Muhammad ibn Muhammad ibn al-Hasan al-Tūsī (Persian:
محمد بن محمد بن حسن طوسی
18 February 1201 – 26 June 1274), better known as Nasir al-Din Tusi (Persian: نصیر الدین طوسی; or simply Tusi
/ˈtuːsi/ in the West), was a Persian polymath, architect, philosopher,
physician, scientist, and theologian. He is often considered the creator of
trigonometry as a mathematical discipline in its own right.
He was a
Twelver Muslim. The Muslim scholar Ibn Khaldun (1332–1406) considered Tusi to
be the greatest of the later Persian scholars.
Biography
Nasir al-Din 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 Quran, hadith, Ja'fari
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 traveled far and wide
to attend the lectures of renowned scholars and acquire the 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.
In Mosul he studied mathematics and astronomy with
Kamal al-Din Yunus (d. AH 639 / AD 1242), a pupil of Sharaf al-Dīn al-Ṭūsī.
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 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
was employed by the Nizari Ismaili state and made his most important
contributions in science during this time when he was moving from one
stronghold to another. He was captured after the invasion of Alamut Castle by
the Mongol forces.
Works
Tusi has
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.
A Treatise on the Astrolabe by Tusi, Isfahan
1505
Here are
some of his major works:
· 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-Birjandi and by Nazzam Nishapuri.
· Akhlaq-i
Nasiri – A work on ethics.
· 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
· Tajrīd
al-Iʿtiqād (Summation of Belief) – A commentary on Shia
doctrines.
· Talkhis
al-Muhassal (summary of summaries).
An example
from one of his poems: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.
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.
Achievements
Tusi couple from
Vat. Arabic ms 319
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 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.
Astronomy
The Astronomical
Observatory of Nasir al-Dīn Tusi.
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, south of the river Aras, and to the 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. His famous student Shams
ad-Din Al-Bukhari was the teacher
of Byzantine scholar Gregory Chioniadis, who had in
turn trained astronomer Manuel Bryennios about 1300
in Constantinople.
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 Ali Qushji. The Tusi couple 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.
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, 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 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.
Logic
Nasir al-Din Tusi 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
develop a method of construing those examples from Aristotle."
Mathematics
A stamp issued in the
republic of Azerbaijan in 2009 honoring Tusi
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 trigonometry, 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.
Biology
In his Akhlaq-i
Nasiri, Tusi wrote about several biological topics. He defended a version
of Aristotle's scala naturae, in which he placed man above animals,
plants, minerals, and the elements. He described "grasses which grow
without sowing or cultivation, by the mere mingling of elements," as
closest to minerals. Among plants, he considered the date-palm as the
most highly developed, since "it only lacks one thing further to reach
(the stage of) an animal: to tear itself loose from the soil and to move away
in the quest for nourishment."
The lowest animals
"are adjacent to the region of plants: such are those animals which
propagate like grass, being incapable of mating [...], e.g. earthworms, and
certain insects". The animals "which reach the stage of
perfection [...] are distinguished by fully developed weapons", such as
antlers, horns, teeth, and claws. Tusi described these organs as adaptations to
each species's lifestyle, in a way anticipating natural theology. He
continued:
"The noblest of
the species is that one whose sagacity and perception is such that it accepts
discipline and instruction: thus there accrues to it the perfection not
originally created in it. Such are the schooled horse and the trained falcon.
The greater this faculty grows in it, the more surpassing its rank, until a
point is reached where the (mere) observation of action suffices as
instruction: thus, when they see a thing, they perform the like of it by
mimicry, without training [...]. This is the utmost of the animal degrees, and
the first of the degrees of Man in contiguous therewith."
Thus, in this paragraph,
Tusi described different types of learning, recognising observational
learning as the most advanced form, and correctly attributing it to
certain animals.
Tusi seems to have
perceived man as belonging to the animals, since he stated that "the Animal
Soul [comprising the faculties of perception and movement ...] is restricted to
individuals of the animal species", and that, by possessing a "Human
Soul, [...] mankind is distinguished and particularized among other animals."
Some scholars have
interpreted Tusi's biological writings as suggesting that he adhered to some
kind of evolutionary theory. However, Tusi did not state
explicitly that he believed species to change over time.
Chemistry
Tusi contributed to the field of chemistry, stating an early law of
conservation of mass.
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. 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 his 812th birthday with a doodle, which was
accessible in its websites with Arabic language calling him al-farsi (the
Persian).
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