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Cemşid bin Mes’ud bin Mahmud et-Tabib el Kâşî

Mathematician and astronomer (B.
1380, Maveraünnehir / Kâş – D. 1437, Semerkand). His full name was Cemşid bin
Mes’ud bin Mahmud et-Tabib el Kâşî and his pseudonym is Gıyaseddin. He started
his education life in Kâş. His father was the leading religious scholar and
scientist of the time. Firstly, he learnt *sarf*
(philology), *nahiv* (syntax) and *fıkıh* (Islamic law) and had comprehensive
knowledge on Islamic law. He studied on logic, rhetoric, mathematic and astronomy.
Due to his passion for science; he went on long journeys and worked fearlessly.
He served under the Karakoyunlu İskender Sultan in 1416. He was invited to the
Semerkand by the ruler of the city, Ulugh Beg, himself a great scientist.

Firstly, he investigated the works
of Nasirüddin Tusi and Kutbuddin Şirazi. He started to work in an observatory
in Meragâ and reorganized the astronomical tables. In this way, he leaded to
expand the horizons of astronomy. He explained the star charts (zic), the distances
of planets, determination of solar and lunar eclipse, the production and usage
of the vehicle named “Tabak-ül-Menatık”, an instrument to determinate
astronomical patterns.

European science historians suggest
that Kepler was the one who discovered that the shape of an orbit was not circular,
but elliptical. In fact, Gıyaseddin Cemşid had explained this fact in his work
named “*Nüzhet-ül Hedaik*” one hundred
year before Kepler. He provided the development of research, observation and
experimental method through his scientific works and his wisdom. He determined
closely the patterns of lunar eclipse on 1406, 1407 and 1408. He explained and
proved that the orbits of the moon and the mercury lied on an ecliptic plane. Thus,
Kepler’s effort to claim that Cemsid’s thesis was his, proved invalid and
groundless.

If the small things that we use in
daily life haven’t been discovered; we wouldn’t reach the state-of-the-art
today. The idiom in Turkish language which means “mere fleabite” to indicate a
valueless case comes from the zero at the left of the comma in decimal
fractions. At the time when the decimal fractions hadn’t been discovered yet;
controversial circumstances happened in all scientific fields, from fractional
numbers to space technology.

“Comma” is an important punctuation
for the texts, but it isn’t a must to use it. However, it is an absolute must
for mathematics. Besides his researches on astronomy, Gıyaseddin Kâşi much more
focused on mathematics. He was the first person who used the comma in
arithmetic operations. When one looks at his work “*Risalet’ül Muhitiyye*” it can be clearly observed. He was also the
first person to discover the decimal fraction system and had a book on this
subject. He made the decimal fraction rule for the first time and used decimal
fractions for addition, subtraction, multiplication and division. However, the
discovery of the decimal fractions was attributed to Simon Stefan. German
science historian Pouluckey proved that Cemsid was the inventor of the decimal
system at the end of his researches on 1948 and the science world accepted his
claim. Cemsid had invented this system 160 years before Simon Stefan did. He
applied four basic operations on decimal numbers. This system was started to be
used after XVI. Century in Europe. In his work on the decimal fractions system,
“*Risalet-ül-Muhitiyye*”, he clearly
showed the proportion of the circumference to the radius of circumference. In
this book, he differentiated the integer from the decimal number without using
comma punctuation, by placing the word “integer” (sihah) for the first time. His
thesis is much more correct than his predecessors. In his thesis on the
business accounts, he used comma punctuation in decimal fractions instead of
using the term “integer”.

Moreover, Gıyaseddin Cemşid is
famous for his original inventions to solve high-degree numerical equations
approximately. He had also inventions in algebra. He explained taking roots of
any degrees especially in “*Miftah-ül
Hisab*” that was devoted to Ulugh Beg. The Western World invented this 300
years later through Isaac Newton. He accounted the ways of taking roots in “*Miftah-ül Hesab*”. Although, it was
claimed that taking roots by using the “Broom Expansion” which is a formula in
mathematics invented by Newton; Derek Stewart proved in his book named “*Sources of Mathematics*” that Cemsid
invented this method three years before Newton and he was the first person to
solve the “Binomial” equations.

Cemşid computed the correct value of
“Pi” number for its nine first decimal digits (3,1415926535898732) and computed
the sine value of 1 degree arc for the 18 digits of decimal numbers accurately.
The basic formula in trigonometry, which is known as the “El Kashi Equity”, was
developed by him and some basic formula in trigonometry was also named after
him. His inventions on arithmetic and trigonometry might be found in “*Risalet-ül Muhitiyye*” and “*Risalet-ül Veter ve’l Ceyb*”.

He invented the hand calculator and
the decimal fraction, found the approximate solutions for the problems with
inaccurate results, found the perfect logarithm and algorithm and computed the
value of “Pi” number to a high degree of accuracy, as well as invented the hand
calculator. At the same time, he is the person who solved the binomial equation
which is named after Newton. The solution of the equation took place in the
book named *“Miftah el-hisab*” (The Key
to Arithmetic). Cemsid, he is also the writer of a masterpiece on the arithmetic
based on the sexadecimal number system, “*Risale
el-muhitiyye*” (Overall Booklet on the Circle).

He has great
contributions to the building of the Semerkand Observatory (1421). He was also
the first director of the observatory. He contributed efforts in preparation of
the “*Zic*” (star charts) of Ulugh Beg
(1394-1449). Citing him, Ulugh Beg said: “*His
works are the perfective of their predecessors*”, *“A person who is able to solve all kind of confusing issues” *and
added that he was known as “Allâme Cemşid” (T.N. Learned Man).

Through his works, he influenced his
colleagues until XVII. Century and drew great attention until XX. century. He
made a distinguished name for himself especially in mathematics on the Western
science world. When we look at the science history between the VIII. and XVI. Centuries,
we realize that he was the most important mathematician and astronomer of the
time. During his time, the astronomy and mathematics developed so much that
European world reached this level around the end of XVII. Century. Gıyaseddin
Cemşid had many works on mathematics and astronomy. His works have been used as
the basic reference guide for long years, especially between XVI. and XVII. Centuries,
by the well-known scientists of the time.

**WORKS**

*Risalet-ül Muhitiyye* (Rules for decimal numbers and the value of Pi number), *Kitab-u Miftah-il-Hisab* (The Key to Calculation:
Five volumes on calculations with integers, calculations for fractional
numbers, calculations for astronomy, calculations for topographical field,
calculation with unknown equations), *Risalet-ül-Kemaliye veya Süllen-üs-Sem’a*
(“Layers of the Sky”: the Determination of Distances and Sizes of the heavenly
bodies, *Kitab-u-Ziye-il-Hakani fi Tekmili Ziye-il-İlhani* (The coordinates
of the stars that are observed on the book of Nasirüddin Tusi’nin
Ziyei’l-İlhani), *Nüzhet-ül-Hadâik* (On
his own discovery Takabül-Menatık which is a telescopic vehicle.)

REFERENCE:
Salih Zeki / Âsâr-ı Bakiye (1329), Aydın Sayılı / Uluğ Bey ve Semerkand’daki
İlim Faaliyeti Hakkında Gıyâsüddîn-i Kâşî'nin Mektubu (1985), Sadettin Ökten /
“Kâşî - Uluğ Bey'in ilmî çevresine mensup
matematikçi ve astronom” (Türkiye Diyanet Vakfı İslam
Ansiklopedisi,
c. 25, s.15,16, 2002), İhsan Işık / Ünlü Bilim Adamları (Türkiye
Ünlüleri Ansiklopedisi, C. 2, 2013) - Encyclopedia of Turkey’s Famous People
(2013).