Abu Ja'far Muhammad ibn al-Husayn al- Khazin al-Kurasani

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Abu Ja’far Al-Khāzin
Name Modifications:
Abū Ja’far Muhammad ibn al-Husayn al-Khāzin
al-Khurasani
Dates of Birth and Death:
(∗) About 900 in possibly Saghan near Merv in Khorasan
(†) About 970 in possibly Rayy
Family Data:
Al-Khazin’s family was from Saba, a kingdom in southwestern Arabia, perhaps
better known as Sheba from the biblical story of King Solomon and the
Queen of Sheba.
Very little information is available
about his personal life apart from
that he lived in Khorasan. It is
said that he was born in a place
known as Saghan, near Merw in
the province Khorasan.
Khorasan in its proper sense
comprised principally the cities
of Mashhad, Nishapur, Sabzevar
and Kashmar (now in
Iran), Balkh and Herat (now in
Afghanistan), Merv, Nisa and
Abiward (now in Turkmenistan),
Samarqand and Bukhara (now in
Uzbekistan).
Fig. 1: Territories during the
Caliphate in 750. Khorasan in
yellowish.
Abu Ja’far al-Khazin belonged to the pagan sect of Sabians 1 of Persian origin
which was tolerated in early Islam. He was called al-Khurasani, i.e., from
Khurasan (or Khorasan). In the book Fihrist, a tenth century survey of
Islamic culture, he is mentioned also as al-Khurasani.
1 Sabians show similarities with Jews and Christians and are a kind of Gnostic, Hermetic
and Abrahamic religion. They are mentioned three times in the Quran.

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Education:
Abu Ja’far Muhammad ibn al-Husayn al-Khāzin was a mathematician and
astronomer. Until 1978 it was believed that Abū Ja’far al-Khazin and Abū
Ja’far Muhammad ibn al-Husayn were two different mathematicians. However,
Adil Anbouba showed that they are the same person (see Anbouba,
1978).
Professional Career:
According to the Islamic Encyclopedia, Khazin served as a treasurer during
the reign of the Samanid Prince Mansur ibn Nūh I (961-976) and then as
a Vizier in Nishapur 2 . He came close to the Buwayhid Prince 3 Rukn ad-
Dawlah and his erudite Vizier al-’Amid and spent a part of his life in Rayy.
During peace negotiations between the Buwayhids and the Samanids, al-
Khazin acted as the envoy of the Buwayhids. Al-Khazin later developed
close friendship with the Vizier, al-’Amid, and spent the rest of his life in
research and authoring books under his protection.
Abū Ja’far al-Khazin realized that a cubic equation could be solved geometrically
by means of conic sections. Al-Māhān (ca. 850 AC) had shown that
an unsolved problem in Archimedes’ On the Sphere and Cylinder 4 could be
reduced to the cubic equation:
x 3 + C = ax 2 .
Abū Ja’far based on a commentary to Archimedes’ work by Eutokius of
Ascalon 5 (fifth century AC) and realized that the equation x 3 + C = ax 2
could also be solved by means of conic sections. He also studied the equation
x 3 + y 3 = z 3
and stated (without proof) that it has no solution in positive integers.
Moreover, he also worked on the isoperimetric problem 6 (see Lorch, 1986),
and he wrote a commentary to Book X of Euclid’s Elements 7 .
2 Nishapur or Nishabur is a city in the Khorasan Province in northeastern Iran.
3 The Buyid dynasty controlled most of modern-day Iran and Iraq in the 10th and 11th
centuries.
4 On the Sphere and Cylinder (about 225 BC) was written by Archimedes in two volumes.
Proposition 4 of Book II deals with the problem how to find the surface area of a
sphere and the volume of the contained ball and the analogous values for a cylinder.
5 Eutokius of Ascalon (c. 480 – c. 540) was a Greek mathematician who wrote commentaries
on several Archimedean treatises and on the Apollonian Conics.
6 The isoperimetric problem can be stated as follows: Among all closed curves in the
plane of fixed perimeter, which curve (if any) maximizes the area of its enclosed region?.
7 Euclid’s Elements consist of 13 books written by the Greek mathematician Euclid in

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Al-Khazin also introduced various mathematical areas, among them the most
important issue of a mathematical proof, for example, indirect proving by
contradiction. Abū Ja’far al-Khazin gives a good example by establishing
some properties of right-angled triangles in the treatise Risalah fi al Muthallathat
al-Qa’imat al-Zawaya.
Abū Ja’far’s main astronomical
work has the title Zīj al-sāih,
which means Tables of the disks
of the astrolabe. An astrolabe is a
device used by astronomers, navigators,
and astrologers for locating
and predicting the positions of
the sun, moon, planets, and stars,
determining local time given local
latitude and vice-versa, surveying,
triangulation 8 , and to cast
horoscopes. Thus it is an Astronomical
Handbook of Plates
which introduces a new version of
an astrolabe.
Fig. 2: Modern reproduction of a
Persian astrolabe.
Unfortunately, this work seems to be lost, but there are some references to
it in the works of later authors. According to King (King, 1986) there is
a manuscript of the book in a private library in India. King also mentions
that such an astrolabe was made, however incomplete, in the twelfth Century
by Hebatullah b. al-Husain. It is said that in Munich, Germany, there
was a replica of the astrolabe in the beginning of the 20th century. However,
it disappeared during the Second World War, but later in 1996, it was
traced by David King in the Museum fur Islamisch Kunst in Eastern Berlin,
and photographs of the instrument were published by King in two separate
articles.
Abū Ja’far is also the author of a geographical treatise in which he gives
latitudes and longitudes for 2402 localities, i.e. cities, mountains, seas, islands,
geographical regions and rivers. Moreover, there are maps which on
Alexandria about 300 BC. Book X attempts to classify incommensurable magnitudes (two
non-zero real numbers a and b are said to be commensurable if a/b is a rational number)
by using the method of exhaustion (a method of finding the area of a shape by inscribing
inside it a sequence of polygons whose areas converge to the area of the containing shape),
a precursor to integration.
8 Triangulation is the process of determining the location of a point by measuring angles
to it from known points at either end of a fixed baseline.

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the whole are more accurate than those of Ptolemy.
Abūa Ja’far developed a solar model, in which the sun moves in a circle with
the earth as its center, in such a way that its motion is uniform with respect
to a point which does not coincide with the center of the earth. Finally, he
dealt with the effect of gravity 9 and thus precedes Newton.
Professional Career:
According to the Islamic Encyclopedia, Khazin served as a treasurer during
the reign of the Samanid Prince Mansur ibn Nūh I (961-976) and then as
a Vizier in Nishapur 10 . He became close to the Buwayhid Prince 11 Rukn
ad-Dawlah and his erudite Vizier al-’Amid, and spent part of his life in
Rayy. During peace negotiations between the Buwayhids and the Samanids,
al-Khazin acted as the envoy of the Buwayhids. Al-Khazin later developed
close friendship with the Vizier, al-’Amid, and spent the rest of his life in
research and authoring books under his protection.
Abū Ja’far al-Khazin realized that a cubic equation could be solved geometrically
by means of conic sections. Al-Māhān (ca. AC 850) had shown that
an unsolved problem in Archimedes’ On the Sphere and Cylinder 12 could be
reduced to the cubic equation:
x 3 + C = ax 2 .
Abū Ja’far based on a commentary to Archimedes’ work by Eutocius of
Ascalon (fifth century AC) realized that the equation x 3 + C = ax 2 could
also be solved by means of conic sections.
Abū Ja’far also studied the equation x 3 + y 3 = z 3 and stated (without proof)
that it has no solution in positive integers. He also worked on the isoperimetric
problem (see Lorch, 1986), and he wrote a commentary to Book X of
Euclid’s Elements 13 .
9 See the Islamic Encyclopedia, http://islamicencyclopedia.org/public/index/
topicDetail/page/11/id/543.
10 Nishapur or Nishabur is a city in the Khorasan Province in northeastern Iran.
11 The Buyid dynasty controlled most of modern-day Iran and Iraq in the 10th and 11th
centuries.
12 On the Sphere and Cylinder (about 225 BC) was written by Archimedes in two volumes.
Proposition 4 of Book II deals with the problem how to find the surface area of a
sphere and the volume of the contained ball and the analogous values for a cylinder.
13 Euclid’s Elements consist of 13 books written by the Greek mathematician Euclid in
Alexandria about 300 BC. Book X attempts to classify incommensurable magnitudes by
using the method of exhaustion, a precursor to integration.

Copyright c○ by Stochastikon GmbH (http://encyclopedia.stochastikon.com) 5
Al-Khazin also introduced various mathematical areas, among them the most
important issue of a mathematical proof, for example, indirect proving by
contradiction. Abū Ja’far al-Khazin gives a good example by establishing
some properties of right-angled triangles in the treatise Risalah fi al Muthallathat
al-Qa’imat al-Zawaya.
Abū Ja’far’s main astronomical work has the title Zīj al-sāih, which means
Tables of the disks of the astrolabe. Thus it is an Astronomical Handbook of
Plates which introduces a new version of an astrolabe. Unfortunately, this
work seems to be lost, but there are some references to it in the work of
later authors. According to King (King, 1986) there is a manuscript of the
book in a private library in India. King also mentions that such an astrolabe
was made, however incomplete, in the twelfth Century by Hebatullah b. al-
Husain. It is said in Munich, Germany, there was a replica of the astrolabe
in the beginning of the 20th century. But, it disappeared during the Second
World War, but later in 1996, it was traced by David King in the Museum
fur Islamisch Kunst in Eastern Berlin and photographs of the instrument
were published by King in two separate articles.
Abū Ja’far is also the author of a geographical treatise in which he gives
latitudes and longitudes for 2402 localities, i.e. cities, mountains, seas, islands,
geographical regions and rivers. Moreover, there are maps which on
the whole are more accurate than those of Ptolemy.
Abūa Ja’far developed a solar model, in which the sun moves in a circle with
the earth as its center, in such a way that its motion is uniform with respect
to a point which does not coincide with the center of the earth. Finally, he
dealt with the effect of gravity 14 and thus preceded Newton.
Publications:
• Zīj al-Safā’ih (Book on astronomy with astronomical tables).
• Risalah fi al Muthallathat al-Qa’imat al-Zawaya. (Book showing that
it is not possible that any triple (x, y, z), with x and y being odd (or
evenly even) could be the sides of a right-angled triangle with z as an
integer.)
• Commentary on Ptolemy’s Almagest, however, only one fragment of
this commentary has survived.
14 See the Islamic Encyclopedia, http://islamicencyclopedia.org/public/index/
topicDetail/page/11/id/543.

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Bibliography:
• Anbouba, A. (1978): L’ Algebre arabe; note annexe: identite d’ Abū Ja’far
al-Khazin. Journal for History of Arabic Science 2: 98–100.
• Calvo, Emilia (2007): Khazin: Abu Ja’far Mu?hammad ibn al-Husayn al-
Khazin al-Khurasani. In Thomas Hockey et al. The Biographical Encyclopedia
of Astronomers. New York: Springer. pp. 628–9., http://islamsci.
mcgill.ca/RASI/BEA/Khazin_BEA.htm.
• Dold-Samplonius, Yvonne (2008): Al-Khazin, Abu Ja’far Muhammad Ibn
Al-Hasan Al-Khurasani. Complete Dictionary of Scientific Biography. Encyclopedia.com.
• Hogendijk, J. (1997): Abū Ja’far Al-Khāzin. In: Encyclopedia of the History
of Science, Technology and Medicine in Non-Western Cultures. Ed.
Helaine Selin, p. 3,4.
• King, D.A. (1980): New Light on the Zīj al-safāih. Centaurus 23, 105-
117. Reprinted in D.A. King, Islamic Astronomical Instruments. London:
Variorum, 1987.
• Lorch, R. (1986): Abū Ja’far al-Khazin on Isoperimetry and the Archimedean
Tradition. Zeitschrift für Geschichte der arabisch-islamischen Wissenschaften
3, 150-229.
• O’Connor, John J.; Robertson, Edmund F.: Abu Jafar Muhammad ibn al-
Hasan Al-Khazin. MacTutor History of Mathematics archive, University of
St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/
Al-Khazin.html.
• Rāshed, Rushdī (1994): The development of Arabic mathematics: between
arithmetic and algebra. Kluwer, London.
• Rāshed, Roshdī (1996): Les Mathématiques Infinitésimales du IXe au XIe
Siècle 1: Fondateurs et commentateurs: Banu Musa, Ibn Qurra, Ibn Sinan,
al-Khazin, al-Quhi, Ibn al-Sam, Ibn Hud. London. Reviews: Seyyed Hossein
Nasr (1998) in Isis 89 (1) pp. 112-113; Charles Burnett (1998) in Bulletin of
the School of Oriental and African Studies, University of London 61 (2) p.
406.
• J. Samsó (1977): A Homocentric Solar Model by Abū Ja’far al-Khazin.
Journal for History of Arabic Science 1: 268–275.
• A.S. Saydan, Treatise on arithmetic triangles by abu Ja’far al-Khazin (Arabic).
Dirasat Res. J. Natur. Sci. 5 (2) (1978), 7-49.
• Islamic Encyclopedia, http://islamicencyclopedia.org/public/index/
topicDetail/page/11/id/543.
Author(s) of this contribution:
Tora von Collani, Claudia von Collani

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