Nasir al-Din al-Tusi
Encyclopedia
Khawaja Muḥammad ibn Muḥammad ibn Ḥasan Ṭūsī (born 18 February 1201 in Ṭūs
, Khorasan
– died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad
), better known as Naṣīr al-Dīn al-Ṭūsī , was a Persian
polymath
and prolific writer: an astronomer
, biologist
, chemist, mathematician
, philosopher
, physician
, physicist
, scientist
, theologian
and Marja Taqleed. He was of the Ismaili
-, and subsequently Twelver Shī‘ah Islam
ic belief. The Muslim scholar Ibn Khaldun
(1332–1406) considered Tusi to be the greatest of the later Persian
scholars.
Nasir al-Din Tusi was born in the city of Tus in medieval Khorasan
(now in north-eastern Iran
) in the year 1201 and began his studies at an early age. In Hamadan and Tus he studied the Qur'an
, Hadith
, Shi'a jurisprudence, logic, philosophy, mathematics, medicine and astronomy.
He was apparently born into a 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. He met also Farid al-Din al-'Attar, the legendary Sufi master who was later killed by Mongol invaders and attended the lectures of Qutb al-Din al-Misri.
In Mosul
he studied mathematics and astronomy with Kamal al-Din Yunus (d. 639/1242). Later on he corresponded with Sadr al-Din al-Qunawi
, 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.
and Arabic
.
During his stay in Nishapur, Tusi established a reputation as an exceptional scholar. "Al-Tusi’s prose writing, which number over 150 works, represent one 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”). His works include the definitive Arabic versions of the works of Euclid
, Archimedes
, Ptolemy
, Autolycus
, and Theodosius of Bithynia
.
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 equinox
es and contributed to the construction and usage of some astronomical instruments including the astrolabe
.
Ṭūsī criticized Ptolemy's use of observational evidence to show that the Earth was at rest, noting that such proofs were not decisive. Although it doesn't mean that he was a supporter of mobility of the earth, as he and his 16th-century commentator al-Bīrjandī
, maintained that the earth's immobility could be demonstrated, but only by physical principles found in natural philosophy. 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, Ṭūsī 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 likend 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.
once consisting of equal and similar element
s. 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 mineral
s, then plant
s, then animal
s, and then human
s. Tusi then goes on to explain how hereditary
variability was an important factor for biological evolution of living thing
s:
Tusi discusses how organisms are able to adapt
to their environments:
Tusi recognized three types of living things: plant
s, animal
s, and human
s. He wrote:
Tusi then explains how humans evolved from advanced animals:
, Tusi stated a 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:
's theory of absolute proposition
s:
, 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.
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, appears the famous law of sines
for plane triangles.
He also stated the law of sines for spherical triangles, discovered the law of tangents
for spherical triangles, and provided proofs for these laws.
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 .
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. The K. N. Toosi University of Technology in Iran
and Observatory of Shamakhy in the Republic of Azerbaijan are also named after him.
Tous, Iran
Tus also spelled as Tous, Toos or Tūs, is an ancient city in the Iranian province of Razavi Khorasan. To the ancient Greeks, it was known as Susia...
, Khorasan
Greater Khorasan
Greater Khorasan or Ancient Khorasan is a historical region of Greater Iran mentioned in sources from Sassanid and Islamic eras which "frequently" had a denotation wider than current three provinces of Khorasan in Iran...
– died on 26 June 1274 in al-Kāżimiyyah district of metropolitan Baghdad
Baghdad
Baghdad is the capital of Iraq, as well as the coterminous Baghdad Governorate. The population of Baghdad in 2011 is approximately 7,216,040...
), better known as Naṣīr al-Dīn al-Ṭūsī , was a Persian
Persian people
The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...
polymath
Polymath
A polymath is a person whose expertise spans a significant number of different subject areas. In less formal terms, a polymath may simply be someone who is very knowledgeable...
and prolific writer: an astronomer
Islamic astronomy
Islamic astronomy or Arabic astronomy comprises the astronomical developments made in the Islamic world, particularly during the Islamic Golden Age , and mostly written in the Arabic language. These developments mostly took place in the Middle East, Central Asia, Al-Andalus, and North Africa, and...
, biologist
Biologist
A biologist is a scientist devoted to and producing results in biology through the study of life. Typically biologists study organisms and their relationship to their environment. Biologists involved in basic research attempt to discover underlying mechanisms that govern how organisms work...
, chemist, mathematician
Islamic mathematics
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed under the Islamic civilization between circa 622 and 1600...
, philosopher
Early Islamic philosophy
Early Islamic philosophy or classical Islamic philosophy is a period of intense philosophical development beginning in the 2nd century AH of the Islamic calendar and lasting until the 6th century AH...
, physician
Islamic medicine
In the history of medicine, Islamic medicine, Arabic medicine or Arabian medicine refers to medicine developed in the Islamic Golden Age, and written in Arabic, the lingua franca of Islamic civilization....
, physicist
Islamic physics
Physics in medieval Islam is the development of physics in the medieval Islamic world in the history of physics. In the course of the expansion of the Islamic world, Muslim scholars encountered the science, mathematics, and medicine of antiquity through the works of Aristotle, Archimedes, Galen,...
, scientist
Islamic science
Science in the medieval Islamic world, also known as Islamic science or Arabic science, is the science developed and practised in the Islamic world during the Islamic Golden Age . During this time, Indian, Iranian and especially Greek knowledge was translated into Arabic...
, theologian
Kalam
ʿIlm al-Kalām is the Islamic philosophical discipline of seeking theological principles through dialectic. Kalām in Islamic practice relates to the discipline of seeking theological knowledge through debate and argument. A scholar of kalām is referred to as a mutakallim...
and Marja Taqleed. He was of the Ismaili
Ismaili
' is a branch of Shia Islam. It is the second largest branch of Shia Islam, after the Twelvers...
-, and subsequently Twelver Shī‘ah Islam
Islam
Islam . The most common are and . : Arabic pronunciation varies regionally. The first vowel ranges from ~~. The second vowel ranges from ~~~...
ic belief. The Muslim scholar Ibn Khaldun
Ibn Khaldun
Ibn Khaldūn or Ibn Khaldoun was an Arab Tunisian historiographer and historian who is often viewed as one of the forerunners of modern historiography, sociology and economics...
(1332–1406) considered Tusi to be the greatest of the later Persian
Persian people
The Persian people are part of the Iranian peoples who speak the modern Persian language and closely akin Iranian dialects and languages. The origin of the ethnic Iranian/Persian peoples are traced to the Ancient Iranian peoples, who were part of the ancient Indo-Iranians and themselves part of...
scholars.
Biography
Greater Khorasan
Greater Khorasan or Ancient Khorasan is a historical region of Greater Iran mentioned in sources from Sassanid and Islamic eras which "frequently" had a denotation wider than current three provinces of Khorasan in Iran...
(now in north-eastern Iran
Iran
Iran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...
) in the year 1201 and began his studies at an early age. In Hamadan and Tus he studied the Qur'an
Qur'an
The Quran , also transliterated Qur'an, Koran, Alcoran, Qur’ān, Coran, Kuran, and al-Qur’ān, is the central religious text of Islam, which Muslims consider the verbatim word of God . It is regarded widely as the finest piece of literature in the Arabic language...
, Hadith
Hadith
The term Hadīth is used to denote a saying or an act or tacit approval or criticism ascribed either validly or invalidly to the Islamic prophet Muhammad....
, Shi'a jurisprudence, logic, philosophy, mathematics, medicine and astronomy.
He was apparently born into a 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
Nishapur
Nishapur or Nishabur , is a city in the Razavi Khorasan province in northeastern Iran, situated in a fertile plain at the foot of the Binalud Mountains, near the regional capital of Mashhad...
to study philosophy under Farid al-Din Damad and mathematics under Muhammad Hasib. He met also Farid al-Din al-'Attar, the legendary Sufi master who was later killed by Mongol invaders and attended the lectures of Qutb al-Din al-Misri.
In Mosul
Mosul
Mosul , is a city in northern Iraq and the capital of the Ninawa Governorate, some northwest of Baghdad. The original city stands on the west bank of the Tigris River, opposite the ancient Assyrian city of Nineveh on the east bank, but the metropolitan area has now grown to encompass substantial...
he studied mathematics and astronomy with Kamal al-Din Yunus (d. 639/1242). Later on he corresponded with Sadr al-Din al-Qunawi
Sadr al-Din al-Qunawi
Sadr ad-Din Qunawi was a Persian Sufi who wrote the first and most influential commentary on Ibn Arabi's Setting of Wisdom. He was adopted by Ibn Arabi and remained his disciple throughout his life.-Biography:...
, 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
Genghis Khan
Genghis Khan , born Temujin and occasionally known by his temple name Taizu , was the founder and Great Khan of the Mongol Empire, which became the largest contiguous empire in history after his death....
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
Hulagu Khan
Hulagu Khan, also known as Hülegü, Hulegu , was a Mongol ruler who conquered much of Southwest Asia...
's ranks, after the invasion of the Alamut
Alamut
Alamut was a mountain fortress located in the South Caspian province of Daylam near the Rudbar region in Iran, approximately 100 kilometres from present-day Tehran, Iran...
castle by the Mongol forces.
Works
Tusi has about 150 works in PersianPersian language
Persian is an Iranian language within the Indo-Iranian branch of the Indo-European languages. It is primarily spoken in Iran, Afghanistan, Tajikistan and countries which historically came under Persian influence...
and Arabic
Arabic language
Arabic is a name applied to the descendants of the Classical Arabic language of the 6th century AD, used most prominently in the Quran, the Islamic Holy Book...
.
- Kitāb al-Shakl al-qattāʴ Book on the complete quadrilateral. A five volume summary of trigonometry.
- 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-BirjandiAl-BirjandiAbd Ali ibn Muhammad ibn Husayn Birjandi was a prominent 16th century Persian astronomer, mathematician and physicist who lived in Birjand, Iran.- His works :...
and by Nazzam Nishapuri. - Akhlaq-i-Nasri – A work on ethics.
- al-Risalah al-Asturlabiyah – A Treatise on astrolabe.
- Zij-i ilkhaniZij-i IlkhaniZīj-i Īlkhānī or Ilkhanic Tables is a Zij book with astronomical tables of planetary movements. It was compiled by the Persian astronomer Nasir al-Din al-Tusi in collaboration with his research team of astronomers at the Maragha observatory...
(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-Itiqadat (A commentary on Shia doctrines)
Achievements
Persian language
Persian is an Iranian language within the Indo-Iranian branch of the Indo-European languages. It is primarily spoken in Iran, Afghanistan, Tajikistan and countries which historically came under Persian influence...
, Nasir al-Din 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
Euclid
Euclid , fl. 300 BC, also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I...
, Archimedes
Archimedes
Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics, statics and an...
, Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
, Autolycus
Autolycus
In Greek mythology, Autolycus was a son of Hermes and Chione. He was the husband of Neaera, or according to Homer, of Amphithea...
, and Theodosius of Bithynia
Theodosius of Bithynia
Theodosius of Bithynia was a Greek astronomer and mathematician who wrote the Sphaerics, a book on the geometry of the sphere. Born in Tripolis, in Bithynia, Theodosius is cited by Vitruvius as having invented a sundial suitable for any place on Earth...
.
Astronomy
Tusi convinced Hulegu Khan to construct an observatory for establishing accurate astronomical tables for better astrological predictions. Beginning in 1259, the Rasad Khaneh observatoryMaragheh observatory
Maragheh observatory is an astronomical observatory which was established in 1259 CE by Nasir al-Din al-Tusi, an Iranian scientist and astronomer...
was constructed in Azarbaijan, west of Maragheh
Maragheh
Maragheh also Romanized as Marāgheh and Marāghen) is a city in and the capital of Maragheh County, East Azerbaijan Province, Iran. At the 2006 census, its population was 146,405, in 38,891 families....
, the capital of the Ilkhanate Empire
Ilkhanate
The Ilkhanate, also spelled Il-khanate , was a Mongol khanate established in Azerbaijan and Persia in the 13th century, considered a part of the Mongol Empire...
.
Based on the observations in this for the time being most advanced observatory, Tusi made very accurate tables of planetary movements
Ephemeris
An ephemeris is a table of values that gives the positions of astronomical objects in the sky at a given time or times. Different kinds of ephemerides are used for astronomy and astrology...
as depicted in his book Zij-i ilkhani
Zij-i Ilkhani
Zīj-i Īlkhānī or Ilkhanic Tables is a Zij book with astronomical tables of planetary movements. It was compiled by the Persian astronomer Nasir al-Din al-Tusi in collaboration with his research team of astronomers at the Maragha observatory...
(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
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
. Between Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
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
Shen Kuo
Shen Kuo or Shen Gua , style name Cunzhong and pseudonym Mengqi Weng , was a polymathic Chinese scientist and statesman of the Song Dynasty...
(1031-1095 AD)
For his planetary models, he invented a geometrical technique called a Tusi-couple
Tusi-couple
The Tusi-couple is a mathematical device in which a small circle rotates inside a larger circle twice the diameter of the smaller circle. Rotations of the circles cause a point on the circumference of the smaller circle to oscillate back and forth in linear motion along a diameter of the larger...
, which generates linear motion from the sum of two circular motions. He used this technique to replace Ptolemy
Ptolemy
Claudius Ptolemy , was a Roman citizen of Egypt who wrote in Greek. He was a mathematician, astronomer, geographer, astrologer, and poet of a single epigram in the Greek Anthology. He lived in Egypt under Roman rule, and is believed to have been born in the town of Ptolemais Hermiou in the...
's problematic equant
Equant
Equant is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of heavenly bodies....
, and it was later employed in Ibn al-Shatir
Ibn al-Shatir
Ala Al-Din Abu'l-Hasan Ali Ibn Ibrahim Ibn al-Shatir was an Arab Muslim astronomer, mathematician, engineer and inventor who worked as muwaqqit at the Umayyad Mosque in Damascus, Syria.-Astronomy:...
's geocentric model
Geocentric model
In astronomy, the geocentric model , is the superseded theory that the Earth is the center of the universe, and that all other objects orbit around it. This geocentric model served as the predominant cosmological system in many ancient civilizations such as ancient Greece...
and Nicolaus Copernicus
Nicolaus Copernicus
Nicolaus Copernicus was a Renaissance astronomer and the first person to formulate a comprehensive heliocentric cosmology which displaced the Earth from the center of the universe....
' heliocentric
Heliocentrism
Heliocentrism, or heliocentricism, is the astronomical model in which the Earth and planets revolve around a stationary Sun at the center of the universe. The word comes from the Greek . Historically, heliocentrism was opposed to geocentrism, which placed the Earth at the center...
Copernican model
Copernican heliocentrism
Copernican heliocentrism is the name given to the astronomical model developed by Nicolaus Copernicus and published in 1543. It positioned the Sun near the center of the Universe, motionless, with Earth and the other planets rotating around it in circular paths modified by epicycles and at uniform...
. He also calculated the value for the annual precession of the equinox
Equinox
An equinox occurs twice a year, when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator...
es and contributed to the construction and usage of some astronomical instruments including the astrolabe
Astrolabe
An astrolabe is an elaborate inclinometer, historically used by astronomers, navigators, and astrologers. Its many uses include locating and predicting the positions of the Sun, Moon, planets, and stars, determining local time given local latitude and longitude, surveying, triangulation, and to...
.
Ṭūsī criticized Ptolemy's use of observational evidence to show that the Earth was at rest, noting that such proofs were not decisive. Although it doesn't mean that he was a supporter of mobility of the earth, as he and his 16th-century commentator al-Bīrjandī
Al-Birjandi
Abd Ali ibn Muhammad ibn Husayn Birjandi was a prominent 16th century Persian astronomer, mathematician and physicist who lived in Birjand, Iran.- His works :...
, maintained that the earth's immobility could be demonstrated, but only by physical principles found in natural philosophy. 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, Ṭūsī 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 likend to milk in color."
Three centuries later the proof of the Milky Way consisting of many stars came in 1610 when Galileo Galilei
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...
used a telescope
Optical telescope
An optical telescope is a telescope which is used to gather and focus light mainly from the visible part of the electromagnetic spectrum for directly viewing a magnified image for making a photograph, or collecting data through electronic image sensors....
to study the Milky Way and discovered that it is really composed of a huge number of faint stars.
Biology
In his Akhlaq-i-Nasri, Al-Tusi put forward a basic theory for the evolution of species. He begins his theory of evolution with the universeUniverse
The Universe is commonly defined as the totality of everything that exists, including all matter and energy, the planets, stars, galaxies, and the contents of intergalactic space. Definitions and usage vary and similar terms include the cosmos, the world and nature...
once consisting of equal and similar element
Classical element
Many philosophies and worldviews have a set of classical elements believed to reflect the simplest essential parts and principles of which anything consists or upon which the constitution and fundamental powers of anything are based. Most frequently, classical elements refer to ancient beliefs...
s. 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 mineral
Mineral
A mineral is a naturally occurring solid chemical substance formed through biogeochemical processes, having characteristic chemical composition, highly ordered atomic structure, and specific physical properties. By comparison, a rock is an aggregate of minerals and/or mineraloids and does not...
s, then plant
Plant
Plants are living organisms belonging to the kingdom Plantae. Precise definitions of the kingdom vary, but as the term is used here, plants include familiar organisms such as trees, flowers, herbs, bushes, grasses, vines, ferns, mosses, and green algae. The group is also called green plants or...
s, then animal
Animal
Animals are a major group of multicellular, eukaryotic organisms of the kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life. Most animals are motile, meaning they can move spontaneously and...
s, and then human
Human
Humans are the only living species in the Homo genus...
s. Tusi then goes on to explain how hereditary
Heredity
Heredity is the passing of traits to offspring . This is the process by which an offspring cell or organism acquires or becomes predisposed to the characteristics of its parent cell or organism. Through heredity, variations exhibited by individuals can accumulate and cause some species to evolve...
variability was an important factor for biological evolution of living thing
Living Thing
Living Thing is the fifth album by Peter Bjorn and John, released on March 30, 2009 in the UK and March 31 in the US. The lead-off single from this album is "Nothing to Worry About."-Reception:...
s:
Tusi discusses how organisms are able to adapt
Adaptation
An adaptation in biology is a trait with a current functional role in the life history of an organism that is maintained and evolved by means of natural selection. An adaptation refers to both the current state of being adapted and to the dynamic evolutionary process that leads to the adaptation....
to their environments:
Tusi recognized three types of living things: plant
Plant
Plants are living organisms belonging to the kingdom Plantae. Precise definitions of the kingdom vary, but as the term is used here, plants include familiar organisms such as trees, flowers, herbs, bushes, grasses, vines, ferns, mosses, and green algae. The group is also called green plants or...
s, animal
Animal
Animals are a major group of multicellular, eukaryotic organisms of the kingdom Animalia or Metazoa. Their body plan eventually becomes fixed as they develop, although some undergo a process of metamorphosis later on in their life. Most animals are motile, meaning they can move spontaneously and...
s, and human
Human
Humans are the only living species in the Homo genus...
s. He wrote:
Tusi then explains how humans evolved from advanced animals:
Chemistry and Physics
In chemistry and physicsIslamic physics
Physics in medieval Islam is the development of physics in the medieval Islamic world in the history of physics. In the course of the expansion of the Islamic world, Muslim scholars encountered the science, mathematics, and medicine of antiquity through the works of Aristotle, Archimedes, Galen,...
, Tusi stated a version of the law of conservation of mass
Conservation of mass
The law of conservation of mass, also known as the principle of mass/matter conservation, states that the mass of an isolated system will remain constant over time...
. He wrote that a body of matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...
is able to change, but is not able to disappear:
Logic
Nasir al-Din al-Tusi was a supporter of Avicennian logic, and wrote the following commentary on AvicennaAvicenna
Abū ʿAlī al-Ḥusayn ibn ʿAbd Allāh ibn Sīnā , commonly known as Ibn Sīnā or by his Latinized name Avicenna, was a Persian polymath, who wrote almost 450 treatises on a wide range of subjects, of which around 240 have survived...
's theory of absolute proposition
Proposition
In logic and philosophy, the term proposition refers to either the "content" or "meaning" of a meaningful declarative sentence or the pattern of symbols, marks, or sounds that make up a meaningful declarative sentence...
s:
Mathematics
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 trigonometrySpherical trigonometry
Spherical trigonometry is a branch of spherical geometry which deals with polygons on the sphere and the relationships between the sides and the angles...
, 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.
He was the first to list the six distinct cases of a right triangle in spherical trigonometry.
This followed earlier work by Greek mathematicians
Greek mathematics
Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 7th century BC to the 4th century AD around the Eastern shores of the Mediterranean. Greek mathematicians lived in cities spread over the entire Eastern Mediterranean, from Italy to...
such as Menelaus of Alexandria
Menelaus of Alexandria
Menelaus of Alexandria was a Greek mathematician and astronomer, the first to recognize geodesics on a curved surface as natural analogs of straight lines.-Life and Works:...
, who wrote a book on spherical trigonometry called Sphaerica, and the earlier Muslim mathematicians Abū al-Wafā' al-Būzjānī and Al-Jayyani
Al-Jayyani
Abū ʿAbd Allāh Muḥammad ibn Muʿādh al-Jayyānī was a mathematician, Islamic scholar, and Qadi from Al-Andalus...
.
In his On the Sector Figure, appears the famous law of sines
Law of sines
In trigonometry, the law of sines is an equation relating the lengths of the sides of an arbitrary triangle to the sines of its angles...
for plane triangles.
He also stated the law of sines for spherical triangles, discovered the law of tangents
Law of tangents
In trigonometry, the law of tangents is a statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposite sides....
for spherical triangles, and provided proofs for these laws.
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 craterImpact crater
In the broadest sense, the term impact crater can be applied to any depression, natural or manmade, resulting from the high velocity impact of a projectile with a larger body...
located on the southern hemisphere of the moon
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
is named after him as "Nasireddin
Nasireddin (crater)
Nasireddin is a lunar impact crater that lies in the rugged terrain in the southern part of the Moon's near side. This crater overlaps two older formations, intruding into the crater Miller to the north and Huggins to the west...
". A minor planet
Minor planet
An asteroid group or minor-planet group is a population of minor planets that have a share broadly similar orbits. Members are generally unrelated to each other, unlike in an asteroid family, which often results from the break-up of a single asteroid...
10269 Tusi
10269 Tusi
10269 Tusi is a main-belt asteroid discovered on September 24, 1979 by N. S. Chernykh at the Crimean Astrophysical Observatory. It is named in honor of medieval Persian astronomer Nasir al-Din al-Tusi....
discovered by Soviet
Soviet Union
The Soviet Union , officially the Union of Soviet Socialist Republics , was a constitutionally socialist state that existed in Eurasia between 1922 and 1991....
astronomer Nikolai Stepanovich Chernykh
Nikolai Stepanovich Chernykh
Nikolay Stepanovich Chernykh was a Soviet and Russian astronomer.Chernykh was born in the city of Usman' in Voronezh Oblast...
in 1979 is named after him. The K. N. Toosi University of Technology in Iran
Iran
Iran , officially the Islamic Republic of Iran , is a country in Southern and Western Asia. The name "Iran" has been in use natively since the Sassanian era and came into use internationally in 1935, before which the country was known to the Western world as Persia...
and Observatory of Shamakhy in the Republic of Azerbaijan are also named after him.
See also
- Persian science
- Islamic Golden AgeIslamic Golden AgeDuring the Islamic Golden Age philosophers, scientists and engineers of the Islamic world contributed enormously to technology and culture, both by preserving earlier traditions and by adding their own inventions and innovations...
- Islamic scienceIslamic scienceScience in the medieval Islamic world, also known as Islamic science or Arabic science, is the science developed and practised in the Islamic world during the Islamic Golden Age . During this time, Indian, Iranian and especially Greek knowledge was translated into Arabic...
- Islamic scholars
- List of Muslim scholars
- List of Shi'a Muslims
- List of Iranian scientists
- Shen KuoShen KuoShen Kuo or Shen Gua , style name Cunzhong and pseudonym Mengqi Weng , was a polymathic Chinese scientist and statesman of the Song Dynasty...
Further reading
- Encyclopædia Iranica, "AḴLĀQ-E NĀṢERĪ", G.M. Wickens http://www.iranicaonline.org/articles/aklaq-e-naseri-by-kaa-nasir-al-din-tusi-the-principal-treatise-in-persian-on-ethics-economics-and-politics-f
- Encyclopædia Iranica, "AWṢĀF AL-AŠRĀF", G.M. Wickens http://www.iranicaonline.org/articles/awsaf-al-asraf-a-short-mystical-ethical-work-in-persian-by-nasir-al-din-tusi-written-late-in-life-ca
- Encyclopædia Iranica, "Nasir al-Din al-Tusi" George Saliba http://www.iranicaonline.org/articles/tusi-nasir-al-din
External links
- Biography by Islamic Insights
- Biography by Islamic Philosophy Online
- Biography by The Internet Encyclopedia of Philosophy
- Kerry Magruder, History of Science Online: Islamic and Early Medieval Science, University of Oklahoma
- Islam Online.
- http://www.famousmuslims.com/NASIR%20AL-DIN%20AL-TUSI.htm
- http://www.britannica.com/eb/article-9073899
- The Rekhaganita. An 18th century Sanskrit translation of Nasir al-Din al-Tusi's recension of Euclid's Elements.
- Richard Covington, Rediscovering Arabic Science, 2007, Saudi Aramco World