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Ebu Ca'fer Muhammed İbn Muhammed İbnül-Hasan Nasıreddin, Nasir al-Din al-Tusi

Mathematician, astronomer, politician (B. February 21st,
1201, Tus / Khorasan – D. June 25th, 1274, Baghdad). His full name
was Ebu Ca'fer Muhammed İbn Muhammed İbnül-Hasan
Nasıreddin. He was the pupil of Kemaleddin İbn
Yunus and Muînüddin Sâlim, having realized that the mathematical system was
about to get destroyed, he succeeded in establishing the system again when he
was very young. Thanks to his having a brilliant command of Greek language, he
managed to translate many Greek works related to mathematics and astronomy into
the Persian and Arabic languages, far better than the ones who had made such
translations up to that time. One of the greatest science historians of our
time, G. Sarton, points out that the number of the works of Tusî was 61, and
this indicates that Tusî showed great efforts in science. The subject fields of
these works are arithmetic, geometry, trigonometry, astronomy, optics,
mineralogy, geography, medicine, logic, philosophy, ethics, music, and
literature.

Among the positive science writers
of the old East, it is rare to encounter with the writers who wrote their works
as didactically, appropriately for today’s scientific methods, and
systematically as Tusî. He was able to distinguish his own opinions and
evidence from the former ones brought by the others, and state the opinions
about which he thought as being superior to his opinions. So much so that, in
his work titled *Kitabı Şeklül Kutta*,
about the problem of solving the spherical triangles with known angles through
the formula of “Şeklü’z Zilî” (tangents theorem), he declared modestly that he
did not have the knowledge of a solution method that could be applied to all
particular circumstances on the sphere.

Tusî, bu eserinde Tusî, in *Kitabı Şeklül Kutta*, carried out such an
extensive analysis on the topological synthesis of the various triangles and
squares, formed of the big circles on the sphere that it made possible for the
modern analytical methods to emerge easily. In short, Tusî, in this work,
examined both the plane trigonometry and spherical trigonometry systematically.
In this work, Tusî showed that he had deep knowledge of the problems related to
the triangles and squares on the sphere. For example, about the solution of the
spherical triangle that has known three angles, he was the first to think of
the geometric conversion mechanism using the polar triangle, as we do today.

The proof of Euclid’s axiom of parallels,
numbered 5, had been a big trouble for many Western mathematicians since the
XVIII century. This axiom had not been proved, Euclidean geometry could only
preserve its validity through its acceptance or substituting its equivalent.
When Tusî came across the numbered 5 axiom, he tried substituting this axiom
for a new one. With this new axiom, Tusî proved that the sum of the interior
angles of a triangle equaled 180 degrees, and he immediately removed Euclid’s
axiom. In the second *Tahrir* and *Kitabı-Şerhi-Masadirat
*(the interpretation of the
geometrical axioms), the 18^{th} book of *Tahrir-ül-Mutavassıtat* collection, there are many authentic
opinions and findings of Tusî. In brief, Tusî, the brightest star of the
world of mathematics of Greece and West, with his axiomatic thoughts, was a
courageous pioneer of modern geometry.

At the beginning of the XIII century, positional
astronomy was undergoing an unproductive period; the astronomical tables needed
being restored. There was no trustworthy astronomical table except for Zic,
resulted of the observations made by İbni Yunus in Cebeli Mokattam observatory,
in

Astronomer Tusî wanted 30 years (approximate the
time in which Saturn rotates around the Sun) from Hulagu for the restoration of
the astronomical tables, providing the data belonging to the astronomical
objects, and control and development of Greek and Arabic observations, made
before him. Because Tusî had the aim of examining the movements of the planets
in the solar system and the geometric codes related to those movements. Instead
of the eccentricity or epicyclic systems which had been used to explain the
movements of the planets up to his time, astronomer Tusî suggested a theory
which was more systematic and convenient for explaining the movements simply.
His works in the field of astronomy were collected in *Tahrir-ül-Mıcısti, Ttezkere fi-ilmül Hey’e *and *Zici İlhani*. Tusî shared his astronomical theories in *Tezkere fil-il-mül Hey’e*. In this work of his, Tusî benefited from the works of the great
astronomers (Hipparchus, Ptolemy, Al-Battani, Ibn Yunus) who had lived before.

In his mature years, Tusî was imprisoned in
famous Kal’atul mevt prison (death castle,

Among the three mathematicians, Abu al-Wafa, Al-Harezmî and Nasir
al-Din al-Tusî, who were the best in the fields of trigonometry, algebra, and geometry,
Tusî was the brightest one. We saw the most advanced form of mathematics,
especially the field of geometry, with him. He was a high quality man. Tusî,
who approached even the oldest information in a critical way, was a great
person who enjoyed working until the last day of his life. This well known
Turkish scholar, who died in Baghdad, was buried around the mausoleum of Musa
al-Kadhim, according to his own will.

Today, most of the works of him, including the original ones,
rewritings, and translated works, are in *Tahrir-ül-Mutavassıta *or *Külliyatı Nasireddin*. This collection,
which mostly consists of the translated works of the old Greek mathematicians
and astronomers, includes also one of his original works titled *Kitab-ı fil Şekil Ma’ruf bil Kutla*.

**HIS WORKS:**

**MATHEMATICS:** *Tahrir-i Usul-ül
Öklidis*, *Kitabı fil Şekil Ma’ruf bil
Kutla*, *Tecrid fil Hendese*, *Kitab-ı Camiül Hesab fi’t Taht ve’t Türab*,
*Kitab-ı Zafer fil Cebir vel Mukabele.*

**ASTRONOMY:** *Tahrir el Mıcıstî*,
*Zic-i İlhanî*, *Tezkere fi ilmül Hey’e*, *Zic-üş-Şahî*,
*Zübdetü’l İdrak fi Hey’etül Eflak.*

KAYNAKÇA:** **Prof.
Dr. M. Fuad Köprülü / XIII. Asırda Maraga Rasathanesi Hakkında
Bazı Notlar (1942), “Türk
Öklit’i Nasireddin Tusî” (Bilim ve Ütopya, Nisan 2000; Prof. Dr. Hamit
Dilgan’ın 1956’da İTÜ Matbaasında basılmış “Büyük Türk Alimi Nesreddin Tusî” başlıklı
broşürünün sadeleştirilerek yeniden basımı), İhsan
Işık / Ünlü Bilim Adamları (Türkiye Ünlüleri Ansiklopedisi, C. 2, 2013) -
Encyclopedia of Turkey’s Famous People (2013).