A Short Biography of Al-Tusi Khwajah Nasir (1201-74)

While Nasir al–Din al–Tusi is his common name, his real name was Muhammad ibn Muhammad ibn al–Hasan al–Tusi. Al-Tusi was actually known under many different names throughout his life, including Muhaqqiq-i Tusi (Khwaja-yi Tusi) and Khwaja Nasir (Khwaja Nasir). Al-Tusi was conceived in Tus in northeastern Iran, near Meshed and high up in the Kashaf River valley. 

He was born in the middle of a century that would see conquests in all of Islamic world, from China to Europe to the west to China to the east. This was the time when vast military power from the Mongols would sweep through vast areas of Islamic world, displaying bitter animosity towards Islam as well as cruelly massacring the people. 

It was a time when great scholars would have little opportunity to continue their work and there was no peace or tranquility. Al-Tusi was inexorably drawn into the civil war that was sweeping his country.

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Al-Tusi’s father, a lawyer in the Twelfth Iam School, was born in Tus. Al-Tusi’s education was in a school that was predominantly religious. The Twelfth imam was the main sect among Shi’ite Muslims. Al-Tusi’s uncle taught him other subjects while he was studying at Tus. This would have a significant impact on his intellectual growth. He was taught logic, physics, and metaphysics, while also studying with other teachers to learn algebra and geometry.

Al-Tusi was thirteen years old when Genghis Khan, the leader of Mongols, began his rapid march towards the west. Al-Tusi would soon see the consequences of these conquests in his own region. But, before that, he was able study advanced topics. Al-Tusi left Tus to go to Nishapur, which is 75km west of Tus.

 Al-Tusi chose Nishapur to finish his education as it was a major centre of learning. Al-Tusi studied medicine, philosophy and mathematics there. Kamal al-Din ibn Yunus taught him mathematics, who was himself a pupil of Sharaf al-Din al-Tusi. While at Nishapur al-Tusi, he gained a reputation for being an outstanding scholar and was well-known throughout the region.

Around 1220, the Mongols invaded Tus and caused great destruction. Genghis Khan turned again his attention to the east, leaving his sons and generals in the west to carry on his conquests. Al-Tusi was attracted to peaceful havens amid the constant fighting in the region. Alamut Castle in the Elburz Mountains was ruled by the Assassins.

They also controlled other impregnable forts. Al-Tusi was invited by the Isma’ili ruler Nasir ad-Din ‘Abd ar-Rahim, to join the Assassins’ service and he accepted. He became a respected member of Isma’ili Court. It is unclear whether he would have been allowed to leave, if he had wanted to.  Al-Tusi’s best work was done while he was moving around the strongholds. He also wrote important works in logic, philosophy, mathematics, and astronomy during this time. In 1232, Akhlaq i nasiri was the first of these works. It was a work about ethics that al-Tusi devoted to Nasir ad-Din ‘Abd ar-Rahim, the ruler of Isma’ili.

Al-Tusi was present at Alamut Castle when it was attacked in 1256 by Hulegu, a Mongol leader who was a grandson to Genghis Khan and was intent on extending Mongol power into Islamic areas. Some believe that al-Tusi lied to Alamut’s defenses against the Mongols. Hulegu’s forces certainly destroyed Alamut, and Hulegu, himself an interested in science, treated al-Tusi very well. Al-Tusi may have felt that he was being held captive in Alamut against all his will. He certainly seemed excited about joining the Mongols who elected him to be their scientific advisor. He was also responsible for religious affairs, and was present with Hulegu’s Mongol forces when they attacked Baghdad 1258.

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Al-Musta’sim was the last Abbasid caliph of Baghdad. He was a weak leader, and he was no match for Hulegu’s Mongol troops when they attacked Baghdad. Al-Musta’sim and 300 other Mongol officials were killed after they laid siege to the city. Hulegu was not sympathetic to a city he had just won with his armies. He plundered and burned the city, killing many of its residents. Al-Tusi was certain to have made the right decision for his safety, and he would also benefit scientifically from his switch of allegiance.

Hulegu was delighted with Baghdad’s conquest and that al-Tusi, an outstanding scholar, had joined him. Hulegu agreed to al-Tusi’s plans for the construction a fine Observatory. Hulegu made Maragheh his capital. Maragheh, in northwestern Iran’s Azerbaijan region, was where the Observatory was built. The Observatory was built in 1259, west of Maragheh. You can still see traces of it today.

Maragheh’s observatory was operational in 1262. The observatory was built and operated by the Persians with the assistance of Chinese astronomers. There were many instruments in the observatory, including a 4-metre-wide wall quadrant of copper and an azimuth quadrant that Al-Tusi invented. Al-Tusi also designed instruments for the Observatory, which was more than just an observatory for astronomy. The Observatory had a large library that covered a broad range of scientific topics. Science, mathematics, and philosophy were all actively pursued.

Al-Tusi used his Observatory to great effect, creating very precise tables of the planetary movements. After 12 years of observations, Al-Tusi published Zij­i ilkhani. It contains tables that can be used to calculate the positions of the planets and a star catalog. 

Al-Tusi’s astronomy work was not limited to this. Al-Tusi was responsible for the most important development of Ptolemy’s model of the planet system, up to the creation of the Heliocentric model during the Copernicus. Al-Tusi’s major treatise on astronomy, al–Tadhkira al-hay’a (Memoir of astronomy), he [ 17]:

em >… created a new model for lunar motion that was fundamentally different from Ptolemy

He abolished the eccentric and centre of prosneusis and founded it entirely on the principle eight uniformly rotating globes. This allowed him to accurately represent lunar motion’s irregularities with the same precision as the Almagest T. It is true that his claim that there is a maximum difference of longitude between the theories amounts to 10 proves correct. His model was the first in the history astronomy to use a theory he invented. It was used again 250 years later in Copernicus’ “De Revolutionibus” III.

This quotation refers to the “Tusi-couple”, which converts linear motion into the sum two circular motions. Al-Tusi’s goal with this result was to eliminate all parts of Ptolemy that weren’t based on uniform circular motion. Copernicus used the Tusi-couple results after finding it in Al-Tusi. However, not all historians agree. See [38], where it is claimed that Copernicus borrowed the result from Proclus’s Commentary on Euclid’s first book.

Al-Tusi also contributed many other works to astronomy. He calculated 51′ for the precession at the equinoxes. His works also covered astronomical instruments such as the construction and use of an astrolabe. Al-Tusi used the teachings of Ibn Sina in logic. The most important work on the subject is the one on inference. This is what Street says in [ 33]:

Tusi is a thirteenth-century logician who writes in Arabic. He uses two logical connectors to construct molecular propositions. Tusi uses a dichotomous tree to show how to choose the correct disjunction relative terms in the disjuncts. He also talks about the disjunctive statements that follow from conditional propositions.

Many commentaries were written by Al-Tusi on Greek texts. These commentaries included Arabic translations of works by Autolycus and Euclid, Euclid. Apollonius, Euclid. Euclid. Apollonius. Archimedes. Hypsicles. Theodosius. Menelaus. He wrote a commentary about Menelaus’s Spherics (see “41” for more details) and Archimedes’ On the sphere & cylinder (see “21] for more details).

 Al-Tusi addressed objections that were raised by mathematicians in the past to comparing lengths for straight and curved lines. Al-Tusi claims that comparisons can be legitimate, despite objections that they are not comparable because they are different entities.

Ptolemy AlmagestT was one of the many works that Arabic scientists devoted their attention to. Al-Tusi published Tahrir al–Majisti in 1247. This was a commentary on the Almagest. For more information, see [ 5]. Like in the Ilkhahi, al-Tusi provided tables of sines with entries that corresponded to three sexual places per half degree.

Al-Tusi made a significant mathematical contribution by creating trigonometry, not as an astronomical tool but as a mathematical discipline. Treatise about the quadrilateral Al-Tusi provided the first extant explanation of the entire system of plane and cylindrical trigonometry. As described in [ 1]:

This is the first history of trigonometry as an independent branch in pure mathematics. It also contains the first time that all six cases for a right-angled, spherical trigonometric triangle have been presented.

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Al-Tusi’s 1265 manuscript concerning the calculation of n and nth roots of an integer was another mathematical contribution. See [ 6] for details about a copy of this manuscript that was made in 1413. Al-Tusi’s work is not likely to be original, but it is his interpretation of methods created by al–Karaji. Al-Tusi found the coefficients for the extension of a binomial at any power given the binomial formula, and the Pascal triangle relationships between binomial coefficients .

It is worth mentioning briefly other areas in which al-Tusi has contributed. Al-Tusi’s famous work on minerals contains a fascinating theory of colour that is based on the combination of black and white. It also includes chapters on jewels, perfumes, and other related topics. His medical works are not as important, but he did write on medicine. Al-Tusi’s contributions to ethics and philosophy were much more important. Al-Tusi was a philosopher who asked crucial questions about the nature of space.

Al-Tusi had many pupils. One of his most well-known was Nizam al-a’Raj, who wrote a commentary about the AlmagestT. Qutb ad-Din ash-Shirazi, another of his pupils, gave the first satisfactory mathematical explanation for the rainbow. These students were influenced by Al-Tusi.

Al-Tusi had a tremendous influence on eastern Islam. If we consider all fields, it is likely that Al-Tusi was more responsible than any other person for the revival and development of Islamic sciences. Maragheh’s gathering of so many talented scientists and scholars resulted in not only the revival of mathematics, astronomy, but also the renewal of Islamic philosophy, and even theology.

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