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Nasir al-Din al-Tusi

Persian Muslim scholar
Commemorated on an Iranian stamp upon the 700th anniversary of his death.
Name: Naṣīr al-Dīn al-Ṭūsī
Title: Khaje Nasir
Birth: 16 February, 1201 (11 Jamadi al-Ula, 597)
Death: 25th June, 1274 (18 Dhu'l-Hijjah 672)
Ethnicity: Persian
Region: Iran
Maddhab: Twelver Shī‘ah school tradition= Avicennism
Main interests: Islamic Theology, Islamic Philosophy, Astronomy, Mathematics, Chemistry, Biology and Medicine, Physics, Science
Notable ideas: Conservation of mass, Evolution, Spherical trigonometry, Tusi-couple
Works: Rawḍa-yi Taslīm, Tajrid al-'Aqaid,
Akhlaq-i-Nasri, Zij-i ilkhani,
al-Risalah al-Asturlabiyah,
Al-Tadhkirah fi'ilm al-hay'ah
Influences: Avicenna, Fakhr al-Din al-Razi, Mo'ayyeduddin Urdi
Influenced: ibn Khaldun, Qutb al-Din al-Shirazi, Ibn al-Shatir, Copernicus

Muḥammad ibn Muḥammad ibn al-Ḥasan al-Ṭūsī (Persian: محمد بن محمد بن الحسن الطوسی) (born February 1201 in Ṭūs, Khorasan – 26 June 1274 in al-Kāżimiyyah, Baghdad), better known as Naṣīr al-Dīn al-Ṭūsī (or Tusi in the West), was a Persian[1][2][3][4] of the Ismaili and subsequently Twelver Shī‘ah Islamic belief.[5] He was a polymath[6] and prolific writer: an astronomer, biologist, chemist, mathematician, philosopher, physician, physicist, scientist, theologian and Marja Taqleed.



Nasir al-Din Tusi was born in Tus east of Iran in the year 1201 and began his studies at an early age. In Tus he studied the Qur'an, Hadith, Shi'a jurisprudence, logic, philosophy, mathematics, medicine and astronomy.[7]

He was apparently born into an Ismaili Shī‘ah 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 travelled far and wide to attend the lectures of renowned scholars and acquire the knowledge which guides people to the happiness of the next world. At a young age he moved to Nishapur to study philosophy under Farid al-Din Damad and mathematics under Muhammad Hasib.[8] He met also Farid al-Din al-'Attar, the legendary Sufi master who was later killed in the hand of Mongol invaders and attended the lectures of Qutb al-Din al-Misri.

In Mawsil he studied mathematics and astronomy with Kamal al-Din Yunus (d. 639/1242). Later on he corresponded with al-Qaysari, the son-in-law of Ibn al-‘Arabi, and it seems that mysticism, as propagated by Sufi masters of his time, was not appealing to his mind and once the occasion was suitable, he composed his own manual of philosophical Sufism in the form of a small booklet entitled Awsaf al-Ashraf The Attributes of the Illustrious".

As the armies of Genghis Khan swept his homeland, he fled to join the Ismailis and made his most important contributions in science during this time when he was moving from one stronghold to another. He finally joined Hulagu Khan's ranks, after the invasion of the Alamut castle by the Mongol forces.


Tusi has about 150 works in Persian and Arabic.

A Treatise on Astrolabe by Tusi, Isfahan 1505
  • Tajrid-al-'Aqaid – A major work on al-Kalam (Islamic scholastic philosophy).
  • Al-Tadhkirah fi'ilm al-hay'ah – A memoir on the science of astronomy. Many commentaries were written about this work called Sharh al-Tadhkirah (A Commentary on al-Tadhkirah) - Commentaries were written by Abd al-Ali ibn Muhammad ibn al-Husayn al-Birjandi and by Nazzam Nishapuri.
  • Akhlaq-i-Nasri – A work on ethics.
  • al-Risalah al-Asturlabiyah – A Treatise on 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


Tusi couple from Vat. Arabic ms 319

During his stay in Nishapur, Tusi established a reputation as an exceptional scholar. "Al-Tusi’s prose writing, which number over 150 works, represent on of the largest collections by a single Islamic author. Writing in both Arabic and Persian, Nasir al-Din Tusi dealt with both religious (“Islamic”) topics and non-religious or secular subjects (the ancient sciences).".[9]. His works include the definitive Arabic versions of the works of Euclid, Archimedes, Ptolemy, Autolycus, and Theodosius of Bithynia.[9].


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 Azarbaijan, west of Maragheh, the capital of the Ilkhanate Empire.

Based on the observations in this for the time being most advanced 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, he is considered by many to be one of the most eminent astronomers of his time, and his work and theory in astronomy can also be compared to that of the Chinese scientist Shen Kuo (1031-1095 AD).

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, and it was later employed in Ibn al-Shatir's geocentric model and Nicolaus Copernicus' heliocentric Copernican model. He 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.

Tusi was also the first to present empirical observational evidence of the Earth's rotation, using the location of comets relevant to the Earth as evidence, which Ali al-Qushji elaborated on with further empirical observations. The arguments of Tusi were similar to the arguments later used by Copernicus in 1543 to explain the Earth's rotation.[10]


Tusi wrote extensively on biology and is one of the early pioneers of biological evolution in scientific thought. He begins his theory of evolution with the universe once consisting of equal and similar elements, which themselves consist of elementary particles. According to Tusi, internal contradictions began appearing, and as a result, some substances began developing faster and differently from other substances. He then explains how the elements evolved into minerals, then plants, then animals, and then humans. Tusi then goes on to explain how hereditary variability was an important factor for biological evolution of living things:[11]

"The organisms that can gain the new features faster are more variable. As a result, they gain advantages over other creatures. [...] The bodies are changing as a result of the internal and external interactions."

Tusi discusses how organisms are able to adapt to their environments:[11]

"Look at the world of animals and birds. They have all that is necessary for defense, protection and daily life, including strengths, courage and appropriate tools [organs] [...] Some of these organs are real weapons, [...] For example, horns-spear, teeth and claws-knife and needle, feet and hoofs-cudgel. The thorns and needles of some animals are similar to arrows. [...] Animals that have no other means of defense (as the gazelle and fox) protect themselves with the help of flight and cunning. [...] Some of them, for example, bees, ants and some bird species, have united in communities in order to protect themselves and help each other."

Tusi recognized three types of living things: plants, animals, and humans. He wrote:[11]

"Animals are higher than plants, because they are able to move consciously, go after food, find and eat useful things. [...] There are many differences between the animal and plant species, [...] First of all, the animal kingdom is more complicated. Besides, reason is the most beneficial feature of animals. Owing to reason, they can learn new things and adopt new, non-inherent abilities. For example, the trained horse or hunting falcon...is at a higher point of development in the animal world. The first steps of human perfection begin from here."

Tusi then explains how humans evolved from advanced animals:[11]

"Such humans [probably anthropoid apes] live in the Western Sudan and other distant corners of the world. They are close to animals by their habits, deeds and behavior. [...] The human has features that distinguish him from other creatures, but he has other features that unite him with the animal world, vegetable kingdom or even with the inanimate bodies. [...] Before [the creation of humans], all differences between organisms were of the natural origin. The next step will be associated with spiritual perfection, will, observation and knowledge. [...] All these facts prove that the human being is placed on the middle step of the evolutionary stairway. According to his inherent nature, the human is related to the lower beings, and only with the help of his will can he reach the higher development level."

Chemistry and Physics

In chemistry and physics, Tusi stated an early version of the law of conservation of mass. He wrote that a body of matter is able to change, but is not able to disappear:[11]

"A body of matter cannot disappear completely. It only changes its form, condition, composition, color and other properties and turns into a different complex or elementary matter."


Nasir al-Din al-Tusi (1201-1274) was a supporter of Avicennian logic, and wrote the following commentary on Avicenna's theory of absolute propositions:

"What spurred him to this was that in the assertoric syllogistic Aristotle and others sometimes used contradictories of absolute propositions on the assumption that they are absolute; and that was why so many decided that absolutes did contradict absolutes. When Avicenna had shown this to be wrong, he wanted to give a way of construing those examples from Aristotle."[12]


Tusi was perhaps the first to treat trigonometry as a separate mathematical discipline, distinct from astronomy, and in his Treatise on the Quadrilateral, he gave the first extensive exposition of spherical trigonometry, which he developed into its present form,[13] as he 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 Abū al-Wafā' al-Būzjānī and Al-Jayyani.

In his On the Sector Figure, he formulated the famous law of sines for plane triangles, which was one of his main mathematical contributions:[14]

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

He also stated the law of sines for spherical triangles, discovered the law of tangents for spherical triangles, and provided proofs for these laws.[14]

In 1265, Tusi wrote a manuscript regarding the calculation for nth roots of an integer. Moreover, he revealed the coefficients of the expansion of a binomial to any power giving the binomial formula and the Pascal triangle relations between binomial coefficients. He also wrote a famous work on theory of colour, based on mixtures of black and white, and included sections on jewels and perfumes.

Influence and legacy

A 60-km diameter lunar crater located on the southern hemisphere of the moon is named after him as "Nasireddin". A minor planet 10269 Tusi discovered by Soviet astronomer Nikolai Stepanovich Chernykh in 1979 is named after him.[15][16] The K. N. Toosi University of Technology in Iran and Observatory of Shamakhy in the Republic of Azerbaijan are also named after him.


  • Persian science
  • Islamic Golden Age
  • Islamic science
  • Islamic scholars
  • List of Muslim scholars
  • List of Shi'a Muslims
  • List of Iranian scientists
  • Shen Kuo


  1. ^ "Tusi, Nasir al-Din al-." Encyclopædia Britannica. 2007. Encyclopædia Britannica Online. 27 Dec. 2007 <http://www.britannica.com/eb/article-9073899>.
  2. ^ Arthur Goldschmidt, Lawrence Davidson. "A Concise History of the Middle East", Westview Press, 2005. Eighth edition, pg 136
  3. ^ Rodney Collomb, "The rise and fall of the Arab Empire and the founding of Western pre-eminence", Published by Spellmount, 2006. pg 127: "..Nasr ed-Din Tusi, the Persian, Khorasani, former chief scholar and scientist of "
  4. ^ Nanne Pieter George Joosse, Bar Hebraeus, "A Syriac encyclopaedia of Aristotelian philosophy: Barhebraeus (13th c.), Butyrum sapientiae, books of ethics, economy, and politics : a critical edition, with introduction, translation, commentary, and glossaries", Published by Brill, 2004. excerpt: " the famous Persian scholar Naslr al-Dln al-Tusi "
  5. ^ Ṭūsī, Naṣīr al-Dīn Muḥammad ibn Muḥammad; Badakchani, S. J. (2005), Paradise of Submission: A Medieval Treatise on Ismaili Thought, Ismaili Texts and Translations, 5, London: I.B. Tauris in association with Institute of Ismaili Studies, pp. 2–3, ISBN 1860644368 
  6. ^ Seyyed Hossein Nasr, Islamic Philosophy from Its Origin to the Present: Philosophy in the Land of Prophecy, SUNY Press, 2006, ISBN 0791467996. page 199.
  7. ^ Dabashi, Hamid. "Khwajah Nasir al-Din al-Tusi: The philosopher/vizier and the intellectual climate of his times". Routledge History of World Philosophies. Vol I. History of Islamic Philosophy. Seyyed Hossein Nasr and Oliver Leaman (eds.) London: Routledge. 1996. p. 529
  8. ^ Siddiqi, Bakhtyar Husain. "Nasir al-Din Tusi". A History of Islamic Philosophy. Vol 1. M. M. Sharif (ed.). Wiesbaden:: Otto Harrossowitz. 1963. p. 565
  9. ^ a b H. Daiber, F.J. Ragep, Al-Tusi, In Encyclopedia of Islam, Leiden, 2007.
  10. ^ F. Jamil Ragep (2001), "Tusi and Copernicus: The Earth's Motion in Context", Science in Context 14 (1-2), p. 145–163. Cambridge University Press.
  11. ^ a b c d e Farid Alakbarov (Summer 2001). A 13th-Century Darwin? Tusi's Views on Evolution, Azerbaijan International 9 (2).
  12. ^ Tony Street (July 23, 2008). "Arabic and Islamic Philosophy of Language and Logic". Stanford Encyclopedia of Philosophy. http://plato.stanford.edu/entries/arabic-islamic-language. Retrieved 2008-12-05. 
  13. ^ "trigonometry". Encyclopædia Britannica. http://www.britannica.com/EBchecked/topic/605281/trigonometry. Retrieved 2008-07-21. 
  14. ^ a b Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 518. ISBN 9780691114859. 
  15. ^ 2003ASPC..289..157B Page 157
  16. ^ http://books.google.com/books?q=10269+tusi&hl=lt

Further reading

  • "Ṭūsī, Muḥammad Ibn Muḥammad Ibn al-Ḥasan al-". Dictionary of Scientific Biography. New York: Charles Scribner's Sons. 1970–80. ISBN 0684101149. 
  • O'Connor, John J.; Robertson, Edmund F., "Nasir al-Din al-Tusi", MacTutor History of Mathematics archive .
  • Encyclopedia Iranica, "AḴLĀQ-E NĀṢERĪ", G.M. Wickens [1]
  • Encyclopedia Iranica, "AWṢĀF AL-AŠRĀF", G.M. Wickens [2]

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