Al-Muradi(11th century)
Alī Ibn Khalaf al-Murādī, (11th
century) Al-Andalus,
was a Mechanical engineer and
author of the unique technological manuscript entitled Kitāb al-asrār fī natā'ij al-afkār (The Book of Secrets in the Results
of Thoughts).[1] It was
copied and used at the court of Alfonso VI of León and Castile in
Christian Spain in the 11th century.[citation needed]
The manuscript provides information about a "Castle and
Gazelle Clock" and many other forms of complicated clocks and ingenious
devices. Al-Muradi was a contemporary ofAbū Ishāq Ibrāhīm al-Zarqālī.[citation needed]
In 2008, the Book of Secrets of al-Muradi has been published in
facsimile, translated in English/Italian/French/Arabic and in electronic edition
with all machines interpreted in 3D, by the Italian study center Leonardo3.
He also devised, with help from al-Zarqali, the universal astrolabe.[2] Both
al-Muradi and al-Zarqali's design were included in the Libros del Saber (1227) of Alfonso X of Castile.[3]
During the period of Islamic-Arabic
extraordinary activity in Science and Technology (9th-13th century), there are
some recorded contributions to the area of Automatic Control mainly in the development
of water clocks using float valve regulators, different level controls using
float valves or combination of syphons and the development of On-Off control.
In this short survey, Professor Dr Mohamed Mansour, former Professor of Control
Engineering At ETH Zürich surveys the subject by investigating the words of
Banu Musa, Al-Muradi, Ridhwan al-Sa'ati and Al-Jazari.
During the period of Islamic-Arabic
extraordinary activity in Science and Technology (9th-13th century), there are
some recorded contributions to the area of Automatic Control mainly in the
development of water clocks using float valve regulators, different level
controls using float valves or combination of syphons and the development of
On-Off control.
The Islamic Arabic Automatic Control
Technology had as a basis the Greek Technology of two scientists, namely Philon
of Byzantium (Rhodes and Alexandria) of the second half of the third century
BCE (his book, the Pneumatica was translated from Arabic into French
and German in 1902 and 1899 respectively), and Heron of Alexandria of the first
century CE (his book the Peumatica was translated into English and German
in 1851 and 1899 respectively).
It is noted in Greek technology the language
is Greek but the scientists need not be Greek as in the case with
Islamic-Arabic technology.
It is known that there are hundreds of
thousands of manuscripts dealing with Islamic Science and Technology to be
edited and it is assumed that some of them deal with technology. This report is
based on the following references [1-6].
1. Automatic Control in Water
Clocks
1.1. "The work of Archimedes
on the Building of Clocks"
This is an Arabic book whose Arabic author is
called pseudo-Archimedes with the earliest reference to it in theFihrist of Al-Nadim (died 955 CE). From the
literary style and the technique of its drawings, this clock book seems to be
an Islamic work based on Greek-Roman technology as mentioned in [1].
This clock used a float level regulator, which makes it a feedback device. A
large float drove the whole apparatus. The description of the complicated clock
is so thorough that it could be reconstructed almost completely. This book did
have considerable influence on the two great chorological books of Al-Jazari
and Ibn Al-Sa'ati and other Arabic authors like Ibn Al-Akfani.
1.
2. "Al-Jami bayna Al-Ilm wa 'l-'amal al-nafi' fi sina'at al-hiyal by
Al-Jazari
This book [5] was written in 1206. Al-Jazari is from
Al-Jazira, the area between Tigris and Euphrates. Sarton[6] mentions: "This treatise is the most
elaborate of its kind and may be considered the climax of this line of Muslim
achievement". "The distinctive feature of the book is its practical
aspect. The book is rich in minute description of various kinds of devices.
Hill maintains: "It is impossible to over-emphasize the importance of
Al-Jazari`s work in the history of engineering. Until modern times, there is no
other document from any cultural area that provides a comparable wealth of
instructions for the design, manufacture and assembly of machines. Al-Jazari
did not only assimilate the techniques of his non-Arab and Arab predecessors,
he was also creative. He added several mechanical and hydraulic devices. The
impact of these inventions can be seen in the later designing of steam engines
and internal combustion engines, paving the way for automatic control and other
modern machinery. The impact of Al-Jazari`s inventions is still felt in modern
contemporary mechanical engineering [3]."
Hill [4] translated the book into English in 1974. A
German translation was made in 1915. The chapter on water clocks describes 10
water clocks, the first two of them use float valve regulators. The various
time-indicating mechanisms are propelled by a float. The other clocks are
regulated differently. Al-Jazari mentions an old machine, which he inspected,
in which a musical automaton was powered by a vertical water wheel. In his
comments on this machine, he clearly implies that he knew how to control the
speed of such a wheel by means of an escapement.
Figure 4: Miniature depicting an automat from a
copy of al-Jazari's Kitab
fi marifat al-hiyal al-handasiyya. MS copied in Syria or Egypt in 1315
CE. Leaf: 31.5 × 22 cm. Copied by Farrukh ibn Abd al-Latif. Opaque
watercolor, ink and gold on paper, H: 30.2 W: 21.7 cm. (Source).
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1.3.
"Book on the Construction of Clocks and their Use" by Ridwan
b.Muhammad Al-Saati Al-Khurasani (1203)
This book
describes the monumental water clock built by Ridwan`s father at the Jayrun
gate in Damascus. A German translation was made in 1915. A large float drives
the clock, float valve regulator and the device for varying the length of the
hours are incorporated.
1.4.
"The Book of Secrets about the Results of Thoughts" by Al-Muradi of
Andalusia (11th century)
This is
the earliest description in Arabic of water clocks. This book deals with water
clocks and other devices using automata. The treatise consists of 31 models of
which 5 are essentially very large toys similar to clocks, in that automata are
caused to move at intervals, but without precise timing. The prime movers are
water wheels that can be overshot or undershot depending on the intensity of
flow. There are nineteen clocks, all of which record the passage of the
temporal hours by the movements of automata. The power came from large outflow
clepsydras provided with concentric siphons. This power was transmitted to
automata by very sophisticated mechanisms, which included segmental and
epicyclic gears and the use of mercury. These are highly significant features;
they provide the first known examples of complex gearing used to transmit high
torque, while the adoption of mercury reappears in European clocks from the
thirteenth century onwards.
Unfortunately,
the only known manuscript of this work is badly defaced and it is not possible
to understand exactly how the clocks worked. A weight driven clock with a
mercury escapement appears in "Libros del Saber", a work written in
Spanish at the court of Alfonsos of Castille about 1277 and consisting of
translations and paraphrases of Arabic works. A novel feature in this treatise
is the use of mercury in balances. Al-Zarquali built two large water clocks on
the banks of the river Tagus at Toledo in 11th century [2].
1.5.
"Kitab Mizan Al-Hikma (The Book on the Balance of Wisdom)",
Al-Khazini (1121-1122)
The
eighth treatise of this work described two steelyard clepsydras. The main one,
called the Universal Balance, was designed for 24-hour operation, and consisted
of an iron beam divided into unequal arms by a fulcrum. An outflow clepsydra
equipped with a syphon was suspended on the end of the short arm, and two
movable weights, one large and one small, were suspended from the long arm,
which was graduated into scales. As water discharged from the clepsydra, the
weights were moved along the scale to keep the beam in balance. At any moment
the hour of the day could be to minutes from the position of the small one.
Figure 6: Two pages from the manuscript of
Al-Muradi Kitab al-asrar fi
nata'ij al-afkarpreserved at the Biblioteca Medicea-Laurentiana in
Florence, Italy, MS Or 152. Note the damaged state of the manuscript. Source:
Eduard Farré Olivé, La
clepsidra de las Gacelas del manuscrito de relojes de Al-Muradi, Arte
y Hora, March-April 1998, N°. 128-H11, pp. 10-18.
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2.
Automatic Control of Banu Musa
Kitab
al-Hiyal (The Book of Ingenious Devices) is a
mechanical writing by Banu Musa bin Shakir (9th century). The three sons of
Musa organized translation and did original work in "Bayt Al-Hikma"
(House of Wisdom) which was the science academy in Baghdad, the greatest
scientific institution since the Museum and Library of Alexandria. Banu Musa
were supporters of the translation movement which gathered momentum as that
important epoch of the Islamic scientific awakening reached fruition in the 9th
century. They extended their patronage to Thabit Ibn Qurra, to Hunayn Ibn Ishaq
and to many other translators and scholars. They left more than 20 works which
are known, including the seminal engineering book "Kitab Al-Hiyal"
translated into English by Donald Hill in 1979 and parts of it into German by
Wiedemann and Hauser in 1918 and Hauser in 1922. The book was edited in Arabic
by Ahmad Al-Hassan in 1981.
Figure
7a-b: Reconstruction of
the clock of Al-Muradi by Spanish scholars. A general view with its side
opening revealing the working of the mechanism. Source: Eduard Farré Olivé , De Mensura Temporis. (1ª
parte) "Arte y
Hora" n. 123-H6, March-April 1997, pp. 8-16 (2ª parte) "Arte y
Hora" n. 127-H10, January-February 1998, pp. 10-17; and Eduard Farré
Olivé, La
clepsidra de las Gacelas del manuscrito de relojes de Al-Muradi.
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The
written Arabic heritage in mechanical technology begins with the Banu Musa book.
It is possible they knew Heron's Mechanics written in Alexandria in the first
century and translated by Qusta Ibn Luqa at the time of Banu Musa. Hero‘s other
books may have been known to the brothers, for he enjoyed great fame among
Arabic scholars in the 10th century.
Banu Musa
describe one hundred ingenious devices. Hill identified twenty five devices
resembling the ones of Heron's and Philon's books. There exist also other parts
of the Banu Musa machines which resemble certain elements in Hero and Philo
work. There are Banu Musa machines which bear no resemblance to either Hero or
Philo. These include the fountains and dredging machine designed to salvage
submerged objects from the bottom of rivers and seas and so on. Banu Musa made
use primarily of the principles of the science of hydrostatics and aerostatics.
They used automatic valves, delayed-action systems and their application of the
principles of automatic control testify of creative mentality. Hill notes the
use of crankshafts for the first time in the history of technology.
In two
models, they used a mechanism similar to the modern crankshaft, thus
outstripping by 500 years the first description of the crankshaft in Europe.
Mayr [1] mentions
that they used syphons, float valves, Philon`s oil lamp, water wheels, etc.
Some control systems work with nonmoving parts combining the principle of
Philon`s oil lamp with some cleverly arranged syphons. They have contributions
in technological refinements and new applications. They install throttling
valves directly in the pipe requiring no constant force to keep them closed.
These appear first in the book of Banu Musa. Also they introduce improvements
on Philon`s oil lamp by ingenious combination of syphons added to the original
system. Most important is the use of On-Off control with upper and lower limit
for the controlled variable. Systems of this class are widely used in modern
technology. The float valve used by Banu Musa, Al-Jazari and other Arabic
engineers emerges again in the middle of the 18th century in Europe and in
England.
Figure 8: Diagram of a selftrimming lamp from Kitab al-hiyal (Book of ingenious mechanical
devices) by Banu Musa, preserved in the Granger Collection in New York. (Source).
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References
[2] Ahmad
Y.Al-Hassan & Donald R.Hill, Islamic Technology.
Cambridge University Press and Unesco, 1986.
[4] Banu
Musa, The Book of Ingenious Devices. An Annotated Translation
of the Treatise of Banu Musa by Donald R. Hill. Dordrecht: Reidel,
1979; reprinted in Islamabad, 1989. The Arabic text of this treatise was edited
by Ahmad Y. Al-Hassan: Banu Musa, Kitab Al-Hiyal, Aleppo:
Publications of the Institute for the History of Arabic Science, University of
Aleppo, 1981.
[5] Al-Jazari, Al-Jami'
bayna al-'ilm wa-'l-'amal al-nafi' fi sina'at al-hiyal (A Compendium on the
Theory and Practice of the Mechanical Arts) by Ibn Al-Razzaz Al-Jazari (1206),
edited by Ahmad Y.Al-Hassan, University of Aleppo,1979.
* Professor Dr. Mohamed Mansour was Emeritus
Professor of Control Engineering at Swiss Federal Institute of Technology (ETH)
in Zurich, Switzerland from September 1968 until September 1993. His fields of
interest are control systems, especially stability theory and digital control,
stability of power systems, and digital filters. He has published about 200
scientific papers, edited 6 books and supervised 47 Ph.D Students. See Prof.
Dr.Mohamed Mansour: Publications and Curriculum
Vitae; Mansour,
Mohamed and Prof. Dr.
Mohamed Mansour.
Kamāl al-Dīn
al-Fārisī1267–1319
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Kamal al-Din
Hasan ibn Ali ibn Hasan al-Farisi or Abu Hasan Muhammad ibn Hasan (1267– 12 January 1319, long assumed
to be 1320)) (Persian: كمالالدين فارسی) was a prominent Persian born in Tabriz,Iran. He made two major contributions to
science, one on optics, the other on number
theory.
Farisi was a pupil of the great astronomer and mathematician Qutb
al-Din al-Shirazi, who in turn was a pupil of Nasir al-Din Tusi.
more from
Wikipedia
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Alī Ibn Khalaf
al-Murādī
Ali Ibn Khalaf al-Muradi was a Mechanical engineer and
author of the treatise "The Book of Secrets about the Results of
Thoughts". This treatise is the earliest description in Arabic of water
clocks. This book deals with water clocks and other devices using automata. The
treatise consists of 31 models of which 5 are essentially very large toys
similar to clocks, in that automata are caused to move at intervals, but
without precise timing. The prime movers are water wheels that can be overshot
or undershot depending on the intensity of flow. There are nineteen clocks, all
of which record the passage of the temporal hours by the movements of automata.
The power came from large outflow clepsydras provided with concentric siphons.
This power was transmitted to automata by very sophisticated mechanisms, which
included segmental and epicyclic gears and the use of mercury. These are highly
significant features; they provide the first known examples of complex gearing
used to transmit high torque, while the adoption of mercury reappears in
European clocks from the thirteenth century onwards.
Unfortunately, the only known manuscript of this work is
badly defaced and it is not possible to understand exactly how the clocks
worked. A weight driven clock with a mercury escapement appears in "Libros
del Saber", a work written in Spanish at the court of Alfonsos of Castille
about 1277 and consisting of translations and paraphrases of Arabic works. A
novel feature in this treatise is the use of mercury in balances. Al-Zarquali
built two large water clocks on the banks of the river Tagus at Toledo in 11th
century.
Qutb al-Din al-Shirazi 1236-1311
From
Wikipedia, the free encyclopedia
Photo taken from medieval manuscript by Qutb al-Din
al-Shirazi. The image depicts an epicyclic planetary model.
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Born
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Died
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Jurisprudence
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Main interest(s)
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Notable work(s)
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Almagest, The
Royal Present,Pearly Crown, etc
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Influenced by
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Influenced
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Qutb al-Din al-Shirazi (1236 – 1311) (Persian: قطبالدین محمود بن مسعود شیرازی) was a 13th-century Persian polymath[1] and poetwho made contributions to astronomy, mathematics, medicine,physics, music theory, philosophy and Sufism.
Biography
He was born in Kazerun in October 1236 to a family
with a tradition of Sufism. His father, Zia' al-Din
Mas'ud Kazeruni was a physician by profession and also a leading Sufi of the Kazeruni order. Zia' Al-Din received his Kherqa (Sufi robe)
from Shahab al-Din Omar Suhrawardi[citation needed]. Qutb al-Din was garbed by
the Kherqa (Sufi robe) as blessing by his father at age of ten[citation needed]. Later on, he also
received his own robe from the hands of Najib al-Din Bozgush Shirazni, a famous Sufiof the time[citation needed]. Quṭb al-Din began studying medicine under his father. His father
practiced and taught medicine at the Mozaffari hospital in Shiraz. After the
passing away of his father (when Qutb al-Din was 14), his uncle and other
masters of the period trained him in medicine. He also studied the Qanun (the Canon) of the famous Persian scholar Avicenna and its commentaries. In
particular he read the commentary ofFakhr al-Din Razi on the Canon of Medicine and Qutb al-Din raised many issues of his own. This led to his own
decision to write his own commentary, where he resolved many of the issues in
the company of Nasir al-Din al-Tusi.
Qutb al-Din lost his father at the age of fourteen and replaced
him as the ophthalmologist at the Mozaffari hospital in Shiraz. At the same time, he pursued his education under his uncle Kamal
al-Din Abu'l Khayr and then Sharaf al-Din Zaki Bushkani, and Shams al-Din
Mohammad Kishi. All three were expert teachers of the Canon of Avicenna. He quit his medical
profession ten years later and began to devote his time to further education
under the guidance of Nasir al-Din al-Tusi. When Nasir al-Din al-Tusi, the renowned scholar-vizier of the Mongol Holagu Khan
established the observatory of Maragha, Qutb al-Din Shirazi
became attracted to the city. He left Shiraz sometime after 1260 and was
in Maragha about 1262. In Maragha, Qutb al-din resumed his
education under Nasir al-Din al-Tusi, with whom he studied the al-Esharat wa'l-Tanbihat ofAvicenna. He discussed the
difficulties he had with Nasir al-Din al-Tusi on understanding the first book of the Canon of Avicenna. While
working in the new observatory, studied astronomy under him. One of the
important scientific projects was the completion of the new astronomical table
(zij). In his testament
(Wasiya),Nasir al-Din al-Tusi advises his son ṣil-a-Din to work with Qutb al-Din in the completion of the Zij.
Qutb-al-Din's stay in Maragha was short. Subsequently, he
traveled to Khorasan in the company of Nasir al-Din al-Tusi where he stayed to study under Najm al-Din Katebi Qazvini in the
town of Jovayn and become his assistant. Some time after 1268, he journeyed to Qazvin, Isfahan, Baghdad and later Konya in Anatolia. This was a time when the Persian poet
Jalal al-Din Muhammad Balkhi (Rumi) was gaining fame there and it is reported that Qutb al-Din also
met him. In Konya, he studied the Jam'e al-Osul of Ibn Al-Athir with Sadr
al-Din Qunawi. The governor of Konya, Mo'in al-Din Parvana appointed him as the
judge of Sivas and Malatya. It was during this time
that he compiled the books the Meftāḥ al-meftāh, Ekhtiārāt al-moẓaffariya, and his commentary on
Sakkāki. In the year 1282, he was envoy on behalf of the Ilkhanid Ahmad Takudar to Sayf
al-Din Qalawun, the Mamluk ruler of Egypt. In his letter to Qalawun, the
Ilkhanid ruler mentions Qutb al-Din as the chief judge. Qutb al-Din during this
time collected various critiques and commentaries on Avicenna's Canon and used them on
his commentary on the Kolliyāt. The last part of Qutb al-Din's active career
was teaching the Canon of Avicenna and the Shefa of Avicenna in Syria. He soon left for Tabriz after that and died shortly
after. He was buried in the Čarandāb cemetery of the city.
Shirazi identified observations by the scholar Avicenna in the 11th century and Ibn Bajjah in the 12th century as transits of Venus and Mercury.[2] However, Ibn Bajjah cannot
have observed a transit of Venus, as none occurred in his lifetime.[3]
Qutb al-Din had an insatiable desire[1] for learning, which is evidenced
by the twenty-four years he spent studying with masters of the time in order to
write his commentary on the Kolliyāt. He was also distinguished by his
extensive breadth of knowledge, a clever sense of humor and indiscriminate
generosity.[1] He was also a master chess
player and played the musical instrument known as the Rabab, a favorite instrument of the Persian poet Rumi.
Works
Mathematical
· Tarjoma-ye Taḥrir-e Oqlides a work on geometry in Persian in fifteen chapters
containing mainly the translation of the work Nasir al-Din Tusi, completed in
November 1282 and dedicated to Moʿin-al-Din Solaymān Parvāna.
Astronomy and Geography
a manuscript
copy of Shirazi's al-Tuhfa al-Shahiya, 15th century
· Eḵtiārāt-e moẓaffari It is a treatise on astronomy in
Persian in four chapters and extracted from his other work Nehāyat al-edrāk.
The work was dedicated to Mozaffar-al-Din Bulaq Arsalan.
· Fi ḥarakāt
al-dahraja wa’l-nesba bayn al-mostawi wa’l-monḥani a written as an appendix to Nehāyat
al-edrāk
· Nehāyat
al-edrāk - The Limit of Accomplishment
concerning Knowledge of the Heavens (Nehāyat
al-edrāk fi dirayat al-aflak) completed in 1281, and The Royal Present (Al-Tuhfat al-Shahiya) completed in
1284. Both presented his models for planetary motion, improving on Ptolemy's principles.[4] In his The Limit of Accomplishment
concerning Knowledge of the Heavens, he also discussed the possibility of heliocentrism.[5]
· Ketāb faʿalta wa lā
talom fi’l-hayʾa, an Arabic work on astronomy, written for Aṣil-al-Din, son
of Nasir al-Din Tusi
· Šarḥ Taḏkera naṣiriya on astronomy.
· Al-Tuḥfa al-šāhiya
fi’l-hayʾa, an Arabic book on astronomy, having four chapters, written
for Moḥammad b. Ṣadr-al-Saʿid, known as
Tāj-al-Eslām Amiršāh
· *Ḥall moškelāt
al-Majesṭi a book on astronomy, titled Ḥall moškelāt
al-Majesṭi
Philosophical
· Dorrat al-tāj
fi ḡorrat al-dabbāj Qutb al-Din al-Shirazi's most famous
work is the Pearly Crown (Durrat al-taj li-ghurratt al-Dubaj),
written in Persian around AD 1306 (705 AH). It is an Encyclopedic work on
philosophy written for Rostam Dabbaj, the ruler of the Iranian land of Gilan. It includes
philosophical outlook on natural sciences, theology, logic, public affairs,
ethnics, mystiicsm, astronomy, mathematics, arithmetics and music.
· Šarḥ Ḥekmat al-ešrāq
Šayḵ Šehāb-al-Din
Sohravardi, on philosophy and mysticism of Shahab al-Din Suhrawardi and his
philosophy of illumination in Arabic.
Medicine
· Al-Tuḥfat al-saʿdiyah also called Nuzhat al-ḥukamāʾ wa rawżat al-aṭibbāʾ, on medicine, a
comprehensive commentary in five volumes on the Kolliyāt of the Canon of Avicenna written in Arabic.
· Risāla
fi’l-baraṣ, a medical
treatise on leprosy in Arabic
· Risāla fi bayān
al-ḥājat ila’l-ṭibb wa ādāb
al-aṭibbāʾ wa waṣāyā-hum
Religion, Sufism, Theology, Law, Linguistics and Rhetoric
and others
· Fatḥ al-mannān fi
tafsir al-Qorʾān a comprehensive
commentary on the Qurʾan in forty volumes, written in Arabic and also known by the title
Tafsir ʿallāmi
· Ḥāšia bar Ḥekmat al-ʿayn on theology; it is a commentary of Ḥekmat al-ʿayn of
Najm-al-Din ʿAli Dabirān Kātebi
· Moškelāt al-eʿrāb on Arabic syntax
· Moškelāt
al-tafāsir or Moškelāt al-Qorʾān, on rhetoric
· Meftāḥ al-meftāhá, a commentary
on the third section of the Meftāḥ al-ʿolum, a book on Arabic grammar and rhetoric by Abu Yaʿqub
Seraj-al-Din Yusof Skkaki Khwarizmi
· Šarḥ Moḵtaṣar al-oṣul Ebn Ḥājeb, a commentary
on Ebn Ḥājeb’s
Montaha’l-soʾāl wa’l-ʿamal fi ʿelmay al-oṣul wa’l-jadwal,
a book on the sources of law according to the Malikite school of thought
· Sazāvār-e Efteḵā, Moḥammad-ʿAli Modarres
attributes a book by this title to Quṭb-al-Din, without providing any information about its
content
· Tāj al-ʿolum A book attributed to him by Zerekli
· al-Tabṣera A book attributed to him by Zerekli
· A book on
ethnics and poetry, Quṭb-al-Din is
also credited with the authorship of a book on ethics in Persian, written for
Malek ʿEzz-al-Din, the ruler of Shiraz. He also wrote poetry but
apparently did not leave a divan (a book of poems)
Shirazi's
Tomb in Tabriz, Charandab
Qutb al-Din was also a Sufi from a family of Sufis in
Shiraz. He is famous for the commentary on Hikmat al-ishraq of Suhrawardi, the most influential work
of Islamic Illuminist philosophy.
Abu'l-Hasan
al-Uqlidisi 952
Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi was an Arab mathematician, who was active in Damascus[1] and Baghdad.[2] As his surname indicates,
he was a copyist of Euclid's works. He wrote the earliest surviving book on the positional use of the Arabic numerals, Kitab
al-Fusul fi al-Hisab al-Hindi (The Arithemetics of Al-Uqlidisi) around 952.[3]It is especially notable
for its treatment of decimal fractions, and that it showed how to carry out calculations without deletions.
While the Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th
century, J. Lennart Berggrenn notes that he was mistaken, as decimal fractions
were first used five centuries before him by al-Uqlidisi as early as the 10th
century.[2]
Al-Uqlidisi is a mathematician who is only
known to us through two manuscripts on arithmetic, Kitab al-fusul fi al-hisab al-Hindi and Kitab
al-hajari fi al-hisab. Despite
this he is a figure of some importance and has prompted an interesting
scholarly argument among historians of science.The manuscript of the Kitab al-fusul fi al-hisab al-Hindi which has survived is a copy of the original which was made in 1157. An English translation of this work has been published by Saidan [4]. The manuscript gives al-Uqlidisi's full name on the front page as well as the information that he composed the text in Damascus in 952-53. In the introduction al-Uqlidisi writes that he travelled widely and learnt from all the mathematicians he met on his travels. He also claimed to have read all the available texts on arithmetic. Other than being able to deduce a little of al-Uqlidisi's character from his writing, we have no other information on his life.
The Kitab al-fusul fi al-hisab al-Hindi of al-Uqlidisi is the earliest surviving book that presents the Hindu system. In it al-Uqlidisi argues that the system is of practical value [4]:-
Most arithmeticians are obliged to use it in their work: since it is easy and immediate, requires little memorisation, provides quick answers, demands little thought ... Therefore, we say that it is a science and practice that requires a tool, such as a writer, an artisan, a knight needs to conduct their affairs; since if the artisan has difficulty in finding what he needs for his trade, he will never succeed; to grasp it there is no difficulty, impossibility or preparation.
This treatise on arithmetic is in four parts. The aim of the first part is to introduce the Hindu numerals, to explain a place value system and to describe addition, multiplication and other arithmetic operations on integers and fractions in both decimal and sexagesimal notation. The part second collects arithmetical methods given by earlier mathematicians and converts them in the Indian system. For example the method of casting out nines is described.
The third part of the treatise tries to answer to the standard type of questions that are asked by students: why do it this way ... ?, how can I ... ?, etc. There is plenty of evidence here that al-Uqlidisi must have been a teacher, for only a teacher would know understand the type of problem that a beginning student would encounter.
The fourth part has considerable interest for it claims that up to this work by al-Uqlidisi the Indian methods had been used with a dust board. A dust board was used because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However, al-Uqlidisi showed how to modify the methods for pen and paper use.
Al-Uqlidisi's work is historically important as it is the earliest known text offering a direct treatment of decimal fractions. It is here that the scholarly argument referred to above arises. At one time it was thought that Stevin was the first to propose decimal fractions. Further research showed that decimal fractions appeared in the work of al-Kashi, who was then credited with this extremely important contribution. When Saidan studied al-Uqlidisi's Kitab al-fusul fi al-hisab al-Hindi in detail he wrote [6]:-
The most remarkable idea in this work is that of decimal fraction. Al-Uqlidisi uses decimal fractions as such, appreciates the importance of a decimal sign, and suggests a good one. Not al-Kashi(d. 1436/7) who treated decimal fractions in his "Miftah al-Hisab", but al-Uqlidisi, who lived five centuries earlier, is the first Muslim mathematician so far known to write about decimal fractions.
Following Saidan's paper, some historians went even further in attributing to al-Uqlidisi the complete credit for giving the first complete description and applications of decimal fractions. Rashed, however, although he does not wish to minimise the importance of al-Uqlidisi's contribution to decimal fractions, sees it as [2]:-
... preliminary to its history, whereas al-Samawal's text already constitutes the first chapter.
The argument depends on how one interprets the following passage in al-Uqlidisi's treatise. He explains how to raise a number by one tenth five times [4]:-
... we want to raise a number by its tenth five times. We write down this number as usual; write it down again below moved one place to the right; we therefore know its tenth, which we add to it. So was have added its tenth to this number. We put the resulting fraction in front of this number and we move it to the unit place after marking it [with the ' sign he uses for the decimal point]thus. We add its tenth and so on five times.
Saidan (writing in [1]) sees in this passage that al-Uqlidisi has fully understood the idea of decimal fractions, saying that earlier authors:-
... rather mechanically transformed the decimal fraction obtained into the sexagesimal system, without showing any sign of comprehension of the decimal idea. ... In all operations where powers of ten are involved in the numerator or the denominator, [al-Uqlidisi] is well at home.
On the other hand Rashed sees this passage rather differently [2]:-
... unlike al-Samawal, al-Uqlidisi never formulates the idea of completing the sequence of powers of ten by that of their inverse after having defined the zero power. That said, in the passage just quoted, three basic ideas emerge whose intuitive resonance may have misled historians; what they thought was a theoretical exposition was merely understood implicitly, and, as a result, they have overestimated the author's contribution to decimal fractions.
The two points of view are almost impossible to decide between since what we are looking at is the development of the idea of decimal fractions by different mathematicians, each contributing to its understanding. To take a particular text as the one where the idea appears for the first time in its entirety must always be a somewhat arbitrary decision. There is no disagreement on the fact that al-Uqlidisi made a major step forward.
A second common system was the base-60 numeration inherited
from the Babylonians via the Greeks and known as the arithmetic of the
astronomers. Although astronomers used this system for their tables, they
usually converted numbers to the decimal system for complicated calculations
and then converted the answer back to sexagesimals.
The third system was Indian arithmetic, whose basic numeral forms,
complete with the zero, eastern Islam took over from the Hindus. (Different
forms of the numerals, whose origins are not entirely clear, were used in
western Islam.) The basic algorithms also came from India, but these were
adapted by al-Uqlīdisī (c. 950) to pen and paper instead of the
traditional dust board, a move that helped to popularize this system. Also, the
arithmetic algorithms were completed in two ways: by the extension of root-extraction procedures,
known to Hindus and Greeks only for square and cube roots, to roots of higher
degree and by the extension of the Hindu decimal system for whole numbers to
include decimal fractions. These fractions appear simply as computational
devices in the work of both al-Uqlīdisī and al-Baghdādī (c. 1000), but in subsequent centuries
they received systematic treatment as a general method. As for extraction of
roots, Abūʾl-Wafāʾ wrote a treatise (now lost) on the topic, and Omar
Khayyam (1048–1131)
solved the general problem of extracting roots of any desired degree. Omar’s
treatise too is lost, but the method is known from other writers, and it
appears that a major step in its development was al-Karajī’s 10th-century derivation by means of
mathematical induction of the binomial theorem for
whole-number exponents—i.e., his discovery that
During the 10th century Islamic algebraists progressed
from al-Khwārizmī’s quadratic polynomials to the mastery of the algebra of
expressions involving arbitrary positive or negative integral powers of the
unknown. Several algebraists explicitly stressed the analogy between the rules
for working with powers of the unknown in algebra and those for working with
powers of 10 in arithmetic, and there was interaction between the development
of arithmetic and algebra from the 10th to the 12th century. A 12th-century
student of al-Karajī’s works, al-Samawʿal, was able to
approximate the quotient (20x2 + 30x)/(6x2 + 12) as
and also gave a rule for finding the coefficients of the
successive powers of 1/x. Although none of this employed symbolic algebra, algebraic symbolism was in
use by the 14th century in the western part of the Islamic world. The context
for this well-developed symbolism was, it seems, commentaries that were
destined for teaching purposes, such as that of Ibn Qunfūdh (1330–1407) of
Algeria on the algebra of Ibn al-Bannāʿ (1256–1321) of Morocco.
Other parts of algebra developed as well. Both Greeks and
Hindus had studied indeterminate equations, and the translation of this
material and the application of the newly developed algebra led to the
investigation of Diophantine
equations by
writers like Abū Kāmil, al-Karajī, and Abū Jaʿfar
al-Khāzin (first half of 10th century), as well as to attempts to prove a
special case of what is now known as Fermat’s last theorem—namely, that there are no
rational solutions to x3 + y3 = z3. The great scientist Ibn
al-Haytham (965–1040)
solved problems involving congruences by what is now called Wilson’s
theorem, which states that, if p is a prime, then p divides
(p − 1) × (p − 2)⋯× 2 × 1 + 1, and al-Baghdādī gave a variant of the idea of amicable numbers by
defining two numbers to “balance” if the sums of their divisors are equal.
However, not only arithmetic and algebra but geometry too underwent extensive development.
Thābit ibn Qurrah, his grandson Ibrāhīm ibn Sinān (909–946), Abū Sahl al-Kūhī
(died c. 995), and Ibn al-Haytham solved
problems involving the pure geometry of conic sections, including the areas and volumes of
plane and solid figures formed from them, and also investigated the optical
properties of mirrors made from conic sections. Ibrāhīm ibn Sinān, Abu Sahl
al-Kūhī, and Ibn al-Haytham used the ancient technique of analysis to
reduce the solution of problems to constructions involving conic sections. (Ibn
al-Haytham, for example, used this method to find the point on a convex
spherical mirror at which a given object is seen by a given observer.) Thābit
and Ibrāhīm showed how to design the curves needed for sundials. Abūʾl-Wafāʾ, whose book on the
arithmetic of the scribes is mentioned above, also wrote on geometric methods
needed by artisans.
In addition, in the late 10th century Abūʾl-Wafāʾ and
the prince Abū Naṣr Manṣurstated and proved theorems of plane and spherical
geometry that could be applied by astronomers and geographers, including the
laws of sines and tangents. Abū Naṣr’s pupil al-Bīrūnī (973–1048),
who produced a vast amount of high-quality work, was one of the masters in
applying these theorems to astronomy and to such problems in mathematical
geography as the determination of latitudes and longitudes, the distances
between cities, and the direction from one city to another.
Al-Khazini 1115–1130
This article is about the 12th
century scientist. For the 10th century astronomer and physician, see Abū Ja'far al-Khāzin.
Abu al-Fath Abd al-Rahman Mansour al-Khāzini or simply Abu
al-Fath Khāzini (Arabic: أبو الفتح الخازني, Persian: ابولفتح خازنی) (flourished 1115–1130) was a Muslim astronomerof Persian Greek ethnicity from Merv, then in the Khorasan province of Persia (located in today's Turkmenistan).
Merv was known for its literary and scientific achievements.[1]
Muslim scientist
Abd al-Rahman al-Khazini |
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Title
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Al-Khazini
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Born
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11th century
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Died
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12th century
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Ethnicity
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Era
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Creed
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Main interest(s)
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Life]
Al-Khazini was a slave in Marw.[2] He was the pupil of Umar
Khayyam.[2] He got his name from his
master al-Khanzin. His master is responsible for his education in mathematics
and philosophy.[1][2] Al-Khazini was known for
being a humble man. He refused thousands of Dinar for his works, saying he
did not need much to live on because it was only his cat and himself in his
household.[1]Al-Khazini is one of the
few Islamic astronomers to be known for doing original observations.[1] His works are used and
very well known in the Islamic world, but very few other places around the
world acknowledge his work.[1]
Achievements[
Al Khazini seems to have been a high government official
under Sanjar ibn Malikshah and the sultan of the Seljuk Empire. He
did most of his work in Merv, where they are known for their libraries.[1] His best-known works are
"The Book of the Balance of Wisdom", "Treatise on Astronomical
Wisdom", and "The Astronomical Tables for Sanjar".[1]
"The Book of the Balance of Wisdom" is an
encyclopedia of medieval mechanics and hydrostatics composed of eight books
with fifty chapters.[1] It is a study of the
hydrostatic balance and the ideas behind statics and hydrostatics, it also
covers other unrelated topics.[1] There are four different
manuscripts of "The Book of the Balance of Wisdom" that have
survived.[1] The balance al-Khazini
built for Sanjar’s treasury was modeled after the balance al-Asfizari, who was
a generation older than al-Khazini, built.[1] Sanjar’s treasurer out of
fear destroyed al-Asfizari’s balance; he was filled with grief when he heard
the news.[1] Al-Khazini called his
balance "combined balance" to show honor towards Al-Asfizari.[1] The meaning of the
balance was a "balance of true judgment".[1] The job of this balance
was to help the treasury see what metals were precious and which gems were real
or fake.[1] In "The Book of the
Balance of Wisdom" al-Khazini states many different examples from the
Koran ways that his balance fits into religion.[1] When al-Khazini explains
the advantages of his balance he says that it "performs the functions of
skilled craftsmen", its benefits are theoretical and practical precision.[1]
The "Treatise on Astronomical Wisdom" is a
relatively short work.[1] It has seven parts and
each part is assigned to a different scientific instrument.[1] The seven instruments
include: a triquetrum, a dioptra, a "triangular instrument," a
quadrant, devices involving reflection, an astrolabe, and simple tips for
viewing things with the naked eye.[1] The treatise describes
each instrument and their uses.[1]
"The Astronomical Tables for Sanjar" is said to
have been composed for Sultan Sanjar, the ruler of Merv and his balance was
made for Sanjar’s treasury.[1] The tables in "The
Astronomical Tables for Sanjar" are tables of holidays, fasts, etc.[1] The tables are said to
have the latitudes and longitudes of forty-three different stars, along with
their magnitudes and (astrological) temperaments.[1] It is said that
al-Khazini’s observations for this work were probably done in Merv in various
observatories with high quality instruments.[1]
He is Abu Al-Fath `Abd al-Rahamn Al-Khazin, or
Al-Khazini: a man of wisdom, an astronomer and an engineer. Of Greek origin, he
grew under the care of his master, Ali Al-Khazin al-Marwazi and studied in Marw
city of Khurasan where he learnt from leading figures of astronomy, mathematics
and physics. Thus, he gained expertise in those sciences while not yet a free
man. He evoked the admiration and astonishment of many when he came out with
his book, Meezan
Al-Hikmah, which was a marvel in the fields of
mechanics, physics and hydrostatics. Alongside these sciences, he was also
interested in astronomy and he determined the direction of the Qiblah in
most Muslim states.
Al-Khazini stands as an
authority in physics for all ages. He even surpassed Ibn al-Haytham who had
worked out the speed of light. Below:A page from Al-Khazini’s book, Mizan
Al-Hikmah, showing that the magnitude of
weight of a small body of any substance is in the same ratio to its volume as
the magnitude of weight of a larger body of the same substance to its volume.
He based his determination of the Qiblah on
his readings from Ibn al-Haytham and Al-Beiruni. Most historians of science are
unanimous that Al-Khazini stands as an authority in physics for all
generations, that he even surpassed his teachers – Ibn Sina(Avicenna),
Al-Beiruni and Ibn al-Haytham (who was the first to attempt the discovery of
the speed of light) – all of whom had discussed gravity, albeit not very
scientifically and accurately. He outstripped them, in general, in this
discipline as well, and particularly in Dynamics and Hydrostatics. His own
theories in these two fields are taught to this day. In astronomy, he excelled
in making tables known as the Sinjari tables. He devoted most of his time to
the study of Hydrostatics and improved the instrument that was designed by Al-Beiruni
which determined the specific weight of liquids: an undertaking in which he
attained a high degree of accuracy. He spoke during his studies about the
resistance which bodies immersed in liquids generally encounter.
Extract from Al-Khazini's geographical table. Source: David A.
King, World-Maps for Finding the Direction and Distance to
Mecca: Innovation and Tradition in Islamic Science. Leiden: Brill/London: Al-Furqan
Islamic Heritage Foundation, 1999, p. 72
He arrived at a formula that determines the abstract
weight of masses composed of two different materials. He preceded Torshilly in
referring to air as matter with mass, and stating that air has mass and
capillary action similar to liquids. He also stated that weights of immersed
masses are less than their real weights. He also explained that the Archimedes’
principle applies to gases in addition to liquids; such revelations paved the
way for the invention of the barometer, air-vacuums, and pumps. He also wrote
on theories of light, and calculated the deflection of light upon its passage
through air. He made great efforts in his work on specific weights and gravity
and demonstrated experimentally how all parts of the body direct their descent
towards the centre of the earth due to gravity; showing that the variation in
gravitational pull on different segments of the descending body result from the
variation in the distance between the respective segments and the centre of the
earth. He based his inferences on experiments and scientific calculations.
Thus, he preceded Newton by several centuries, though not acknowledged by the
West. He authored many books including the Mizan
Al-Hikmah which came in eight volumes. It
spoke about hydrostatics, weights, theories on gravity, Archimedes’ and
Menelaus’s views on hydrostatics, specific weights of different materials, and
astronomy. It solved problems, stated exercises and listed the specific weights
of different materials in tabulated form. Al-Khazini discussed the relation
between the speed at which a body falls to the distance and time it takes; he
gave that in a formula for discovering which scientists in the West – like
Galileo, Newton, and others – claimed credit several centuries later. His other
books include those on conical instruments, Sinjari astronomical tables etc.
He was a man of fine Islamic character, an ascetic and a
self-reliant person. When his fame spread, the ruler of the time sent him 1000
Dinars. He accepted ten and returned the rest saying, “I have no need for the
rest. My entire expenses are three Dinars per year.” A princes also sent him
1000 Dinars, but he refused all of it.
(Sources: Tatimmah Mizan Al-Hikmah Al-I`lam (Zarkali),
Mu`jam al-Mu’allifieen, Mafaheem al-Islamiyyah - MS)
Muslim
Scientists and Thinkers–Abdal Rahman al-Khazini
Abdal Rahman al-Khazini was a
Muslim of Greek origin who was brought to Merv as a slave by the Seljuk king
after his victory over the Byzantine Emperor.
His master, al-Khazini, gave
him his name and the best possible education in mathematics, philosophy,
science and astronomy.
Al-Khazini was also a pupil of the famous Persian poet and mathematician Omar Khayyám (d 1131 CE) who was living in Merv at that time. Very little is known about his life, but it is known that he was a man who refused rewards and handout sent to him by the wife of the emir.
Al-Khazini was also a pupil of the famous Persian poet and mathematician Omar Khayyám (d 1131 CE) who was living in Merv at that time. Very little is known about his life, but it is known that he was a man who refused rewards and handout sent to him by the wife of the emir.
He preferred to live a simple
life on a meager income which he earned himself. The exact date of
his death is also not known, but it is believed that he died by the middle of
12th century.
Al-Khazini was a great
physicist, astronomer, mathematician, philosopher and an alchemist. He is
better known for his contributions to physics.
His
treatise; Kitab Mizan al-Hikma (The Book of Balance of Wisdom) written in four
volumes, remained an important part of physics among the Muslim
scientists. The first volume deals with his predecessor’s theories of centers
of gravity, including al-Biruni, al-Razi and Omar Khayam. In this book
al-Khazini draws attention to the Greek philosopher’s failure to
differentiate clearly between force, mass and weight. He explains how the
weight of the air and its density decrease with altitude. By
looking at his predecessor’s science, al-Khazini provides crucial records of
their contributions that could have remained unknown or lost.
The remaining treatises deal
with hydrostatics, most particularly the determination of specific gravities.
Al-Khazini goes to extreme lengths in describing the equipment necessary to
obtain accurate results. He was very careful in the preparation of his
equipment and materials while doing his experiment.
He carried out
various experiments with his balances with rigorous attention to
scientific accuracy. His interest to determine the specific
gravities of precious metals and alloys had some commercial purposes in mind.
With the accurate value of specific gravity he could determine the purity of
gold and silver without any chemical treatment. To determine the specific
gravity of a substance, its weight has to be known in air and water, and the
volume of air and water displaced, so most researchers used water balances in
their experiments.
Using the same
instruments Al-Khazini made repeated experiment with several metals and
gemstones. He also measured the specific gravities of many other substances
like salt, clay, liquids and amber–a total of fifty one substances.
He developed his own
hydrostatic balance, and specialized balances which was extremely precise. He
could find the weight of an object on the microgram level, a precision only
surpassed in the 20th century.
In another experiment, he
discovered that the density of water is greater nearer the earth’s center,
which was proved by Roger Bacon two centuries later. Al-Khazini defines
heaviness in traditional terms, he says in his book;
“A heavy body is one which is
moved by an inherent force, constantly, towards the center of the world.
I mean that a heavy body is one which has a force moving it towards the central
point, and constantly in the direction of the center, without being moved by
that force in any different direction; and that the force referred to is
inherent in the bodyâ€
It appears that what al-Khazini
meant by gravity, is both an idea similar to the modern concept of
gravitational potential energy. In any case, al-Khazini appears to have
been the first to propose that the gravity of a body varies with its distance
from the center of the Earth. In his first sense of the word gravity, the
concept was not considered again, till five centuries later by Isaac Newton.
Al-Khazini
contributions in astronomy includes a astronomical treatise
Zij as-Sanjari or ‘Sinjaric Tables’. In this treatise he gave a
description of his construction of a 24 hour water clock designed for
astronomical purposes which he invented. This was an early example of an
astronomical clock. He computed the positions of 46 stars for the year (1115-16
CE). and tables for the observation of celestial bodies at the latitude of
Merv. His astronomical treatise was translated into Greek and was studied in
the Byzantine Empire.
Al-Khazini’s
book Risala fi’l-alat (Treatise on Instruments) consisted of seven chapters in
which he has described about a number of highly specialized and
innovative mechanical devices. These instruments include dioptra, (a classical
surveying instrument) triangular instruments, triquetrum, (an instrument to
find altitude of heavenly bodies) quadrant, sextant and the astrolabe.
Al Khazini, no doubt was a
great physicist and astronomer of the middle age who made tremendous
advancement in the field of physics and instrument-making. Charles Jillispe,
editor of the Dictionary of Scientific Bibliography proclaimed him the greatest
of any time.
KHASINI :Merv: History, Science and Learning
Merv, was a major
oasis-city in Central Asia, on the historical Silk Road, located near today's
Mary in Turkmenistan. Several cities have existed on this strategic site, which
was significant for the interchange of trade, culture and politics. In the
early Islamic period, Merv was the capital of the province of Khorasan, and in
the 12th century it was the largest city in the world. The following article
surveys some aspects of learning, science and history of Merv as an Islamic
city between the 10th and the 13th century. A special focus is laid on the
scholars and scientists of Merv, the greatest of whom was Abd Al-Rahman
Al-Khazini. Besides being a gifted astronomer, he is the author of Kitab mizan al-hikma,
an encyclopedia of mechanics structured about the theory and the practice of
various kinds of balances, especially the universal balance, an extremely
precise scientific instrument for measuring the weights of bodies and their
specific gravities.
Figure
1: Map showing Merv at
the heart of trade routes of the Islamic east and central Asia.
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Merv is the
city which dominated the province of Khorasan in today's Turkmenistan. Early Islamic
geographers recorded a great economy based upon thriving farming and
irrigation: a highly organised system of maintenance, a system of irrigation
canals and a dam above the city with the supply of water regulated and measured
by a metering device [1].
Under the
Abbasids, Merv continued to be the capital of the East. The great prosperity of
Merv belongs to the period dating from the 8th to the 13th century. [2]. In the latter half of the 10th
century, when the geographer Al-Muqaddasi knew Merv, a third part of the
suburbs wa already in ruins, and the citadel was in no better state; however,
in the next century, the citadel gained in size and importance under the
Seljuks[3]. By the 11th century, Merv was a
great commercial centre of the Oriental type with a bazaar, traversed by two
main streets, the centre of the market roofed by a dome, shops for artisans,
money changers, goldsmiths, weavers, coppersmiths, and potters. It was an
administrative and religious centre, containing mosques, madrasas, palaces, and
other buildings [4]. The dome of the mausoleum of
Sultan Sanjar, one such place, was of turquoise blue, and could be seen at a
distance of a day's journey away [5].
One of
Merv's trademarks was its textile products, silk produced in abundance, and
also a school for its study. The region was also famed for its fine cotton and
exports, of raw products and manufactured, sent to different lands [6]. Merv was one of the great
emporia of the caravan routes between western and eastern Asia, including to
China. This meant that gradually trade and urban activities became the source
of wealth rather than agriculture [7].
Yaqut al-Hamawi, the famous geographer (d. 1229), spent
two years studying in the many libraries of Merv which he admired [8]. According to him,
there were ten wealthy libraries in the city around 1216-1218, two in the chief
mosque and the remainder in the madrasas [9]. Yaqut was in Merv
for three years, collecting the materials for his great geographical
dictionary, for before the Mongol invasion the libraries of Merv were
celebrated [10]. "Verily but
for the Mongols I would have stayed and lived and died there", he writes,
"and hardly could I tear myself away" [11]. Among others, he
mentions the two libraries of the Friday mosque, namely the
"Aziziyah" with 12,000 or so volumes, and the "Kamaliyah"[12]. There was also the
library of Sharaf al-Mulk, in his madrasa, and that of the great Seljuk wazir
Nizam al-Mulk [13]. Among the older
libraries were those founded by the Samanids, and one in the college of the
Umaydiyah; also that in the Khatuniyah College and that which had belonged to
Majd al-Muluk [14].
Merv produced one of the
earliest and greatest scientists of Islam, Ahmad ibn 'Abdallah al-Marwazi
(Marwazi means from Merv) best known as Habash al-Hasib (the calculator), who
flourished in Bagdad and died between 864 and 874. He was an astronomer under
the Caliphs al-Ma'mun and al-Mu'ttasim [15]. Habash made observations from 825 to 835 and
completed three astronomical tables, the best known being the mumtahin (tested) tables, which may be a
collective work of al-Ma'mun's astronomers, for there was a whole team involved
in observation at the court at the time [16]. Apropos of the solar eclipse of 829, Habash gives us
the first instance of a determination of time by an altitude (in this case, of
the sun); a method which was generally adopted by Muslim astronomers. He seems
to have introduced the notion of "shadow," umbra (versa), equivalent
to our tangent, and he compiled a table of such shadows which seems to be the
earliest of its kind [17]. One of Habash's son, called Djafar was also a
distinguished astronomer and instrument maker [18].
Figure
3: View from Merv, used
in contemporary research. See Tim Williams, The landscapes of Islamic Merv,
Turkmenistan: Where to draw the line?,
outlining approaches for interpreting the Islamic city of Merv between the
8th and the 13th centuries, based upon aerial photographic and satellite
imagery.
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A lesser known scholar also from
Merv is Al-Saghani, who was a mathematician and astronomer attached to the
Buyid observatory in Baghdad [19]. In mathematics, he followed up the work of
the Banu Musa, tackling the problem of trisecting the angle, which had
preoccupied the ancient Greek [20]. He was particularly versed in mechanics, and
constructed, if he did not invent, the instruments he used for his astronomical
observations [21].
Also coming from Merv is Ibn Ahmad
Al-Kharaqi. His name refers probably to the place Kharaq (or Kharak) near Merv
and he too was called al-Marwazi. He died in Merv in 1138-1139. He was a
mathematician, astronomer and geographer whose works included:
(1) Muntaha al-idrak fi taqsim
al-aflak, the highest understanding on the division of spheres, (2) Kitab al-tabsira fi 'ilm al-hay'a,
a shorter astronomical treatise improving on some problems treated in Ibn
al-Haytham's astronomy;
(3) Al-risala
al-shamila, the comprehensive treatise, concerning arithmetic; and
Al-Kharaqi's most important work is the Muntaha (the
first cited). It is divided into three discourses (maqalas) covering of
(1) the arrangement of spheres (tarkib al-aflak), their movements,
etc.;
(2) the shape of the earth, and its subdivision into a
part which is inhabited and another which is not, the differences in the
ascendents (tali') and
ascensions (matali') due to
geographical positions;
(3) chronology or eras (tawarikh),
conjunctions (qiranat), chiefly
of Saturn and Jupiter, periods of revolution (adwar)—for
example, dawr al-qiran or 'awd al-qiran (return
of the conjunction) [23].
The Tabsira is
shorter and covers essentially the same ground; however, it does not contain
the elaborate description of the five seas which forms the second chapter of
the second part of the Muntaha [24].
Al-Kharaqi developed the theory
according to which planets are not supported by imaginary circles, rather by
massive revolving spheres. That theory had been previously expounded by
al-Khazin (not to be confounded with al-Khazini), and it found its way into
Western Europe through Hebrew and Latin translations of Ibn al-Haytham's
treatise Fi hay'at al-'alam [25].
Figure
4: Extract from
Al-Khazini's geographical table. Source: David A. King, World-Maps for Finding the
Direction and Distance to Mecca: Innovation and Tradition in Islamic Science. Leiden: Brill/London: Al-Furqan
Islamic Heritage Foundation, 1999, p. 72.
|
The part of the Muntaha describing the five seas was edited
and translated into Latin [26]. There are also details in German by the
excellent Wiedemann on the works of Al-Kharaqi[27].
Another scholar to come from Merv
was a historian, his name al-Tamimi al-Sam'ani (that is, of the tribe of
Sam'an, a branch of the tribe of Tamim), Taj al-Islam. He was born in Merv in
1113, travelled extensively in the Eastern Islamic world and died in Merv in
1166 [28]. He continued the annals of Baghdad begun by
al-Khatib (second half of the 11th century). In 1155, he undertook an extensive
study of Arabic patronymics (nisba) in eight volumes, which is of
great historical and geographical interest. Apropos of the names of prominent
persons he supplies biographical and topographical explanations, which had been
collected by him in the course of his journeys, during which he had met for
that very purpose a large number of learned men. His work called Kitab al-ansab is particularly valuable with regard
to Persia, Transoxiana, and Central Asia, for which countries it is our
principal and often only source of information[29]. The Kitab
al-ansab is better known
through an abridgment of it, theLubab, compiled by the renowned
historian Ibn al-Athir; or through a further abridgment, the Lubb al-lubab, by al-Suyuti [30]. There is no complete edition of the Ansab, unfortunately, and
traces of the work had to be found in Ibn al-Athir and al-Suyuti (second half
of the 15th century) [31]. There are extracts and details in German on
both the author and his work by Wüstenfeld [32].
Without a doubt, the greatest of
all scholars to come from Merv was al-Khazini. Abderahman al-Khazini flourished
ca. 1115-ca 1130 at Merv. He was a slave boy to whom his master gave the best
education in mathematical and philosophical subjects. He became a mathematical
practitioner under the patronage of the Seljuk court.
Of his life very little is known.
He was very much an ascetic, refusing rewards and handed back 1000 Dinars sent
to him by the wife of an Emir. He lived on 3 dinars a year [34].
Figure
5: Exert of the
beginning of Kitab Mizan
al-Hikma in the manuscript
kept at the Russian National Library in St Petersburg, Khanikoff Collection,
Codex 117, folio 1 verso
|
His accomplishments in astronomy
can be summed up with his description of his construction of a 24-hour water
clock designed for astronomical purposes and for his treatise Al-Zij al-Mu'tabar al-Sinjari(The
esteemed Sinjaric tables), giving the positions of the stars for the year
1115/16 at the latitude of Merv [35]. Al-Khazini is, however, better known for his
book Kitab Mizan al-Hikma (The Book of the Balance of Wisdom) [36], completed in 1121. This encyclopaedic
treatise has remained a centrepiece of Muslim physics. Kitab Mizan al-Hikma was written for Sultan Sanjar's
treasury by Al-Khazini, and has survived in four manuscripts, of which three
are independent [37]. It studies the hydrostatic balance, its
construction and uses along with the theories of statics and hydrostatics that
lie behind it and other topics. It was partly translated and edited by the
Russian envoy Khanikoff in the mid-19th century [38].
It is important to mention that the
first of its eight chapters deal with the theories of centres of gravity,
specific gravity and the steelyard theory of his predecessors' including
al-Biruni, Al-Razi, 'Umar al-Khayam, Thabit ibn Qurra, al-Isfizari, alongside
the Greek authors Archimedes and Euclid. Al-Khazini most particularly draws
attention to the Greeks' failure to differentiate clearly between force, mass
and weight, and shows awareness of the weight of the air, and of its decrease
in density with altitude [39]. By looking at his predecessors' scientific
legacy, al-Khazini provides crucial records of their contributions that could
have remained unknown or lost [40].
Figure
6: Colourful diagram of Mizan al-Hikma (the balance of wisdom) designed by
Al-Isfizari and Al-Khazini and described in detail by Al-Khazini in Kitab Mizan al-Hikma (515 H). This image was displayed in
2001 by Sam Fogg (www.samfogg.com) as part of an original manuscript that was being
exhibited among its holdings. Since then, this manuscript is referred to
among the holdings of the University of Pennsylvania: Lawrence J. Schoenberg
Database of Manuscripts, MS LJS 386
|
A significant part of the book is devoted to
hydrostatics, most particularly the determination of specific gravities.
Al-Khazini goes to extreme length in describing the equipment necessary to
obtain accurate results. His scrupulousness in the preparation of his
equipment, materials employed, as well as carrying out varied applications of
his balances make his book one of the best examples "of rigorous attention
to scientific accuracy" [41]. His interest is
devoted to the determination of the specific gravities of metals, precious
stones and alloys with commercial purposes in mind, so as to determine the
purity of various substances and to detect fraud. To determine the specific
weight of a specimen, its weight has to be known in air and water, and the volume
of air and water displaced by the specimen. Hence, most Muslim researchers used
water balances in their experiments. Using the same instrument as al-Biruni,
Al-Khazini made repeated trials with several metals and gemstones. He also
measured the specific gravities of other substances such as salt, amber and
clay, noting whether the substance sank or floated on water.
In all, he records the specific gravities of fifty
substances that include precious stones, metals and liquids. The accuracy of
such measures is impressive and is offered by Hill, together with modern
values. Mieli sees the determination of specific weights by al-Biruni and
al-Khazini as some of the most outstanding results obtained by the Muslims in
experimental physics [42].
The strict definition for specific weight is given by
al-Khazini:
"The magnitude of weight
of a small body of any substance is in the same ratio to its volume as the
magnitude of weight of a larger body (of the same substance) to its volume [43]."
Figure
7: Line drawing of the
balance of wisdom or Al-Mizan al-Jami' (the universal balance) of
al-Khazini as it was drawn by the publishers of Kitab Mizan al-Hikma in Hyderabad in 1358H/1940, p. 130.
|
As a student of statics and
hydrostatics, Al-Khazini borrowed immensely from al-Biruni and al-Isfizari [44]. Al-Khazini also devotes a large space to the
description of various balances by his predecessors, but the focus is on what
he calls 'The Balance of Wisdom'. Al-Khazini's own balance of wisdom is a
unique instrument. Although this balance owes much to Muzaffar b. Ismail
al-Isfizari, al-Khazini added refinements which made it into an instrument that
could perform the most accurate measurements[45]. Such accuracy is due to the length of the
beam, the special method of suspension, the fact that the centre of gravity and
the axis of oscillation were very close to each other, and of course to the
very precise construction of the whole. With this, al-Khazini stated that he
obtained an accuracy of 1 in 60,000. His uses of this balance were for varied
purposes, from ordinary weighing to taking specific gravities, examining the
composition of alloys, changing dirhams to dinars and many other transactions [46]. In all his processes, he moved the scales
about until he obtained equilibrium. Al-Khazini in his descriptions gives
particular focus to determining the proportions of two constituents in an
alloy. Hall states that Al-Khazini's hydrostatic balance can leave no doubt
that "as a maker of scientific instruments he is the greatest of any time [47]."
Figure
8: Diagram of the
balance of wisdom drawn by H. Bauereiss in his dissertation under the
direction of E. Wiedeman: Zur
Geschichte des spezifischen Gewichtes im Altertum und Mittelalter.
Erlangen, 1914, p. 31.
|
Al-Khazini also made many
observations and propositions in his book which constitute some of the
foundations of modern physics. Hence, he states:
"For each heavy body of a
known weight positioned at a certain distance from the centre of the universe,
its gravity depends on the remoteness from the centre of the universe. For that
reason, the gravities of bodies relate as their distances from the centre of
the universe [48]."
Al-Khazini was, thus, the first to propose the hypothesis
that the gravities of bodies vary depending on their distances from the centre
of the earth; this phenomenon was only discovered in the 18th century (six
centuries after al-Khazini) after a certain development in the theory of
gravitation[49].
Al-Khazini also found that there was greater density of
water when nearer to the centre of the earth more than a century before Roger
Bacon (1220-1294) propounded and proved the same hypothesis [50].
Figure 9a-b: Two views of the balance of wisdom as reconstructed
by H. Bauereiss and F. Keller (1908-1911), rediscovered by M. Abattouy and
Professor Jürgen Renn (director of the Max Planck Institute for the History
of Science, Berlin) in the Deutsches Museum in Munich in 2002 (item invent.
Nr. 31116). © Max Planck Institut für Wissenschaftgeschichte, 2002. See
Mohammed Abattouy, Muslim Heritage in Mechanics and
Technology: Outline of a Program for Future Research.
|
|
The Muslims who were already facing the Crusades
(1095-1291), suffered further invasions form the east, which devastated their
eastern empire. In 1220, Genghis Khan and his hordes flattened the eastern
parts of the Muslim land. In just one year the Mongols seized the most
populous, the most beautiful, and the best cultivated part of the earth whose
inhabitants excelled in character and urbanism [51]; and inflicted all
ills on them. An army under Genghis's son Jagtai, captured and sacked Otrar,
whilst another under Genghis himself, burned Bukhara to the ground, raped
thousands of women, and massacred 30,000 men [52]. Samarkand and
Balkh surrendered but suffered pillage, and wholesale slaughter; so much so
that a century later Ibn Battuta (14th century) described these cities as still
largely in ruins [53]. Through Khorasan,
the Mongols ravaged every town on their march, placing captives in their
vanguard, giving them the choice between fighting their fellow men in front, or
being cut down from behind [54]. Amidst the toll of
destruction was that of al-Jurjaniyah dam south of the Aral Sea, which diverted
the River Oxus from its course and deprived the Aral Sea of water, causing it
to nearly dry out centuries later [55].
Merv was captured and was burnt to the ground; its
libraries were consumed in the conflagration. All the glories of the Merv
libraries fell prey to the flames, which followed in the wake of the Mongol
sack of this great city [56]. Ibn al-Athir tells
that the invaders set on fire the Tomb of Sultan Sanjar with most of the
mosques and other public buildings [57]. The city's
inhabitants were allowed to march out through the gates with their treasures,
only to be massacred. The total slaughter cost 1.3 million lives [58]. Ibn al-Athir wrote
"For several years, I put
off reporting this event (of the Mongol invasion). I found it terrifying and
felt revulsion at recounting it and therefore hesitated again and again. Who
would find it easy to describe the ruin of Islam and the Muslims? … O would
that my mother had never borne me, that I had died before and that I were
forgotten! Though so many friends urged me to chronicle these events, I still
waited. Eventually I came to see that it was no use not complying. The report
comprises the story of a… tremendous disaster such as had never happened
before, and which struck all the world, though the Muslims above all. If any
one were to say that at no time since the creation of man by the Great God had
the world experienced anything like it, he would only be telling the truth. In
fact nothing comparable is reported in past chronicles… Those they (the
Mongols) massacred, for a single city whose inhabitants were murdered numbered
more than all the Israelites together. It may well be that the world from now
until its end… will not experience the like of it again, apart perhaps from Gog
and Magog. Dadjal will at least spare those who adhere to him, and will only
destroy his adversaries. These (the Mongols), however, spared none. They killed
women, men and children, ripped open the bodies of the pregnant and slaughtered
the unborn. Truly: we belong to God and shall return to Him; only with Him is
strength and power [59].'
Figure
10: Page from the
Persian translation of Kitab
Mizan al-Hikma.
|
When Merv was visited in the 14th
century by Ibn Battuta, it was still in great ruin [60]. Mustawli also saw that it was still largely
in ruins, and the sands had begun encroaching [61]. Hafiz Abru adds that the Mongols had broken
down all the great dams and dykes, which under the Seljuks had grown in number,
and had been carefully maintained, in order thus to regulate the irrigation of
the oasis; now everything had lapsed into a desert swamp [62].
However, some Western historians
praise the Mongols. Thus, Saunders, tells us:
`The Mongol massacres,
genocide, perhaps arose from mixed motives of military advantage and
superstitious fears. By massacres they hastened the surrender of other places
and speeded the conquest. However merciless their rage for destruction, after a
decent interval, they commonly permitted the rebuilding of the cities they had
burnt and ruined'[63]
Rebuilding may have been permitted
but many devastated places were still in ruins centuries later. Wiet et al.
tell us that Genghis Khan's
‘means were still limited, but
he had on his side the moderation and the deliberation of a great leader and,
above all, a magnificent army, the exploits of whose horsemen, incomparable
bowmen and seasoned warriors take their place in history and legend. [64]’
Figure
11: Exert from the
beginning of the edition and translation of Kitab
Mizan al-Hikma by Nicholai
Khanikoff: "Analysis and Extracts of Kitab
Mizan al-Hikma, an Arabic Work on the Water-balance, written by
al-Khazini in the Twelfth Century. By the Chevalier N. Khanikoff, Russian
Consul-general at Tabriz, Persia." Journal
of the American Oriental Society vol.
6 (1860): pp. 1-128.
|
Wiet and his group also make the
point that:
`What legend portrays so
exultantly, however, the chronicles reveal as a grievous ordeal for the
city-dwellers of Asia. The Mongols, lagging behind the other barbarians of Asia
in their development, did not know what to do with the towns. On the principle
that only terror is profitable, only the steppe liveable and only the way to
heaven valuable, they pillaged, destroyed and massacred. The list of their
conquests is a litany of disaster: the marvellous cities of Bukhara, Samarkand,
Nishapur, Baghdad and countless others were razed to the ground and their
inhabitants slain. [65]'
They further argue that:
`The sword, however, fell only
on those who offered resistance. Those who welcomed the Mongol as a liberator…
escaped the terror. [66]'
However, most of the places that were
devastated surrendered without a fight and it is a contradiction to say that
only those who fought were slaughtered and then to agree that all the
inhabitants, including women and children were slaughtered.
Ibn al-Athir: Kitab
al-kamil; ed. K.J. Tornberg; 12 vols., Leiden; 1851-72.
Ibn Battuta: Voyages
d'Ibn Battuta, Arabic text accompanied by French translation by C.
Defremery and B.R. Sanguinetti, preface and notes by Vincent Monteil, I-IV,
Paris, 1968, reprint of the 1854 edition.
Ibn Battuta: Travels
in Asia and Africa; translated and selected by H.A.R. Gibb; George
Routledge and Sons Ltd; London, 1929.
C. E. Bosworth: "Merv"; Encyclopaedia of Islam;
New Series; vol. 6; pp. 618-21.
J.L.E. Dreyer: A
History of Astronomy from Thales to Kepler; Dover Publications Inc,
New York, 1953.
W. Durant: The
Age of Faith, Simon and Shuster, New York; 6th printing; 1950.
R.E. Hall: "Al-Khazini", in Dictionary of Scientific Biography;
vol. VII, 1973: 335-51.
D.R. Hill: Islamic
Science and Engineering; Edinburgh University Press; 1993.
Al-Khazini: Kitab
Mizan al-Hikma, Hyderabad; partial English translation by N.
Khanikoff (1860); "Analysis and extracts of Kitab mizan al-Hikma (book
of balance of Wisdom), an Arabic work on the water balances, written by
al-Khazini in the twelfth century,' Journal
of the American Oriental Society 6:1-128; also Russian translation:
by M.M. Rozhanskaya and I.S. Levinova, Al-Khazini.
Kniga vesov midrosti,' Nauchnoye nasledstvo, Moscow, vol 6, 1983;
pp 15-140.
G. Le Strange: The
Lands of the Eastern Caliphate; Cambridge University Press; 1930.
A. Mieli: La
Science Arabe et son rôle dans l'évolution mondiale, Leiden, E, J.
Brill, 1966.
M. Meyerhof: "Science and Medicine", in The Legacy of Islam; edited by Sir
T Arnold, and A. Guillaume; Oxford University Press; 1931.
J. Pedersen; The
Arabic Book (1928) translated by Geoffrey
French; Princeton University Press; Princeton, New Jersey (1984).
G. Sarton: Introduction
to the History of Science; The Carnegie Institution; Washington;
1927 ff.
J.J. Saunders: The
History of the Mongol Conquests; Routlege & Kegan Paul; London;
1971.
C. Schoy: Liber
den Gnomonschatten und die Schattentafel; Hanover, 1923.
R.B. Sergeant: Islamic
textiles up to the Mongol Conquest; Beirut 1972.
N. Smith: A
History of Dams, The Chaucer Press, London, 1971.
B. Spuler: History
of the Mongols; London, Routledge & Kegan Paul, 1972, p.31.
H. Suter: Die
Mathematiker und Astronomer der Araber; 1900.
J. W. G. Wiet et
al.: History of mankind; Vol. III: The Great Medieval Civilisations.
Part Two: section two; Part three; Translated from the French. UNESCO; 1975.
References
[1] C. E.
Bosworth: Merv; Encyclopaedia of Islam; New Series; vol. 6; pp. 618-21.p. 618.
[2] G. Le
Strange: The Lands of the Eastern Caliphate; Cambridge University Press; 1930;
pp. 401 ff.
[3] G. Le
Strange: The Lands; p. 401.
[4] C. E.
Bosworth: Merv; p. 619.
[5] For Merv
topography, see G. Le Strange: Lands; op cit.; pp. 397-403.
[6] R.B.
Sergeant: Islamic textiles up to the Mongol conquest; Beirut 1972; pp. 87-90.
[7] C. E.
Bosworth: Merv; op cit.; p. 619.
[8] C. E.
Bosworth: Merv; op cit.; p. 620.
[9] Yaqut
al-Hamawi in J. Pedersen; The Arabic Book, New Jersey (1984), p. 128.
[10] G. Le
Strange: The Lands; op cit.; p. 401.
[11] G. Le Strange:
The Lands; p. 401-2.
[12] G. Le
Strange: The Lands; p. 401-2.
[13] G. Le Strange:
The Lands; p. 401-2.
[14] G. Le
Strange: The Lands; p. 401-2.
[15] G. Sarton:
Introduction to the History of Science; The Carnegie Institution; Washington;
1927 ff.; vol. I; p. 565.
[16] G. Sarton:
Introduction; I; p. 565.
[17] G. Sarton:
Introduction; I; p. 565.
[18] For more on
Habbash and his accomplishments, consult: H. Suter: Die Mathematiker und
Astronomer der Araber; 1900; pp. 12, 27; J.L.E. Dreyer: A History of Astronomy from Thales to Kepler;
Dover Publications Inc., New York, 1953; C. Schoy: Liber den Gnomonschatten und
die Schattentafel; Hanover, 1923.
[19] G. Wiet; V.
Elisseeff; P. Wolff; and J. Naudu: History of Mankind; Vol 3: The Great
medieval Civilisations; Translated from the French; George Allen & Unwin
Ltd; UNESCO; 1975; p. 647.
[20] G. Wiet; V.
Elisseeff; P. Wolff; and J. Naudu: History of Mankind; p. 647.
[21] G. Wiet; V.
Elisseeff; P. Wolff; and J. Naudu: History of Mankind; p. 647.
[22] G. Sarton:
Introduction; op cit.; vol. ii; pp. 204-5.
[23] G. Sarton:
Introduction; ii; pp. 204-5.
[24] G. Sarton:
Introduction; ii; pp. 204-5.
[25] G, Sarton:
Introduction; ii; pp. 204-5.
[26] By C. A.
Nallino: Albatenii opus astronomicum; vol. 1, 169-175, Milan.
[27] E Wiedemann:
Beitrage zur Geschichte der Naturwissenschaften, 20; Sitaungsber. der phys.
med. Sozietat sur Erlang vol. 42, 72, 1910.
[28] G. Sarton:
Introduction; op cit.; II; pp. 444-5.
[29] Sarton II;
pp. 444-5.
[30] Sarton II;
pp. 444-5.
[31] Sarton II;
pp. 444-5.
[32] F.
Wustenfeld: Geschichtschreiber der Araber; no. 54, P. 87, 1881.
[33] Well
documented, though, by R.E. Hall, "Al-Khazini", in the Dictionary of
Scientific Biography; vol. VII, 1973: 335-51.
[34] R.E. Hall:
Al-Khazini.
[35] G. Sarton:
Introduction; vol. 2; p.122.
[36] Al-Khazini:
Kitab Mizan al-Hikma, Hyderabad; partial English translation by N. Khanikoff (1860);
`Analysis and extracts of Kitab mizan al-Hikma (book of balance of Wisdom), an
Arabic work on the water balances, written by al-Khazini in the twelfth
century,' Journal of the American Oriental Society 6:1-128; also Russian
translation: by M.M. Rozhanskaya and I.S. Levinova `Al-Khazini. Kniga vesov
midrosti,' Nauchnoye nasledstvo, Moscow, vol 6, 1983; pp 15-140. See also R.E.
Hall, Dictionary of Scientific Bibliography VII, 1973: 335-51.
[37] N.Khanikoff
ed. p.16; in R.E. Hall: Al-Khazini; Dictionary of Scientific Biography, VII,
1973: pp.335-51.
[38] Al-Khazini:
Kitab Mizan al-Hikma, Hyderabad; partial English translation by N. Khanikoff
(1859); op cit.
[39] D.R. Hill:
Islamic Science and Engineering; Edinburgh University Press; 1993, p. 61.
[40] D.R. Hill: op
cit.; p. 61.
[41] D.R. Hill:
Islamic, op cit., p 70.
[42] A. Mieli: La
Science Arabe et son rôle dans l'évolution mondiale, Leiden, E, J. Brill, 1966,
p. 101.
[43] D.R. Hill:
Islamic science; op cit; 61.
[44] R.E. Hall:
Al-Khazini: Dictionary, op cit.
[45] For details,
see R.E. Hall: Al-Khazini.
[46] D.R. Hill:
Islamic, op cit., p 69.
[47] R.E. Hall:
Al-Khazini; Dictionary, op cit.
[48] Kitab Mizan
al-Hikma, English translation, p.24. in M. Rozhanskaya: Statics, op cit., pp.
621-2.
[49] Rozhanskaya;
p. 622.
[50] Max Meyerhof:
Science and Medicine, in The Legacy of Islam; edited by Sir T Arnold, and A.
Guillaume; Oxford University Press; 1931; p. 342.
[51] B. Spuler:
History of the Mongols; London, Routledge & Kegan Paul, 1972, p. 31.
[52] W. Durant:
The Age of faith, Simon and Shuster, New York; 6th printing; 1950; p.339
[53] Ibn Battuta:
Voyages d'Ibn Battuta, Arabic text accompanied by French translation by C.
Defremery and B.R. Sanguinetti, preface and notes by Vincent Monteil, I-IV,
Paris, 1968, reprint of the 1854 edn; Ibn Battuta: Travels in Asia and Africa;
trsltd and selected by H.A.R. Gibb; George Routledge and Sons Ltd; London,
1929.
[54] W. Durant:
The Age of faith, op cit.; Chapter XIV; p.339.
[55] N. Smith: A
History of Dams, Chaucer Press, London, 1971; p 86.
[56] G. Le Strange:
The Lands; op cit.; p. 402.
[57] G. Le
Strange: The Lands; p. 402.
[58] Browne: in W.
Durant: The Age offaith, op cit; p.339
[59] Ibn al-Athir:
Kitab al-kamil; ed K.J. Tornberg; 12 vols; Leiden; 1851-72; vol 12; pp. 233-34.
[60] G. Le
Strange: The Lands; op cit; p. 402.
[61] C. E.
Bosworth: Merv; op cit; p. 621.
[62] G. Le
Strange: The Lands; op cit; p. 402.
[63] J.J.
Saunders: The History of the Mongol Conquests; Routlege & Kegan Paul;
London; 1971. p. 56.
[64] J. W. G. Wiet
et al: History ofmankind; Vol III:The Great Medieval Civilisations.Part Two:
section two; Part three; Translated from the French. UNESCO; 1975.; p. 218
[65] J. W. G. Wiet
et al: History ofmankind; p. 218
[66] J. W. G. Wiet
et al: History ofmankind; p. 218.
