The 100 Greatest Muslims (2022): 70 - Nasir al-Din al-Tusi, 13th Century Persian Polymath Who Became The Father of Trigonometry

70

Nasir al-Din al-Tusi

Muhammad ibn Muhammad ibn al-Hasan al-Tusi (b. February 18, 1201, Tus, Khurasan, Khwarazmid Empire [now in Iran] – d. June  26, 1274, Al-Kadhimiya, Baghdad, Ilkhanate [now in Iraq]), better known as Nasir al-Din al-Tusi (or simply Tusi in the West), was a Persian architect, philosopher, physician, scientist, and theologian. Nasir al-Din al-Tusi was a well published author, writing on subjects of math, engineering, prose, and mysticism. Additionally, al-Tusi made several scientific advancements. In astronomy, al-Tusi created very accurate tables of planetary motion, an updated planetary model, and critiques of Ptolemaic astronomy. He also made strides in logic, mathematics (especially trigonometry), biology, and chemistry. Nasir al-Din al-Tusi left behind a great legacy as well. Tusi is widely regarded as one of the greatest scientists of medieval Islam, since he is often considered the creator of trigonometry as a mathematical discipline in its own right. The Muslim scholar Ibn Khaldun (1332–1406) considered al-Tusi to be the greatest of the later Persian scholars. There is also reason to believe that he may have influenced Copernican heliocentrism.  Nasir proposed that humans are related to animals and that some animals have a limited level of awareness while humans have a superior level of awareness amongst animals. He also framed a very basic evolutionary theory (though markedly different from modern evolutionary theory).

Nasir al-Din al-Tusi was born in the city of Tus in medieval Khorasan (northeastern Iran) in the year 1201 and began his studies at an early age. In Hamadan and Tus, he studied the Qur'an, hadith, Ja'fari jurisprudence, logic, philosophy, mathematics, medicine, and astronomy.

Al-Tusi was born into a Shi‘a family and lost his father at a young age. Fulfilling the wish of his father, the young Muhammad took learning and scholarship very seriously and traveled far and wide to attend the lectures of renowned scholars and acquired knowledge, an exercise highly encouraged in his Islamic faith. At a young age, he moved to Nishapur to study philosophy under Farid al-Din Damad and mathematics under Muhammad Hasib. He met also Attar of Nishapur, the legendary Sufi master who was later killed by the Mongols, and he attended the lectures of Qutb al-Din al-Misri. 

Nasir-al-Din Tusi writes in his work, Desideratum of the Faithful (Maṭlub al-muʾminin),“To become people of spiritual reality, it is incumbent to fulfill the symbolic elucidation (ta'wil) of the seven pillars of the religious law (shari'at)". He also explains that fulfilling the religious law is much easier than fulfilling its spiritual interpretation.

Nasir-al-Din explains in his book Aghaz u anjam that the sacred accounts of history that we perceive within the bounds of space and time symbolize events that have no such restrictions. They are only expressed in this way so that humans are able to comprehend them.

In Mosul, al-Tusi studied mathematics and astronomy with Kamal al-Din Yunus (d. 639 AH /1242 CC), a pupil of Sharaf al-Din al-Tusi.  Later on he corresponded with Sadr al-Din al-Qunawi, the son-in-law of Ibn Arabi, and it seems that mysticism, as propagated by Sufi masters of his time, was not appealing to him. Once the occasion was suitable, he composed his own manual of philosophical Sufism in the form of a small booklet entitled Awsaf al-Ashraf, or "The Attributes of the Illustrious".

As the armies of Genghis Khan swept his homeland, he was employed by the Nizari Ismaili state and, while moving from stronghold to stronghold, made his most important contributions in science, first in those of the Quhistan region under Muhtasham Nasir al-Din Abd al-Rahim ibn Abi Mansur (where he wrote the Nasirean Ethics). He was later sent to the major castles of  Alamut and Maymun-Diz to continue his career under Nizari Imam Ala al-Din Muhammad.  He was captured after the fall of Maymun-Diz to the Mongol forces under Hulagu Khan. 

Nasir al-Din Tusi’s autobiography, The Voyage (Sayr wa-Suluk) explains that a literary devastation such as the devastation of the Alamut libraries in 1256 would not waver the spirit of the Nizari Ismaili community because they give more importance to the “living book” (the Imam of the Time) rather than the "written word". Their hearts are attached to the Commander of the Believers (amir al-mu'minin), not just the "command" itself. There is always a present living Imam in the world, and following him, a believer will never go astray.

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. Some sources claim that al-Tusi betrayed the defenses of Alamut to the invading Mongols. After Hulegu's forces destroyed Alamut and, Hulegu himself being interested in the natural sciences, treated al-Tusi with great respect, appointing al-Tusi as his scientific adviser and becoming a permanent member of his inner council. To great controversy, it is widely assumed al-Tusi was with the Mongol forces under Hulegu when they attacked and massacred the inhabitants of Baghdad in 1258.  Soon after, he was given the full authority of administering the finances of religious foundations, and visited many of the Shi'a shrines once the siege of Baghdad was over. Being in a position of power, Tusi was able to champion the Twelver Shi'a cause throughout Persia and Iraq.

During his stay in Nishapur, Tusi established a reputation as an exceptional scholar. Tusi’s prose writing, which numbers over 150 works, represent one of the largest collections by a single Islamic author. Writing in both Arabic and Persian, Nasir al-Din al-Tusi dealt with both religious ("Islamic") topics and non-religious or secular subjects ("the ancient sciences"). His works include the definitive Arabic versions of the works of Euclid, Archimedes, Ptolemy, Autolycus, and Theodosius of Bithynia. 

Tusi convinced Hulegu Khan to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the Rasad Khaneh observatory was constructed in Azerbaijan, south of the river Aras, and to the west of Maragheh, the capital of the Ilkhanate Empire. 

Based on the observations made in the Rasad Khaneh observatory, Tusi made very accurate tables of planetary movements as depicted in his book Zij-i ilkhani (Ilkhanic Tables). This book contains astronomical tables for calculating the positions of the planets and the names of the stars. His model for the planetary system is believed to be the most advanced of his time, and was used extensively until the development of the heliocentric model in the time of Nicolaus Copernicus. 

Between Ptolemy and Copernicus, al-Tusi is arguably the most eminent astronomer of his time.  For his planetary models, he invented a geometrical technique called a Tusi-couple, which generates linear motion from the sum of two circular motions. He used this technique to replace Ptolemy's problematic equant for many planets, but was unable to find a solution to Mercury, which was solved later by Ibn al-Shatir as well as by Ali Qushji.  The Tusi-couple was later employed in Ibn al-Shatir's geocentric model and Nicolaus Copernicus' heliocentric Copernican model. Al-Tusi also calculated the value for the annual precession of the equinoxes and contributed to the construction and usage of some astronomical instruments including the astrolabe. 

Al-Tusi criticized Ptolemy's use of observational evidence to show that the Earth was at rest, noting that such proofs were not decisive. Although it does not mean that al-Tusi was a supporter of mobility of the earth, as he and his 16th-century commentator al-Birjandi, maintained that the earth's immobility could be demonstrated, only by physical principles found in natural philosophy.  Al-Tusi's criticisms of Ptolemy were similar to the arguments later used by Copernicus in 1543 to defend the Earth's rotation.

About the real essence of the Milky Way, al-Tusi in his Tadhkira writes: "The Milky Way, i.e. the galaxy, is made up of a very large number of small, tightly-clustered stars, which, on account of their concentration and smallness, seem to be cloudy patches. because of this, it was likened to milk in color."  Three centuries later the proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei used a telescope to study the Milky Way and discovered that it is really composed of a huge number of faint stars.

Al-Tusi was the first to write a work on trigonometry independently of astronomy.  Al-Tusi, in his Treatise on the Quadrilateral, gave an extensive exposition of spherical trigonomety, distinct from astronomy. It was in the works of al-Tusi that trigonometry achieved the status of an independent branch of pure mathematics distinct from astronomy, to which it had been linked for so long.

Al-Tusi was the first to list the six distinct cases of a right triangle in spherical trigonometry. This followed earlier work by Greek mathematicians such as Menelaus of Alexandria, who wrote a book on spherical trigonometry called Sphaerica, and the earlier Muslim mathematicians Abu al-Wafa' al-Buzjani and Al-Jayyani.  

In al-Tusi's On the Sector Figure, appears the famous Sine Law for plane triangles.

${\displaystyle {\frac {a}{\sin A}}={\frac {b}{\sin B}}={\frac {c}{\sin C}}}$

Al-Tusi also stated the sine law for spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for these laws.

While Aristotle (d. 322 BCT) had suggested that all colors can be aligned on a single line from black to white, Ibn-Sina (d. 1037) described that there were three paths from black to white, one path via grey, a second path via red and the third path via green. Al-Tusi (ca. 1258) stated that there are no less than five of such paths, via lemon (yellow), blood (red), pistachio (green), indigo (blue) and grey. This text, which was copied in the Middle East numerous times until at least the nineteenth century as part of the textbook Revision of the Optics (Tanqih al-Manazir) by Kamal al-Din al-Farisi (d. 1320), made color space effectively two-dimensional. Robert Grosseteste (d. 1253) proposed an effectively three-dimensional model of color space.

Al-Tusi contributed to the field of chemistry, stating an early law of conservation of mass. 

Al-Tusi contributed many writings to the topic of philosophy. Amongst his philosophical work are his disagreements with fellow philosopher Ibn Sina (Avicenna). His most famous philosophical work is Akhlaq-i nasiri or Nasirean Ethics in English. Within this work he discusses and compares Islamic teachings to the ethics of Aristotle and Plato. Al-Tusi's book became a popular ethical work in the Muslim world, specifically in India and Persia. Tusi's work also left an impact on Shi'ite Islamic theology. His book Targid also called Catharsis is significant in Shi'ite theology. He also contributed five works to the subject of logic; which were highly regarded by his contemporaries and achieved notoriety in the Muslim world.

A 60-kilometer diameter lunar crater located on the southern hemisphere of the moon is named after al-Tusi as "Nasireddin". A minor planet 10269 Tusi discovered by Soviet astronomer Nikolai Stepanovich Chernykh in 1979 is named after al-Tusi. The K. N. Toosi University of Technology in Iran and Observatory of Shamakhy in the Republic of Azerbaijan are also named after him. In February 2013, Google celebrated al-Tusi's 812th birthday with a doodle, which was accessible in its websites with Arabic language calling him al-farsi (the Persian). His birthday is also celebrated as Engineer's Day in Iran.

Naṣir al-Din al-Ṭusi, in full Muḥammad ibn Muḥammad ibn al-Ḥasan al-Ṭusi, was educated first in Ṭus, where his father was a jurist in the Twelver Shi'a school, the main sect of Shi'a Muslims. Al-Ṭusi finished his education in Neyshabur, about 75 kilometers (50 miles) to the west. This was no doubt a prudent move as Genghis Khan (d. 1227), having conquered Beijing in 1215, turned his attention to the Islamic world and reached the region around Ṭus by 1220. In about 1227, the Isma'ilite governor Nasir al-Din ʿAbd al-Raḥim offered al-Ṭusi sanctuary in his mountain fortresses in Khorasan.  Al-Ṭusi in turn dedicated his most famous work, Akhlaq-i naṣiri (1232; Nasirean Ethics), to the governor before being invited to stay in the capital at Alamut, where he espoused the Ismaʿilite faith under the new imam, Alauddin Muhammad (r. 1227–1255). (This Ismāʿīlīte state began in 1090 with the conquest of Alamut by Hasan-e Sabbah and ended with the fall of the city to the Mongols in 1256.) During this period, al-Ṭusi wrote on Ismaʿilite theology (Tasawwurat; “Notions”), logic (Asas al-iqtibas; “Foundations of Inference”), and mathematics (Tahrir al-Majisti; “Commentary on the Almagest”).

With the fall in 1256 of Alamut to Hulegu Khan (c. 1217–1265), grandson of Genghis Khan, al-Ṭusi immediately accepted a position with the Mongols as a scientific adviser. (The rather quick manner in which al-Tusi went to work for the Mongols fueled accusations that his conversion to the Ismaʿilite faith was feigned, as well as rumors that he had betrayed the city’s defenses.) Al-Ṭūsī married a Mongol and was then put in charge of the ministry of religious bequests. The topic of whether al-Ṭūsī accompanied the Mongol capture of Baghdad in 1258 remains controversial, although he certainly visited nearby Shiʾa centers soon afterward. Profiting from Hulegu’s belief in astrology, al-Ṭusi obtained support in 1259 to build a fine observatory (completed in 1262) adjacent to Hulegu’s capital in Maragheh (now in Azerbaijan). More than an observatory, Hulegu obtained a first-rate library and staffed his institution with notable Islamic and Chinese scholars. Funded by an endowment, research continued at the institution for at least 25 years after al-Ṭusi’s death, and some of its astronomical instruments inspired later designs in Samarkand (now in Uzbekistan).

Al-Ṭusi was a man of exceptionally wide erudition. He wrote approximately 150 books in Arabic and Persian and edited the definitive Arabic versions of the works of Euclid, Archimedes, Ptolemy, Autolycus and Theodosius.  He also made original contributions to mathematics and astronomy.  Al-Tusi's Zij-i Ilkhani (1271; “Ilkhan Tables”), based on research at the Maragheh observatory, is a splendidly accurate table of planetary movements. Al-Ṭusi’s most influential book in the West may have been Tadhkirah fi ʿilm al-hayʿa (“Treasury of astronomy”), which describes a geometric construction, now known as the al-Ṭūsī couple, for producing rectilinear motion from a point on one circle rolling inside another. By means of this construction, al-Ṭusi succeeded in reforming the Ptolemaic planetary models, producing a system in which all orbits are described by uniform circular motion. Most historians of Islamic astronomy believe that the planetary models developed at Maragheh found their way to Europe (perhaps via Byzantium) and provided Nicolaus Copernicus (1473–1543) with inspiration for his astronomical models.

Today al-Ṭusi’s Tajrid (“Catharsis”) is a highly esteemed treatise on Shiʾa theology. He made important contributions to many branches of Islamic learning, and under his direction Maragheh sparked a revival of Islamic mathematics, astronomy, philosophy, and theology. In the East, al-Ṭusi is an example par excellence of the hakim, -- the wise man.

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Nasir al-Din al-Tusi  was one of the most prolific authors in Muslim history and a major thirteenth century intellectual.  His range was broad as he treated both religious and scientific subjects and produced significant treatises in philosophy, mathematics, law, medicine, and astronomy. 

Even during his lifetime, Nasir al-Din al-Tusi's scholarly impact was extraordinary.  His defense of, and commentaries on, the philosophical works of Ibn Sina (Avicenna) (ca. 980-1037) revived the study of philosophy in the thirteenth century.  His Abstract on Theology left an indelible stamp on Shi'a thought and inspired subsequent Shi'a theologians to adopt his metaphysical terminology and to write commentaries on the work.  Al-Tusi advanced the scientific studies of his day by publishing definitive Arabic editions of notable works by such scholars as Ptolemy and Euclid.  Al-Tusi's most significant scientific contributions were in astronomy, as he devised sophisticated tables of celestial motion and created an astronomical model to explain the Ptolemaic system of planetary movement. 

Al-Tusi witnessed the watershed moment of medieval Islamic history -- the Mongol destruction of Baghdad in 1258 -- and throughout his life proved exceptionally adept at adjusting to tumultuous events.  His ability to thrive during such upheavals underscores his considerable talents outside scholarship.  

Born in Tus (in what is today northeastern Iran), al-Tusi began his studies under the tutelage of his open-minded father, a noted Shi'a jurist, who not only instructed him in traditional subjects such as the Qur'an, hadith, and law but also encouraged him to explore fields beyond religious learning.  From Tus, he went to Nishapur, where he spent eight years (1213-1221) under the guidance of scholars who had studied with Fakhr al-Din al-Razi (1149/50-1210).  He next traveled to Iraq for further training in mathematics, astronomy, and jurisprudence, completing his education there in 1233. 

Returning to Iran, al-Tusi entered the court of Muhtasham Nasir al-Din 'Abd al-Rahim ibn Abi Mansur (d. 1257), the Isma'ili governor of Quhistan, a province in northeast Iran.  He remained with the Isma'ilis for about twenty years and may have embraced their beliefs (either sincerely or for reasons of political expediency).  In 1255, the Isma'ili leadership sent him to negotiate with the advancing Mongol army and its leader, Hulegu (c. 1217-1265).  Negotiations failed, and the Isma'ili capital of Alamut fell in 1256.  Impressed by al-Tusi's reputation and abilities, however, Hulegu invited him to join his retinue. 

Hulegu entrusted al-Tusi with the administration of religious endowments and appointed al-Tusi court astrologer.  After the capture of Baghdad, al-Tusi began construction, under Mongol patronage, of an observatory at Maragha, in modern day Azerbaijan.  Upon its completion, in 1262, al-Tusi became its first director.  He spent most of his remaining years at Maragha, whose observatory and important library made it a scholarly center, and wrote some of his most important astronomical treatises there.  In 1274, al-Tusi died in Baghdad.  

Al-Tusi wrote about 150 works, of which 25 are in Persian and the remaining are in Arabic, and there is one treatise in Persian, Arabic and Turkish.  Some al-Tusi's more prominent works are: 

• Sayr wa-Suluk (The Voyage) - An autobiography
• Kitab al-Shakl al-qatta' -  A treatise on the complete quadrilateral and five-volume summary of trigonometry
• Al-Tadhkirah fi'ilm al-hay'ah - A memoir on the science of astronomy
• Akhlaq-i Nasiri (Nasirian Ethics) - A work on ethics

Al-Tusi initially undertook Akhlaq-i Nasiri at the behest of his first major patron, the Isma'ili governor Muhtasham Nasir al-Din.  According to al-Tusi, the governor asked him to translate The Refinement of Character by Miskawayh (ca. 932-1030) into Persian for the benefit of his people.  Al-Tusi suggested that a mere translation would not be enough and proposed an expanded treatise.  The governor approved this suggestion, and al-Tusi completed the first version in 1235.  After joining Hulegu's retinue, al-Tusi revised Akhlaq-i Nasiri, changing its introduction and conclusion.  In this new version, he apologized for having earlier glorified, Isma'ilism,, explaining that he had felt compelled to do so.

Akhlaq-i Nasiri consists of three parts, the first deeds with personal ethics, the second with the correct way to organize and manage a household, and the third with politics and government -- served as a model for many later works on ethics that strove for a similar level of comprehensiveness. 

• al-Risalah al-Asturlabiyah - A treatise on the astrolabe
• Zij-i Ilkhani (Ilkhanic Tables) – A major astronomical treatise, completed in 1272
• Sharh al-Isharat (Commentary on Avicenna's Isharat)
• Awsaf al-Ashraf - A short mystical-ethical work in Persian
• Tajrid al-I'tiqad (Summation of Belief) - A commentary on Shi'a doctrines
• Maṭlūb al-muʾminīn (Desideratum of the Faithful)
• Aghaz u anjam - An esoteric interpretation of the Qur'an

A notable sample of al-Tusi's humble wisdom is as follows:

Anyone who knows, and knows that he knows,
makes the steed of intelligence leap over the vault of heaven. 

Anyone who does not know, but knows that he does not know,
can bring his lame little donkey to the destination nonetheless. 

Anyone who does not know, and does not know that he does not know, is stuck forever in double ignorance.

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https://en.wikipedia.org/wiki/Nasir_al-Din_al-Tusi

https://www.britannica.com/biography/Nasir-al-Din-al-Tusi

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