he was only nineteen: " … if we subtract a deficient number from a deficient number larger than it, there remains the difference [e.g. – 5 – (– 2) = – (5 – 2)], deficient; but in the other case there remains their difference, excess. [e.g. – 2 – (– 5) = + (5 – 2)]."

Al-Samaw'al's personal life makes for interesting reading. He was actually born into a Jewish family and was forced to complete the study of the remaining volumes of Euclid's Elements on his own. This was on account of not finding a sufficiently competent teacher of Mathematics in Baghdad at the time. He proceeded to study, again by himself, the work of Al-Karaji, which he then elaborated and extended. His conversion to Islam, according to his autobiography, was inspired by a dream he had in 1163. He spent his life traveling as a medical doctor, treating Princes on occasion, and died in Maragha, northern Iran, around 1180. In total, Al-Samaw'al's encyclopedic achievements spanning mathematics, astronomy, medicine and theology, fill eighty-five works, only a few of which have survived. Along with the rules relating to manipulating negative numbers described above, the law of exponents and division of polynomials are all considered in one of Al-Samawa'al's surviving mathematical studies, The Shining. What we would express today in modern notation as x-3 x-4 = x-7, Al-Samaw'al records in the language of his time as in this excerpt:

"Opposite [above] the order of part of cube is 3 and opposite part of mal mal is 4. We add them to obtain 7 and opposite it is the order of part of mal mal cube."

Such excursions in the world of exponents assisted Al-Samaw'al as he applied his sharp mind to the problem of dividing one polynomial by another. The details of the procedure need not concern us here; it suffices to reproduce Berggren's summary:

"… the discovery of this procedure of long division, which is in all its computation precisely our present-day one, is a fine contribution to the history of mathematics, and it seems to be a joint accomplishment of al-Karaji and al-Samaw'al."

Nasir al-Din al-Tusi was born in 1201 in the city of Tus. He spent his childhood and early youth in Tus, and received his primary education from his father. He learnt mathematics from a well-known scholar of the era, Kamal al-Din Muhammad Hasib, and received his logarithm, logic, philosophy and cognition tuition from Abul-?asan Bahmanyar ibn Marzuban ‘Ajami Adarbayijani (d. 1067) who was an Azerbaijani scholar and also Ibn Sîna's student. We have the impression that he was a passionate, freethinking researcher with an expansive wisdom, wide imagination and a sharp memory even at a young age.

After completing his education, Nasir al-Din al-Tusi arrived in Kuhistan at the invitation of Nasir Muhtasham, the Ismaili governor, and gained a great deal of respect amongst the Ismailis, also influencing them with his ideas. However, their relationship soured with time, and Nasir al-Din al-Tusi was then kept under surveillance in the castle of Alamut under the control of the Ismaili's for twenty-two years. There, despite his harsh living conditions, he produced his most important works on astronomy, philosophy, logic and related areas of science.

In 1256 when the Ismaili's were defeated by Hulagu, Nasir al-Din al-Tusi regained his freedom and became advisor to the Moghol ruler. In 1258, he obtained permission from Hulagu to build the Maragha observatory and began to make observations there after its completion in 1259. Nasir al-Din al-Tusi remained in his position during the regency of Abaka Khan, Hulagu's successor, and died in Bagdad in 1274 [2]. He was a great figure in the Islamic scientific tradition and a key contributor to both political and intellectual life during a century that witnessed enormous changes in the world.

3. The impact of Al-Tusi on the Ottoman world

Nasir al-Din al-Tusi was one of the most prolific authors of the Islamic medieval period, writing in both Persian and Arabic, over 150 works (excluding his poetry). He wrote on both religious and secular topics. He was a well-recognised scholar in the Ottoman world, as well as other parts of the Islamic world. The fact that al-Tusi held an important place in the Ottoman scientific literature is well understood from the fact that his books were introduced into the madrasas as textbooks and numerous copies were kept in many Ottoman libraries [3].

Furthermore, his works were utilised and translated into Turkish by many Ottoman scholars from the time of the formation of the Empire. His works including annotations were copied and translated, and several works based upon them were produced. In addition to Nasir al-Din al-Tusi's actual written legacy, some observational tools that he had developed in the Maragha Observatory were also been copied and revised by Taqi al-Din Rasid in Istanbul in the late 16th century [4]. This shows that al-Tusi was not only influential in the literature of the Ottoman world, but also in developing astronomical devices.

In addition to commentaries and translations of al-Tusi's works, direct copies of them were made, including copies of the so-called "Middle-books" or Mutawassitat, a collection of various works redacted by al-Tusi in astronomy, mechanics and music [5]. One such copy was produced at the request of the Ottoman Sultan Muhammad II in 1477–1478 [6].

In short, it can be said that the source of works that influenced the Ottoman astronomy and that comprised Ottoman astronomical literature are the works of scholars who were members of the Maragha, the Samarkand and the Egyptian astronomy-mathematic schools. Amongst these are the important works of Nasir al-Din al-Tusi, the head of the Maragha School. Some of the works that we will be discussing in this paper are Zij Ilhani, al-Tadhkirat al-Nasiriyya, Si Fasl, Bist Bab and Tahrir al-Majisti.

3.1. Si Fasl dar Ma'rifat-i Taqwim

The title of this treatise, which was written initially in Persian, namely Si Fasl dar Ma'rifat-i Taqwim (Thirty Chapters on the Knowledge of the Calendar) show clearly its subject and purpose [7].

This is also known as Risala-i Si Fasl. As one can guess from the title, this work is made up of thirty chapters and is one of the most famous and widely known works of Nasir al-Din al-Tusi on calendar making. This work was written in the State of Assassins. The treatise chapters concern the following topics: 1) on literal numeration, 2-6) on calendars and eras including Jalali calendar of Khayyam (1048–1131), 7-16) on the Sun, the Moon, and the planets, 17-30) on astrological problems.

The book was translated into Turkish by Ahmed-i Dai of Germiyan [8] (d. after 1421). It was used by Ottoman scholars in the madrasas as a textbook on astronomy and especially on calendar making. The number of annotations from both the pre and post Ottoman era and the relatively high number of translations made during the Ottoman era indicates how commonly and frequently it was used. Twenty-six copies of this book are being displayed in various libraries throughout Turkey. Ibrahim Hakki of Erzurum also mentions Tartib al-Ulum in his book Ma'rifatnama. These citations show how common this work was at madrasas in the 18th century. Between 1649 and 1650, similarly, Hajji Khalifa advised his students to read Si Fasl [9].

3.1.2. Commentaries on ‘Si Fasl' during the Ottoman Period

a. Sharhu Si Fasl (in Arabic), written by ‘Abd al-Wacid b. Muhammad al-Kutahi (d. 1435); it was translated later on into Turkish by Ahmed-i Raci [10].

b. Muvadhdhih al-Rusum fi ‘ilm al-Nujum (in Persian), with a commentary by Dellakoglu (d. 1495) in 1478 and dedicated to Sultan Muhammad II (1451-1481) [11].

c. Mukhtasar dar Ma'rifat Taqwim (in Persian), written by Hizir-Shah al-Mantashavi (d. 1449) [12].

3.1.2. Turkish Translations of Si Fasl

A. Tarjama-i Si Fasl [13]: Translated by Ahmed-i Dai of Germiyan [14]. A note in the introduction to the book shows that it was a textbook in the Ottoman madrasas [15]. In the introduction, Ahmed-i Dai said that he dedicated the translation to Sultan Celebi Muhammad [16]. There are two different editions of this translation [17]. I. H. Ertaylan first published the translation of the book with Turkish transliteration as Eskâl-i Nâsir-i Tûsî Tercümesi (Istanbul 1952). Later on, it was published again by Muammer Dizer and T. N. Gencan with Turkish transliteration, footnotes and explanations [18].

B. Tarjama-i Mukhtasar dar Ma'rifat-i Taqwim: A translation of Nasir al-Din al-Tusi's book on calendar making. Since it has seven chapters, it might be an abridged version of Si Fasl. It is the first book on calendar making during the Ottomans period. The only copy of the book contains the year 1397 [19].

C. Tarjama-i Sharh-i Si Fasl [20]. The Turkish translation of Abd al-Wacid Kutahi's (d. 1435) commentary on Si Fasl (Sharh Si Fasl). It was translated by Ahmed-i Raci (c. 1621) with the encouragement of Grand Vizier Sokullu Mehmed Pasha's son Grand Vizier Ibrahim Pasha (d. 1622) [21].

In the Ottoman world, al-Tusi's tables were also extensively used for calendar making and other activities related to astronomy and astrology. In the book Istikhraj Dustur by Osman Efendizade Abdullah Efendi (d. 1780) for instance, there are ru'yat al-ahilla's (crescents observation) tables for the year 1754–55 according to al-Tusi's tables for Istanbul's longitude [22].

3.2. Tahrir Kitab usul al-Handasa li-Uqlidis

This famous book is a very important teatise of the Arabic Euclidean tradition of geometry. It is the recension (tahrir) in Arabic by Al-Tusi of the Elements of Euclid. Known in general under the title Tahrir Kitab usul al-Handasa li-Uqlidis (Recension of the Book "Elements of Geometry" of Euclid), it had also the following title in some copies: Tahrir Uqlidis fi ‘ilm al-Handasa (Recension or Exposition of Euclid on the Science of Geometry") [23].

Euclid's' Elements (Kitab al-Usul) was extensively used and commentaries made on it in the Islamic world. Among them Nasir al-Din al-Tusi's commentary Tahrir Usul al-Handasa completed in 1248 is the most successful and valuable work focussing on Euclidean geometry [24].

According to Seyyed Hossein Nasr, Nasir al-Din al-Tusi's Tahrir and the commentaries of al-Sayyid al-Sharif al-Jurjani were used since the 13th century as the main course book for geometry lessons among the madrasa students in both the Islamic world and the Ottoman State [25].

Kawakib-i Sab'a reports that students were taught Euclid's' Book ranking at istiksâ, after Sharhu Ashkâl al-Ta'sis ranking at iktisar. Here, what is meant by "Euclid's' Book" is Tahrir Usul al-Handasa [26].

In the geometry section of his De La Littérature des Turcs, Abbé Toderini provides the following information on the Ottoman teaching of geometry:

"Geometry falls under the group of Turkish studies. In academies (madrasa), there are professors (mudarris) for teaching it [geometry] to young people. The time period between mathematics and rhetoric classes is allocated to this mathematical branch... This science is taught in a special manner. I have been to the Valide Madrasa twice, during which time students had gathered to listen to the geometry class. They used an Arabic translation of Euclid. There are many versions as well as commentaries of this book. Nasir al-Din et-Tusi's commentary, which is regarded as the best of these, has already become popular thanks to the Medicis Publishing House. This copy contains a copy of the Turkish license granted by Sultan Murad III (1574-1595) in Istanbul in 1587 [27]. "He has granted permission for the sale of this book without any tax or liability within the entire Ottoman territory..." [28].

There are also other records which show that the Tahrir Usul al-Handasa was used at Ottoman madrasas. For example Munajjimbashi Mustafa Zeki al-Istanbuli (d. 1739) was tutored with this book in 1712 by La'lizade ‘Abdülbaki b. Muhammad b. Ibrâhim (d. 1746); Yanyali As'ad Efendi with Usul-i Uqlidis by Müneccimek Muhammad Efendi; and Hasan al-Jabarti at his home (d. 1774) with Tahrir Uqlidis by Husam al-Din al-Hindi in 1731 [29].

3.2.2. Commentaries on Tahrir Usul al-Handasa

Hajji Khalifa reports that the Ottomans scholars Al-Sayyid al-Sharif and Kadizade-i Rumi had written one commentary each on Tahrir Usul al-Handasa, and that Kadizade's commentary went as far as the seventh treatise [30].

During the Ottoman period, the first study on the Tahrir is Ilhaku Abu Ishaq by Abu Ishaq Abdullah al-Kirmani (15th century). This work meticulously annotates the first four treatises of the Tahrir [31].

Another study on the Tahrir is the Ta'lik of the chief astronomer Munajjimbashi Darwish Ahmed Dede b. Lütfullah (d. 1702) titled Tahrir al-Fawa'id (in Arabic). It is referred to as Ta'likat ‘ala Uqlidis (Notes on Euclid) in some sources [32].

An additional work on the Tahrir is the Sharh Ba'd al-Makalat al-Uklidisiyya (in Arabic) by Bedruddin Muhammad b. As'ad b. Ali b. ‘Osman b. Mustafa al-Yanyavi al-Islamboli (d. 1733), son of Yanyali As'ad Efendi [33]. However, this work is not covered in the literature. Containing some problems on Euclidian geometry, this book is one of the most important works on Euclidian geometry produced during the Ottoman period [34].

3.3. Risala-i bist bab dar ma'rifet-i asturlab

This work of Nasir al-Din al-Tusi in the field of the astrolabe is one of the books most used, studied and taught in Ottoman madrasas [36]. It is titled Risala-i bist bab dar ma'rifet-i asturlab (in Persian), that is Treatise in Twenty Chapters on the Knowledge of the Astrolabe) [37]. There are fifty-two copies of this book in Turkish libraries. Erzurumlu Ibrahim Hakki recommended this book to madrasa students by saying "regard the astrolabe as one of the applied sciences / Fly with Bist Bab to watch the solar system" in his Tartib-i Ulum. The book was taught by Hajji Khalifa many times to students between 1649 and 1650.

3.3.1. Commentaries on Bist bab

a. Sharh-i bist bab dar ma'rifat-i asturlab (in Persian): This commentary was written by Muhammad b. Haci b. Suleyman al-Bursavi (d. c. 1495) also known as Efezade, and presented to Sultan Bayezid II (1481-1512) [38].

b. Sharh-i bist bab dar ma'rifat-i asturlab (in Persian): Authored in Persian by al-Birjandi in 1494, this work was taught at madrasas. There are around 30 copies of it [39].

3.3.2. Translations of Bist Bab

A. Tarjama-i bist bab (in Turkish): This was translated into Turkish by an anonymous translator who explains in the introduction that the translation was done for Ayaz Aga, one of the entourage of the sultan of the time. This person is probably Ayaz Pasha, who served as Janissary Aga and Grand Vizier in the time of Yavuz Sultan Selim and Suleiman the Magnificent [40].

B. Nuzhat al-Tullab fi ‘ilm al-asturlab (in Arabic): Translated by Haydar b. ‘Abdurrahman al-Husayni al-Jazari (d. c. 1689) from Persian into Arabic, there are currently forty three copies of this book [41].

C. Risala-i fi ma'rifet-i sihhat al-Asturlab (in Arabic): The chapters on whether the astrolabe was built with accurately, and showing of fixed stars on the orbit of the spider, it was translated in 1716 by an unknown person [42].

Bist Bab was also partly translated. For example, Ibrahim b. Halil al-Erzurumi al-Haddadi, also known as "Yekdest," translated into Turkish the section on "Signs of Twenty Seven Stars" at the end of Bist Bab [43].

3.4. Al-Tadhkira al-Nasiriyya fi ‘ilm al-hay'a

Nasir al-Din al-Tusi's Al-Tadhkira fi ‘ilm al-hay'a (Memoir on the Science of Astronomy) [44] (in Arabic) is one of the most original and influential Arabic works in astronomy. It is a text devoted to disclose the general principles of astronomy for the general reader, whence its title as Tadhkira (Memoir). The treatise described Ptolemaic concepts such as the epicycle theory and introduced new planetary models. Al-Tadhkira is one of the two books which the Samarkand school of mathematics/astronomy studied, read, taught, discussed and commented on the most. It is placed at the heart within the Islamic astronomical tradition. At the same time, it was also taught as a textbook at Samarkand Madrasa [45].

Used in the Ottoman world as an astronomy textbook at the madrasas, this book of al-Tusi consisted of four chapters. Having many commentaries, the most famous of which in the Muslim world is that of al-Birjandi. The book has kept its popularity until today. It too was taught at Iranian madrasas. A commentary on Al-Tadhkira was produced on by its author under the name Tavdhih Al-Tadhkira.

While Taskoprülüzade also places this work in the group of compendia, Hajji Khalifa places it under the heading Al-Tadhkirat al-Nasiriyya fi al-hay'a, explaining that it is a compendium containing issues and certain findings of astronomy. Twenty copies are found in Turkish libraries.

3.4.1. Commentaries during the Ottoman Period

We learn from the commentaries that this work by Nasir al-Din al-Tusi was respected as a textbook and taught at Ottoman madrasas:

a. Sharh Al-Tadhkira fi al-hay'a [46] (in Arabic): Fathullah Shirwani (d. 1486) first wrote commentaries on the works of his mentor and then penned some additional commentaries on the important theoretical work of Nasir al-Din al-Tusi (d. 1273) on astronomical history, Al-Tadhkira fi ilm al-hay'a. Making use of commentaries previously written by al-Sayyid al-Sharif al-Jurjani and Nizam al-Din al-A'raj al-Nishaburi, Shirwani wrote this commentary completed in 1475, to build on these previous works and to offer a complete textbook to his students [47]. Some chapters of this book tell the reader about the Ulugh Bey Madrasa and his own student years there. The 54-page appendix following the first chapter is like an individual book on optics.

b. Sharh-i al-Tadhkira-i Haja Nasir-i Tusi (in Persian) was authored by al-Birjandi in 1507 [48].

c. Sharh al-Tadhkira al-Nasiriyye fi al-hay'a (in Arabic): Belongs to Kadizade Rumi [49].

3.5. Tansuq-nama-yi Ilhani

One of the books most widely used in mineralogy was Tansugname-i Ilhani or Jawahir-nama (Book on Precious Stones) of Nasir al-Din al-Tusi [50]. Al-Tusi wrote this book in Persian in Maragha and dedicated it to Hulagu Han [51]. It was known and used in the Ottoman world from the earliest period. Taskoprülüzade Ahmed Efendi pointed out the importance of this work describing it as "the most useful and compact text on mineralogy" [52]. Hajji Khalifa, who referred to it as Tansugname-i ilhani, said that "it belongs to Nasir al-Din Muhammad b. Muhammad al-Tusi. It is a compendium. It is organized into four treatises; on minerals, precious stones, ores, and fragrant plants" [53].

This work was translated by Mustafa b. Seydi [54] (15th century) for Beylerbeyi Karacabey in the time of Sultan Murad II (1421–1451) [55] with the title Tarjama-i Tansugname-i Ilhani or Jawahirnama-i Sultan Muradi [56]. On the cover of the translation, the title of the book is Tarjama-i Kitab al-Jawahir al-Musamma bi-Tansikh-i Ilhani [57]. It is a reorganized and abridged adaptation of Tansugname-i Ilhani. Mutarjim Mustafa ibn Saydi removed the First, Third and Fourth treatises of the original text, and only included the Second treatise which dwells on the characteristics of mineral ores [58].

Another important characteristic of this work is that its First Treatise contains information about ancient Chinese and Turkish medicine. The book provides information about precious stones and their characteristics. It consists of seven treatises each of which is called a Maqal [59]. While the first six treatises deal with pearl, ruby, emerald, diamond and turquoise, the seventh treatise provides organized information on musk, zebad, anbar, sandal, ud (various perfumes) and camphor, and other eccentric and bizarre stones [60].

That this book was translated into Turkish in the time of Sultan Murad II, and that it was included in the bibliography of the book Yak'tat al-Mahazin fi Jawahir al-Ma'adin written by Yahya b. Muhammad al-Gaffari in the name of Prince Korkut, suggests that this book was in demand among the Ottomans [61].

3.6. Tahrir al-Majisti

The Almagest was Ptolemy's most influential work in the Islamic world. The Tahrir al-Majisti (Exposition of the Almagest) [62] by Al-Tusi (in Arabic) was also very popular in the Islamic world. The author states he wrote the book due to the encouragement of Husam al-Din al-Hasan b. Muhammad al-Sivasi, whom Al-Tusi calls sayf al-munadhirin (sword of the debaters). There are twenty-two known copies of the work in Turkish libraries.

Nizam al-Din al-Nishaburi wrote a commentary of the work with the title Ta'bir al-Tahrir. Later, Kadizade-i Rumi wrote a work entitled Hashiya ‘ala Kitab al-Majasti (in Arabic) in which he explained certain sections of the commentary of al-Nishaburi [63].

3.7. Kashf al-qina' ‘an asrar al-Shakl al-qatta'

This treatise Kashf al-qina' ‘an asrar al-Shakl al-qatta' (Removal of the Veil from the Mysteries of the Secants Figure) bears sometimes other titles, that is al-Risalat al-qatta' fi ‘ilm al-Handasa (Treatise on Secants in the Science of Geometry) and Kitab al-shakl al-qatta' (The Book on the Secant Figure). In all manuscripts, it is in Arabic.

Al-Tusi's work is the first systematic trigonometry text, independent of astronomy in Muslim civilization. Hajji Khalifa proposes that this book is related to the first figure in the first chapter of Menelaus of Alexandria's (c. 70-140 CE) Kitâb al-Ukar's (Sphaerica). It was also first written in Arabic and then translated into Persian by the author himself as a five-chapter book [64]. The number of copies of the Kashf al-qina' in the libraries indicates how commonly and frequently it was used through scholars [65]. The French and the Turkish translations of the book in the Ottoman state at the last quarter of 19th century and first quarter of the 20th century shows that this book still very well-liked.

Alexandr Carathéodory published an Arabic edition of the text, accompanied by a French translation [66]. The work was also translated into Turkish by Celal Saygin (d. 1954) [67]. The printing of this book in the Ottoman state at the end of the 19th century and translation of it in the beginning of the 20th century shows how the Ottomans were still interested al-Tusi's works. "The work in 5 books was written in the State of Assassins for the great magister al-Muayyad ibn Husayn, in 1. On composed ratios (in proposition 1 the notion of "quantity of a ratio" is introduced, for ratio A/B it is quantity Q such that Q/1=A/B, therefore these quantities are equivalent to our real numbers, and the quantity of a ratio composed from two ratios is equal to product of quantities of quantities of these ratios. 2. Theorem of plane figure of secants (plane complete quadrilateral) and proof of the Menelaus theorem for this figure. 3. Introduction to the theory of spherical figure of secants (spherical complete quadrilateral). 4. Proof of the Menelaus theorem for spherical figure of secants. 5. "Methods replacing figure of secants", that is, spherical theorems of sines and tangents and solution of spherical triangles by three known elements for all six cases, for triangles with three known angles – by means of polar triangle" [68].

Tarjama-i al-Bah al-Shahiyya wa al-tarkibat al-Sultaniyya

Kitab al-bab al-bahiya fi al-tarakib al-sultaniya or Bahnama-i Padishahi or al-Bah al-Shahiyya [69], written in Persian, is attributed to al-Tusi [70]. A regimen for the ailing son of the sultan of Qazan, it is divided into three parts of which the first two deal with dietetics and health rules and the third with sexual intercourse. It was translated from Persian into Turkish for the Ottoman Sultan Murad II by a certain Musa b. Mas'ud [71], about whom nothing is known [72]. Consisting of seventeen chapters, the work takes up subjects such as the temperament of humans, aphrodisiacs, sorbets, pastes and healing drugs [73].

Al-'Ikd al-Yamani fi Hall-i Zij Ilhani

It is a commentary in Arabic of Ibn al-Nakib [74] (d. 1563) on Nasir al-Din al-Tusi's Zij Ilhani [75].

Muhammad ibn Muhammad ibn Hasan al-Tusi (born in 18 February 1201 in Tus, Khorasan – died on 26 June 1274 in Baghdad), better known as Nasir al-Din al-Tusi, was a Muslim Persian scholar and prolific writer in different fields of science and philosophy. He was an astronomer, mathematician, physicist, philosopher, and theologian. Born in Tūs (northeast Iran), 17 February 1201 (11 Jumada al-Ula 597H) Died in Baghdad (Iraq), 25 June 1274 (18 Dhu'l-Hijjah 672H)

Muhammad ibn Muhammad ibn Hasan al-Tūsī (born in 18 February 1201 in Tūs, Khorasan – died on 26 June 1274 in Baghdad), better known as Nasīr al-Dīn al-Tūsī, was a Muslim Persian scholar and prolific writer in different fields of science and philosophy. He was an astronomer, mathematician, physicist, philosopher, and theologian.

Al-Tūsī wrote over 150 works, in Arabic and Persian, that dealt with mathematical sciences, philosophy, and the religious sciences (fiqh, kalām, and Sufism). By his prolific oeuvre, the wide diffusion of his works and their influence, he acquired the honorific titles of khwāja (distinguished scholar and teacher), ustādh al-bashar (teacher of mankind), and al-mu'allim al-thālith (the third teacher, after Aristotle and Al-Fārābī). In addition, Al-Tūsī was the director of the Islamic major astronomical observatory of Marāgha (northern Iran).

Al-Tūsī was born into a family of learned scholars. His father and his uncles encouraged him to pursue the Islamic religious sciences as well as the the rational sciences. He studied philosophy and mathematics in his native town Tūs, but eventually traveled to Nīshāpūr (after 1213) in order to continue his education in sciences, medicine, and philosophy. He studied the works of Ibn Sīnā, who became an important formative influence. Al-Tūsī then traveled to Iraq where his studies included legal theory; in Mosul (sometime between 1223 and 1232), one of his teachers was Kamāl al-Dīn ibn Yūnus (died 1242), a legal scholar who was also renowned for his expertise in astronomy and mathematics.

In the early 1230s, after completing his education, Tūsī found patrons at the Ismā'īlī courts in eastern Iran. He eventually relocated to Alamūt, the Ismā'īlī capital, and witnessed its fall to the Mongols in 1256. Al-Tūsī then served under the Mongols as an advisor to their leader Hūlāgū, becoming court astrologer as well as minister of religious endowments (awqāf). In his new position, Al-Tūsī convinced Hūlāgū to found an astronomical observatory and he oversaw the construction of this major scientific institution and its instruments in Marāgha, the Mongol headquarters in Azerbaijan, and he became its first director until his death in 1274. The Marāgha Observatory also comprised a library and school. It was one of the most ambitious scientific institutions established up to that time and may be considered the first full-scale observatory. It attracted many famous and talented scientists and students from the Islamic world and even from as far away as China. The observatory lasted only about 50 years. However, even after its activity stopped, the scientific legacy of Maragha observatory had repercussions from China to Europe for centuries to come. Indeed, it is said that Ulugh Beg's childhood memory of visiting the remnants of the Marāgha Observatory as a youth contributed to his decision to build the Samarqand Observatory. Mughal observatories in India, such as those built by Jai Singh in the 18th century, clearly show the influence of these earlier observatories, and it has been suggested that Tycho Brahe in late 16th century Europe might have been influenced by them as well. In 1274 Tūsī left Marāgha with a group of his students for Baghdad, where he died soon after.

Al-Tūsī's writings are both synthetic and original. His recensions (tahārīr) of Greek and early Islamic scientific works, which included his original commentaries, became the standard in a variety of disciplines. These works included Euclid's Elements, Ptolemy's Almagest, and the so called mutawassitāt (the "Intermediate Books" that were to be studied between Euclid's Elements and Ptolemy's Almagest) with treatises by Euclid, Theodosius, Hypsicles, Autolycus, Aristarchus, Archimedes, Menelaus, Thābit ibn Qurra, and the Banū Mūsā. In mathematics, Al-Tūsī published a sophisticated "proof" of Euclid's parallels postulate that was important for the development of non-Euclidian geometry, and he treated trigonometry as a discipline independent of astronomy, which was in many ways similar to what was accomplished later in Europe by Johann Müller (Regiomontanus). Other important and influential works include books on logic, ethics, and a famous commentary on a philosophical work of Ibn Sīnā.

Nasīr al-Dīn al-Tūsī's major scientific writings in astronomy, including Al-Tadhkira fī ‘ilm al-hay'a, in which he endeavoured to reform Ptolemaic astronomy, had an enormous influence upon late medieval Islamic astronomy as well as the work of early-modern European astronomers, including Copernicus.

Al-Tūsī wrote several treatises on practical astronomy (taqwīm), instruments, astrology, and cosmography/theoretical astronomy (‘ilm al-hay'a). He also compiled a major astronomical handbook (in Persian) entitled Zīj-i Īlkhānī for his Mongol patrons in Marāgha. Virtually all these works were the subject of commentaries and supercommentaries, and many of his Persian works were translated into Arabic. They were influential for later generations, some still being used into the 20th century.

In planetary theory, Al-Tūsī sought to reform the Ptolemaic system by correcting its inconsistencies, in particular its violations of the fundamental principle of uniform circular motion for heavenly bodies. For this purpose, he especially set forth an astronomical device (known among the historians as the Tūsī-couple) that consisted of two circles, the smaller of which was, internally, tangent to the other that was twice as large. The smaller rotated twice as fast as the larger and in the opposite direction. Wit this device, Al-Tūsī proved that a given point on the smaller sphere would oscillate along a straight line. By incorporating this device into his lunar and planetary models, Al-Tūsī reproduced Ptolemaic accuracy while preserving uniform circular motion, a condition reconciling astronomy with the prevalent natural philosophy. A second version of this device could produce (approximately) oscillation on a great circle arc, allowing Al-Tūsī to deal with irregularities in Ptolemy's latitude theories and lunar model.

Al-Tūsī disclosed these models in several of his works, mainly in his famous Arabic treatise Al-Tadhkira fī ‘ilm al-hay'a (Memoir on astronomy). His models were of major significance in the history of astronomy. First, they produced models that adhered to both physical and mathematical requirements; the two versions of the Tūsī couple, from the perspective of mathematical astronomy, allowed for a separation of the effect of distance of the planet from its speed (which had been tied together in the Ptolemaic models). Al-Tūsī was thus able, for example, to circumvent Ptolemy's reliance on a circular motion to produce a rectilinear, latitudinal effect. Second, these new models were greatly instrumental for Al-Tusi's successors in Islamic astronomy, such as his student Qutb al-Dīn al-Shīrāzī and Ibn al-Shātir (14th century) as well as the work of early-modern European astronomers such as Copernicus. Their influence crossed the borders of astronomy written in Arabic or Persian and they are found in Sanskrit and Byzantine texts.

Al-Tūsī also influenced his astronomical and cosmological successors with his discussion of the Earth's motion. Although he remained committed to a geocentric universe, Al-Tūsī criticized Ptolemy's reliance on observational proofs to demonstrate the Earth's stasis, noting that such proofs were not decisive. Recent research has revealed a striking similarity between Al-Tūsī's arguments and those of Copernicus.

Conclusion

Works of Nasir al-Din al-Tusi have always attracted the interest of Ottoman scholars from the earliest days until the last period. Some of his works were translated into Turkish and various annotations or commentaries were written upon them. The fact that some of his books were introduced in the madrasas as textbooks shows the importance of his work. A large number of Nasir al-Din al-Tusi's works, copies of his books and written annotations have lasted until today. It is import to note that most of al-Tusi's works are being displayed in many libraries of Turkey, especially Istanbul, and in many countries previously governed by the Ottomans in order to understand the broader aspects of his influence. This study examines al-Tusi's work on scientific fields such as mathematics, astronomy, or mineralogy and demonstrates how important he was to the Ottoman world. In addition, it is important to show how al-Tusi influenced the Ottomans way of thinking by carefully considering his works on religion, faith, philosophy and other social sciences. As a result of this study, Nasir al-Din al-Tusi's contribution to European philosophy and science via the Ottoman world can also be revealed.

The Influence of Nasir al-Din al-Tusi on Ottoman Scientific Literature

The works of Nasir al-Din al-Tusi have always attracted the interest of Ottoman scholars as early as the 14th century. Some of his works were translated into Turkish and various annotations or commentaries were written upon them. They were also introduced in the school curriculum as textbooks, which testify to the wide scope of his impact on Ottoman scholarship. Another aspect of his remarkable influence is represented by the presence of very numerous manuscript copies of al-Tusi's works in many libraries of Turkey, especially Istanbul, and in many countries previously governed by the Ottomans. This article examines al-Tusi's work on scientific fields practiced under the Ottomans such as mathematics, astronomy, scientific instrumentation, and mineralogy and demonstrates how important he was to the scholarship of the Ottoman world.

Nasir al-Din Abu Ja'far Muhammad ibn Muhammad ibn al-hasan Muhammad ibn Muhammad b. Hasan Abu Bakr al-Tusi (1201–1273/74)

Nasir al-Din Abu Ja'far Mu?ammad ibn Mu?ammad ibn al-?asan Muhammad ibn Muhammad b. Hasan Abu Bakr al-Tusi (1201–1273/74) was a polymath scholar of science and philosophy who wrote many books in diverse areas of learning such as astronomy, mathematics, medicine, music, logic, physiology, philosophy, literature, geography, theology and occult sciences. He also founded and directed the famous Maragha observatory, one of the largest astronomical observatories in the Islamic world [1].

2. Short biography

3. The impact of Al-Tusi on the Ottoman world

3.1. Si Fasl dar Ma'rifat-i Taqwim

The title of this treatise, which was written initially in Persian, namely Si Fasl dar Ma'rifat-i Taqwim (Thirty Chapters on the Knowledge of the Calendar) show clearly its subject and purpose [7].

3.1.2. Commentaries on ‘Si Fasl' during the Ottoman Period

a. Sharhu Si Fasl (in Arabic), written by ‘Abd al-Wacid b. Muhammad al-Kutahi (d. 1435); it was translated later on into Turkish by Ahmed-i Raci [10].

b. Muvadhdhih al-Rusum fi ‘ilm al-Nujum (in Persian), with a commentary by Dellakoglu (d. 1495) in 1478 and dedicated to Sultan Muhammad II (1451-1481) [11].

c. Mukhtasar dar Ma'rifat Taqwim (in Persian), written by Hizir-Shah al-Mantashavi (d. 1449) [12].

3.1.2. Turkish Translations of Si Fasl

3.2. Tahrir Kitab usul al-Handasa li-Uqlidis

In the geometry section of his De La Littérature des Turcs, Abbé Toderini provides the following information on the Ottoman teaching of geometry:

3.2.2. Commentaries on Tahrir Usul al-Handasa

Figure 2: First pages of Bist bab dar ma'rifat-i asturlab, Istanbul, Suleymaniye Library, Ayasofya, MS 2620.

3.3. Risala-i bist bab dar ma'rifet-i asturlab

3.3.1. Commentaries on Bist bab

b. Sharh-i bist bab dar ma'rifat-i asturlab (in Persian): Authored in Persian by al-Birjandi in 1494, this work was taught at madrasas. There are around 30 copies of it [39].

3.3.2. Translations of Bist Bab

Figure 3: First pages of Sharh-i bist bab dar ma'rifet-i asturlab, Istanbul, Süleymaniye Library, Ayasofya, MS 2641.

3.4. Al-Tadhkira al-Nasiriyya fi ‘ilm al-hay'a

3.4.1. Commentaries during the Ottoman Period

We learn from the commentaries that this work by Nasir al-Din al-Tusi was respected as a textbook and taught at Ottoman madrasas:

b. Sharh-i al-Tadhkira-i Haja Nasir-i Tusi (in Persian) was authored by al-Birjandi in 1507 [48].

c. Sharh al-Tadhkira al-Nasiriyye fi al-hay'a (in Arabic): Belongs to Kadizade Rumi [49].

3.5. Tansuq-nama-yi Ilhani

Figure 4: The drawing of Nasir al-Din Tusi on a recent Iranian stamp.

3.6. Tahrir al-Majisti

3.7. Kashf al-qina' ‘an asrar al-Shakl al-qatta'

Figure 5: The portrait of the Ottoman Sultan Mehmet II (Muhammad II, 1451-1481).

3.8. Tarjama-i al-Bah al-Shahiyya wa al-tarkibat al-Sultaniyya

3.9. Al-'Ikd al-Yamani fi Hall-i Zij Ilhani

It is a commentary in Arabic of Ibn al-Nakib [74] (d. 1563) on Nasir al-Din al-Tusi's Zij Ilhani [75].

Born in Tūs (northeast Iran), 17 February 1201 (11 Jumada al-Ula 597H)

Died in Baghdad (Iraq), 25 June 1274 (18 Dhu'l-Hijjah 672H)

References

4. Conclusion

Works of Nasir al-Din al-Tusi have always attracted the interest of Ottoman scholars from the earliest days until the last period. Some of his works were translated into Turkish and various annotations or commentaries were written upon them. The fact that some of his books were introduced in the madrasas as textbooks shows the importance of his work. A large number of Nasir al-Din al-Tusi's works, copies of his books and written annotations have lasted until today. It is import to note that most of al-Tusi's works are being displayed in many libraries of Turkey, especially Istanbul, and in many countries previously governed by the Ottomans in order to understand the broader aspects of his influence. This study examines al-Tusi's work on scientific fields such as mathematics, astronomy, or mineralogy and demonstrates how important he was to the Ottoman world. In addition, it is important to show how al-Tusi influenced the Ottomans way of thinking by carefully considering his works on religion, faith, philosophy and other social sciences. As a result of this study, Nasir al-Din al-Tusi's contribution to European philosophy and science via the Ottoman world can also be revealed.

5. References

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