424 khatt
Fritz Zimmermann (Oxford: Oxford University Press,
2000); Elie Adib Salem, Political Theory and Institutions
of the Khawarij (Baltimore: Johns Hopkins Press,
1956); Julius Wellhausen, The Religio-Political Factions
in Early Islam,ed. R. C. Ostle and trans. R. C. Ostle
and S. M. Walzer (1901; reprint, Amsterdam: North-
Holland, 1975).
khatt SeeCALLIGRAPHY,ISLAMIC.
Khayyam, Omar SeeOMARKHAYYAM.
Khazars They were a confederation of Turkish tribes,
some of whose leaders converted to Judaism, from around
the Caucasus mountains. They allied themselves with the
BYZANTINEemperor HERAKLEIOSto fight the Persians and
provided help against the AVARS. The Khazars appeared at
the time of the collapse of an empire of central Asian
TURKSin the early seventh century. They then associated
various Turkish elements under the leadership of a royal
clan from whom was chosen the khagan, a sacred figure
put to death if fortune failed him. Their first capital at
Balandja, south of the Caucasus, was captured in 642 by
the Arabs. From then on their rule was reduced to an area
from the Caucasus to the middle Volga and Khwarezm.
Itil on the Volga was its capital.
Their relations with the Byzantines were usually
good, as two emperors married Khazar princesses, and
the Byzantines built for the khagan a fortress on the Don
in an attempt to contain Hungarians and Petchenegs who
had already captured the eastern part of Khazar territory.
They also had to deal with the Rus ́from KIEV. In 965, Svi-
atoslav (r. 962–972) destroyed Itil and Sarkel, the heart of
the Khazar state. In 1015 the Rus ́helped the Byzantine
emperor BASILII conquer Crimea from the Khazars. The
Khazar state disappeared in the first half of the 11th cen-
tury, and most of them converted to ISLAM.
AN EARLY JEWISH STATEThe capital of the empire, Itil, was at the center of
several commercial routes. The Khazars soon became
MERCHANTS. This also brought in various religious influ-
ences. Islam had won over some families. JEWSmanaged
to convert a ruler, Bulan (r. 786–809), and, for a long
period from the early ninth century, the religion of the
state and of the khagan was a form of Judaism. Recently
discovered letters have confirmed the existence of a
considerable Jewish element at the royal court. Chris-
tianity also spread among them from their close neigh-
bors, the ALANS, and others. From Byzantium, Saint
CYRILarrived in about 861 to evangelize them, with
little lasting success.
Further reading: Norman Golb, Khazarian Hebrew
Documents of the Tenth Century(Ithaca, N.Y.: Cornell Uni-
versity Press, 1982); D. M. Dunlop, The History of the
Jewish Khazars (Princeton, N.J.: Princeton University
Press, 1954); Arthur Koestler, The Thirteenth Tribe: The
Khazar Empire and Its Heritage (London: Hutchinson,
1976).khitan SeeCIRCUMCISION, AND THECHRISTIAN FEAST OF
THECIRCUMCISION.al-Khwarizmi, Muhammad ibn Musa (ca. 780–ca.
845)Persian mathematician, astronomer, geographer
Perhaps born in Khwarizm in IRAN, al-Khwarizmi flour-
ished at the court of the ABBASID CALIPH AL-MAMUN. The
caliph’s interest in SCIENCEand PHILOSOPHYgave great
impetus to scholarly investigation and promoted science
and an intense TRANSLATIONproject from Greek via Syriac
into Arabic. Little has been found on al-Khwarizmi’s life;
his name indicated at least an origin in the Persian cul-
ture of the Oxus River delta. He may have been part of al-
Mamun’s scientific academy in BAGHDAD, the House of
Wisdom (Dar al-Hikma). He most likely participated in
the calculation of the length of a degree of latitude, which
took place during al-Mamun’s reign.
To al-Khwarizmi we owe the words algorithmand
algebra, from the title of his important mathematical
work, Calculation for Integration and Equation.The book
was twice translated into LATIN, by both GERARDof Cre-
mona and Robert of Chester in the 12th century. In it al-
Khwarizmi worked out several hundred simple quadratic
equations by analysis and intuitive geometrical example.
It also treated in an algebraic form methods of dividing
inheritances and surveying plots of land. Al-Khwarizmi
was one of the first users in the Islamic world of the sys-
tem of numbers, along with the concept of zero, that was
later called Arabic in the West but actually was borrowed
at about this time from Hindu India. Al-Khwarizmi wrote
a treatise on arithmetic.
Arabic bibliographies of the period included two
books by him on the ASTROLABEand one on sundials;
neither has survived. Al-Khwarizmi compiled the first
astronomical tables in the Muslim world. They were
translated into Latin by ADELARD OFBAT Hin 1126. Al-
Khwarizmi made a contribution to medieval geography,
The Shape [or Image] of the Earth.Its maps have unfortu-
nately not come down to us, but modern scholars recon-
structed them from al-Khwarizmi’s descriptions. He died
about 845.
Further reading:Carl B. Boyer and Uta C. Merzbach,
A History of Mathematics(New York: John Wiley & Sons,
1989); Victor J. Katz, A History of Mathematics: An Intro-
duction(New York: Harper Collins College Publishers,
1993); David A. King, Al-Khwarizmi and New Trends in
Mathematical Astronomy in the Ninth Century(New York:
Hagop Kevorkian Center for Near Eastern Studies, New
York University, 1983).