91-521: The Toubou or Tubu (from Old Tebu , meaning "rock people") are an ethnic group native to the Tibesti Mountains that inhabit the central Sahara in northern Chad , southern Libya , northeastern Niger , and northwestern Sudan . They live either as herders and nomads or as farmers near oases . Their society is clan-based, with each clan having certain oases, pastures and wells. The Toubou are generally divided into two closely related groups:
182-685: A dust board. Called takht in Arabic (Latin: tabula ), a board covered with a thin layer of dust or sand was employed for calculations, on which figures could be written with a stylus and easily erased and replaced when necessary. Al-Khwarizmi's algorithms were used for almost three centuries, until replaced by Al-Uqlidisi 's algorithms that could be carried out with pen and paper. As part of 12th century wave of Arabic science flowing into Europe via translations, these texts proved to be revolutionary in Europe. Al-Khwarizmi's Latinized name, Algorismus , turned into
273-536: A generic manner, insofar as it does not simply emerge in the course of solving a problem, but is specifically called on to define an infinite class of problems. According to Swiss-American historian of mathematics, Florian Cajori , Al-Khwarizmi's algebra was different from the work of Indian mathematicians , for Indians had no rules like the restoration and reduction . Regarding the dissimilarity and significance of Al-Khwarizmi's algebraic work from that of Indian Mathematician Brahmagupta , Carl B. Boyer wrote: It
364-569: A list of his books. Al-Khwārizmī accomplished most of his work between 813 and 833. After the Muslim conquest of Persia , Baghdad had become the centre of scientific studies and trade. Around 820 CE, he was appointed as the astronomer and head of the library of the House of Wisdom . The House of Wisdom was established by the Abbasid Caliph al-Ma'mūn . Al-Khwārizmī studied sciences and mathematics, including
455-543: A number to both sides of the equation to consolidate or cancel terms) described in this book. The book was translated in Latin as Liber algebrae et almucabala by Robert of Chester ( Segovia , 1145) hence "algebra", and by Gerard of Cremona . A unique Arabic copy is kept at Oxford and was translated in 1831 by F. Rosen. A Latin translation is kept in Cambridge. It provided an exhaustive account of solving polynomial equations up to
546-453: A particular clan, land, trees (usually date palms), and nearby wells may have different owners. Each family's rights to the use of particular plots of land are recognized by other clan members. Families also may have privileged access to certain wells and the right to a part of the harvest from the fields irrigated by their water. Within the clan and family contexts, individuals also may have personal claims to palm trees and animals. Much of
637-708: A rate of 5%. The study also found that 20–30% of Toubou autosomal DNA was Eurasian in origin, and their African ancestral component was best represented by Laal-speaking populations. The most likely source of this Eurasian DNA, according to the analysis, was central European Neolithic farmers ( Linearbandkeramik culture ). Other ethnic groups in the Chad , such as the Sara people and the Laal speakers had considerably lower Eurasian admixture, at only 0.3–2% (Sara) and 1.25–4.5% (Laal). In 2019, B Lorente-Galdos using whole genome analysis, found that in
728-499: A semi-nomadic pastoralist lifestyle. Those who prefer a settled life typically live in palm-thatched, rectangular or cylindrical mud houses. The Toubou are patrilineal, with an elder male heading the lineage. The second order of Toubou kinship is to the clan . According to Jean Chapelle, a colonial officer of history specializing in Chadian ethnic groups (although his book in Borkou has caused
819-409: A significant degree of wrongdoing), the clan system developed out of necessity. Nomadic life means being scattered throughout a region; therefore, belonging to a clan means that the individual is likely to find hospitable clan people in most settlements or camps of any size. A second factor is the maintenance of ties with the maternal clan. Although the maternal clan does not occupy the central place of
910-420: A whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. Roshdi Rashed and Angela Armstrong write: Al-Khwarizmi's text can be seen to be distinct not only from
1001-404: A world map for al-Ma'mun , the caliph, overseeing 70 geographers. When, in the 12th century, his works spread to Europe through Latin translations, it had a profound impact on the advance of mathematics in Europe. Al-Jabr (The Compendious Book on Calculation by Completion and Balancing , Arabic : الكتاب المختصر في حساب الجبر والمقابلة al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wal-muqābala )
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#17330848190561092-598: Is a derde (spiritual head) who is recognized as the clan judge, and arbitrates conflict and levies sanctions. The Toubou people, states Jean Chapelle, have been socially stratified with an embedded caste system. The three strata have consisted of the freemen with a right to own property, the artisanal castes and the slaves. The endogamous caste of Azza (or Aza ) among Toubou have the artisanal occupations, such as metal work, leather work, salt mining, well digging, dates farming, pottery and tailoring, and they have traditionally been despised and segregated by other strata of
1183-417: Is a stub . You can help Misplaced Pages by expanding it . Muhammad ibn Musa al-Khwarizmi Muhammad ibn Musa al-Khwarizmi ( Persian : محمد بن موسى خوارزمی ; c. 780 – c. 850 ), or simply al-Khwarizmi , was a polymath who produced vastly influential Arabic-language works in mathematics , astronomy , and geography . Around 820 CE, he was appointed as the astronomer and head of
1274-406: Is a mathematical book written approximately 820 CE. It was written with the encouragement of Caliph al-Ma'mun as a popular work on calculation and is replete with examples and applications to a range of problems in trade, surveying and legal inheritance. The term "algebra" is derived from the name of one of the basic operations with equations ( al-jabr , meaning "restoration", referring to adding
1365-554: Is a work consisting of approximately 37 chapters on calendrical and astronomical calculations and 116 tables with calendrical, astronomical and astrological data, as well as a table of sine values. This is the first of many Arabic Zijes based on the Indian astronomical methods known as the sindhind . The word Sindhind is a corruption of the Sanskrit Siddhānta , which is the usual designation of an astronomical textbook. In fact,
1456-550: Is generally referred to by its 1857 title Algoritmi de Numero Indorum . It is attributed to the Adelard of Bath , who had translated the astronomical tables in 1126. It is perhaps the closest to Al-Khwarizmi's own writings. Al-Khwarizmi's work on arithmetic was responsible for introducing the Arabic numerals , based on the Hindu–Arabic numeral system developed in Indian mathematics , to
1547-512: Is generally thought to have come from this region. Of Persian stock, his name means 'from Khwarazm', a region that was part of Greater Iran , and is now part of Turkmenistan and Uzbekistan . Al-Tabari gives his name as Muḥammad ibn Musá al-Khwārizmī al- Majūsī al-Quṭrubbullī ( محمد بن موسى الخوارزميّ المجوسـيّ القطربّـليّ ). The epithet al-Qutrubbulli could indicate he might instead have come from Qutrubbul (Qatrabbul), near Baghdad. However, Roshdi Rashed denies this: There
1638-457: Is important to note that this term was introduced and propagated by Europeans, and there is a belief that it has inaccurately misquoted, misconstrued, and distorted the sound of "y" to "dj" or "j" in the names of various clans, tribes, communities, rural areas, organisms, and numerous other entities throughout the entirety of Chad. On the other end of the spectrum, the nomenclature of Kamaya has signification, value, and historical origins rooted in
1729-735: Is lost, but a version by the Spanish astronomer Maslama al-Majriti ( c. 1000 ) has survived in a Latin translation, presumably by Adelard of Bath (26 January 1126). The four surviving manuscripts of the Latin translation are kept at the Bibliothèque publique (Chartres), the Bibliothèque Mazarine (Paris), the Biblioteca Nacional (Madrid) and the Bodleian Library (Oxford). Al-Khwārizmī's Zīj as-Sindhind contained tables for
1820-518: Is more entitled to be called "the father of algebra" than Diophantus because al-Khwarizmi is the first to teach algebra in an elementary form and for its own sake, Diophantus is primarily concerned with the theory of numbers. Victor J. Katz adds : The first true algebra text which is still extant is the work on al-jabr and al-muqabala by Mohammad ibn Musa al-Khwarizmi, written in Baghdad around 825. John J. O'Connor and Edmund F. Robertson wrote in
1911-424: Is no need to be an expert on the period or a philologist to see that al-Tabari's second citation should read "Muhammad ibn Mūsa al-Khwārizmī and al-Majūsi al-Qutrubbulli," and that there are two people (al-Khwārizmī and al-Majūsi al-Qutrubbulli) between whom the letter wa [Arabic ' و ' for the conjunction ' and '] has been omitted in an early copy. This would not be worth mentioning if a series of errors concerning
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#17330848190562002-456: Is quite unlikely that al-Khwarizmi knew of the work of Diophantus, but he must have been familiar with at least the astronomical and computational portions of Brahmagupta; yet neither al-Khwarizmi nor other Arabic scholars made use of syncopation or of negative numbers. Nevertheless, the Al-jabr comes closer to the elementary algebra of today than the works of either Diophantus or Brahmagupta, because
2093-607: Is settled directly between the families of the victim and the murderer. Toubou honour requires that someone from the victim's family try to kill the murderer or a relative; such efforts eventually end with negotiations to settle the matter. Reconciliation follows the payment of the Goroga (Islamic tenet of Diyya ), or blood money . Among the Tumagra clan of the Teda people in the Tibesti region, there
2184-584: Is true that in two respects the work of al-Khowarizmi represented a retrogression from that of Diophantus . First, it is on a far more elementary level than that found in the Diophantine problems and, second, the algebra of al-Khowarizmi is thoroughly rhetorical, with none of the syncopation found in the Greek Arithmetica or in Brahmagupta's work. Even numbers were written out in words rather than symbols! It
2275-470: Is worth noting that these terms lack inherent significance. The solitary form of the female term, "Kamadjedo" or "Kamadjero", might be seen as implausible and without coherence, whilst the plural form of the female term, "Kamadjeda", has an exceptionally peculiar and irrational quality. These terms are devoid of any discernible significance. The mispronunciation in question may be attributed to the challenges faced by French colonists while attempting to articulate
2366-664: The MacTutor History of Mathematics Archive : Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of al-Khwarizmi, namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry. Algebra was a unifying theory which allowed rational numbers , irrational numbers , geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics
2457-487: The Babylonian tablets , but also from Diophantus ' Arithmetica . It no longer concerns a series of problems to be solved , but an exposition which starts with primitive terms in which the combinations must give all possible prototypes for equations, which henceforward explicitly constitute the true object of study. On the other hand, the idea of an equation for its own sake appears from the beginning and, one could say, in
2548-643: The Bahr el Gazel in the south and also the Tibesti mountains and the neighbouring countries. There is a diaspora community of several thousand Daza living in Omdurman , Sudan and a couple of thousand working in Jeddah , Saudi Arabia . The ancient history of the Toubou people is unclear. They may be related to the 'Ethiopians' mentioned by Herodotus in 430 BCE, as a people being hunted by
2639-622: The Garamantes , but this is speculative, as Jean Chapelle argues. Furthermore, scholars such as Laurence P. Kirwan stress that the Garamantes and the Toubou seem to occupy the same lands. Which spans from the Fezzan (Phazania) as far south as Nubia. Further evidence is given by Harold MacMichael states that the Bayuda desert was still known as the desert of Goran; a name as MacMichael has shown, connected with
2730-543: The House of Wisdom in Baghdad , the contemporary capital city of the Abbasid Caliphate . His popularizing treatise on algebra , compiled between 813–833 as Al-Jabr ( The Compendious Book on Calculation by Completion and Balancing ), presented the first systematic solution of linear and quadratic equations . One of his achievements in algebra was his demonstration of how to solve quadratic equations by completing
2821-705: The Kanembou , Yedina , Arab, Kouri and Danawa. Marriage between a member of the Azza and a member from a different strata of the Toubou people has been culturally unacceptable. The Azza are Dazaga-speaking people who sprang from the Dazagara. The majority of Teda speak and understand Dazaga, however, the Dazagada do not always clearly grasp Tedaga. Dazaga is the most commonly used language in BET by all its inhabitants. The lowest social strata were
Toubou people - Misplaced Pages Continue
2912-618: The Saharawi , and 76.0% for the Libyan. North African samples were closer to Eurasian populations than to Sub-Saharan populations, implying that the Sahara Desert might have represented a major barrier within Africa. In contrast, the three Khoisan groups presented significantly small proportions of a Eurasian component (3.83–4.11%). Toubou life centers on raising and herding their livestock , or on farming
3003-489: The name of method used for computations, and survives in the term " algorithm ". It gradually replaced the previous abacus-based methods used in Europe. Four Latin texts providing adaptions of Al-Khwarizmi's methods have survived, even though none of them is believed to be a literal translation: Dixit Algorizmi ('Thus spake Al-Khwarizmi') is the starting phrase of a manuscript in the University of Cambridge library, which
3094-513: The trigonometric functions of sines and cosine. A related treatise on spherical trigonometry is attributed to him. Al-Khwārizmī produced accurate sine and cosine tables, and the first table of tangents. Al-Khwārizmī's third major work is his Kitāb Ṣūrat al-Arḍ ( Arabic : كتاب صورة الأرض , "Book of the Description of the Earth"), also known as his Geography , which was finished in 833. It
3185-570: The "black nomads of the Sahara". They are distributed across a large area in the central Sahara, as well as the north-central Sahel . They are particularly found north of the Tibesti mountains , which in Old Tebu means "Rocky Mountains". The first syllable "Tu" refers to the Tibesti mountains, as known by the natives (Tuda), and the second syllable "bo" refers to blood in the Kanembou language; thus, people from
3276-411: The "thing" ( شيء shayʾ ) or "root", is given by the steps, Let the roots of the equation be x = p and x = q . Then p + q 2 = 50 1 2 {\displaystyle {\tfrac {p+q}{2}}=50{\tfrac {1}{2}}} , p q = 100 {\displaystyle pq=100} and So a root is given by Several authors have published texts under
3367-577: The Daza and Teda regions into corresponding territorial units called cantons and appointing chiefs to administer them and in 1936, the French created cantons, and appointed al-haj Kelleï Chahami from the Kamaya canton in Borkou region's Faya city the first highest official chief who executed great noble missions. Toubou legal customs are generally based on Islamic law, that allows restitution and revenge. Murder, for example,
3458-494: The Daza of Kanem, Bahr el-Ghazal, and certain clans of Borkou and Ennedi marry close cousins since it is not prohibited in the Quran, they also doubt the origins of individuals and misalliance. A man may marry and have multiple wives according to Islamic tenets, however, this practice is only somewhat prevalent in Toubou society. The ownership of land, animals, and resources takes several forms. Within an oasis or settled zone belonging to
3549-571: The Daza, or Gouran , include the Alala, Altafa, Anakaza , Ankorda, Ayya, Sharara, Sharfada, Shuna, Daza, Djagada, Dogorda, Donza, Gadwa, Gaeda, Howda, Kamaya, Kamsoulla, Kara, Ketcherda, Kokorda, Maghya, Medelea, Mourdiya, Nara, Salma, Tchiroua, Tchoraga, Wandala, Wandja, Warba, Warda, Yira and many more. The Daza cover the northern regions of Chad such as the Bourkou , the Ennedi Plateau , the northern Kanem,
3640-730: The Dazagra, replaced Goukouni of the Teda in 1982, and eventually lost power to the Zaghawa Idriss Déby after 8 years. The Toubou minority in Libya suffered what has been described as "massive discrimination" both under the leadership of Muammar Gaddafi as well as after the Libyan civil war . In a report released by the UNHCR , the Society for Threatened Peoples (STP) reported "massive discrimination" against
3731-433: The Kamaya canton. All of these individuals' concerns were conveyed to the colonizers via the Kamaya canton. The descendants of freed slaves who located in the Tibesti region for many years approach their former masters inquiring about their past. In response, the Teda deliberately allege their identity as "Kamadja" to their freed captives, who question about the significance of this designation. The Teda respond that they know
Toubou people - Misplaced Pages Continue
3822-469: The Kamaya's history was fabricated by the French colonists and Teda took advantage of the situation by misleading their freed slave descendants and the general public. The linguistic analysis reveals that the term "Kamadja" does not exist in either the Dazaga or Tedaga languages. The tone terms, namely "Kamadja" for the male plural and as general and "Kamadji" for the male singular, are used as generic phrases. It
3913-529: The Kura'án of today. This reaffirms that the Kura'án (Goran) of today, occupy much of the same territory as the Garamantes once did. In Islamic literature , the earliest mention as the Toubou people is perhaps that along with the Zaghawa people in an 8th-century text by Arabic scholar Ibn Qutaybah . The 9th century al-Khwarizmi mentions the Daza people (southern Teda). During the expansive era of Trans-Saharan trade ,
4004-585: The Middle East. Another major book was Kitab surat al-ard ("The Image of the Earth"; translated as Geography), presenting the coordinates of places based on those in the Geography of Ptolemy , but with improved values for the Mediterranean Sea , Asia, and Africa. He wrote on mechanical devices like the astrolabe and sundial . He assisted a project to determine the circumference of the Earth and in making
4095-612: The Salvation of Libya (TFSL) staged an uprising in November 2008 which lasted for five days and claimed 33 lives before being crushed by government security forces. Despite resistance and public condemnation, the Gaddafi regime continued its persecution of the Toubou minority in Libya. Beginning in November 2009, the government began a program of forced eviction and demolition of Toubou homes, rendering many Toubou homeless. Several dozens who protested
4186-555: The Teda (or Tuda, Téda, Toda, Tira) and the Daza (or Dazzaga, Dazagara, Dazagada). They are believed to share a common origin and speak the Tebu languages , which are from the Saharan branch of the Nilo-Saharan language family. Tebu is divided further into two closely related languages, called Tedaga (Téda Toubou) and Dazaga (Daza Toubou). Of the two groups, the Daza, found to the south of
4277-553: The Teda, are more numerous. The Toubou people are also referred to as the Tabu, Tebu, Tebou, Tibu, 'Tibbu, Toda, Todga, Todaga, Tubu, Tuda, Tudaga, or Gorane people. The Daza are sometimes referred to as Gouran (or Gorane, Goran, Gourane), an Arabian exonym. Many of Chad's leaders have been Toubou (Gouran), including presidents Goukouni Oueddei and Hissène Habré . The Toubou people have historically lived in northern Chad, northeastern Niger, and southern Libya. They have sometimes been called
4368-512: The Tibesti region are referred to as Tubou." Their name is derived from this. The Teda are found primarily in the Sahara regions around the borders of southeast Libya, northeast Niger and northern Chad . They consider themselves a warrior people. The Daza live towards the Sahel region and are spread over much of north-central Chad. The Daza consist of numerous clans. Some major tribes, clans, societies of
4459-700: The Toubou inhabited lands which were frequently used by merchant caravans, specifically along the Kufra oasis routes. It is unknown if the Toubou enganged with the caravans. According to a study published in The American Journal of Human Genetics (Haber et al. 2016) that examined Y-DNA haplogroups from samples obtained from 75 Toubou men, haplogroups associated with paternal Eurasian ancestry were present at rates of 34% for R1b (R1b-V88), 31% for T1a , and 1% for J1 . The North African associated haplogroup E-M78 were present at rates of 28%, while E-M81 appeared at
4550-454: The Toubou minority, which resides in the southeastern corner of the country around the oasis town of Kufra . In December 2007, the Gaddafi government stripped Toubou Libyans of their citizenship, claiming that they were not Libyans, but rather Chadians. In addition, local authorities denied Toubou people access to education and healthcare. In response, an armed group called the Toubou Front for
4641-557: The Toubou to the National Liberation Front of Chad (FROLINAT). Moral authority became military authority shortly thereafter when his son, Goukouni Oueddei , became one of the leaders of the Second Liberation Army of FROLINAT. Goukouni was to become a national figure; he played an important role in the battles of N'Djamena in 1979 and 1980 and served as head of state for a time. Another northerner, Hissène Habré of
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#17330848190564732-471: The Toubou, much like the Hadahid caste in southeastern Chad among the Zaghawa people . According to Paul Lovejoy – a professor of African History, the 19th century records show that these segregated Toubou castes followed the same customs and traditions as the rest of the Toubou, but they were independent in their politics and beliefs, much like the artisan castes found in many ethnic groups of western Chad such as
4823-557: The Toubou. The derde , Oueddei Kichidemi , recognized but little respected up to that time, protested the excesses, went into exile in Libya , and, with the support of Toubou students at the Islamic University of Bayda , became a symbol of opposition to the Chadian government. This role enhanced the position of the Derde from the Tumagra tribe of Toubou. After 1967 the derde hoped to rally
4914-516: The Western world. The term "algorithm" is derived from the algorism , the technique of performing arithmetic with Hindu-Arabic numerals developed by al-Khwārizmī. Both "algorithm" and "algorism" are derived from the Latinized forms of al-Khwārizmī's name, Algoritmi and Algorismi , respectively. Al-Khwārizmī's Zīj as-Sindhind ( Arabic : زيج السند هند , " astronomical tables of Siddhanta " )
5005-450: The Yin oasis as Jin, the Yarda oasis as Jarda, the Faya oasis as Faja, the Bidayet community as Bidajet, and the Goli Yeskou as Goli Jeskou (Black snake), many more other carelessness. These oversights and misinterpretations are notable in the exploration literatures. The term "Kamadja" has become somewhat entrenched a certain level of permanence but is losing its relevance of the Kamaya ethnic group due to its lack of self-identification and it
5096-415: The book is not concerned with difficult problems in indeterminant analysis but with a straight forward and elementary exposition of the solution of equations, especially that of second degree. The Arabs in general loved a good clear argument from premise to conclusion, as well as systematic organization – respects in which neither Diophantus nor the Hindus excelled. Al-Khwārizmī's second most influential work
5187-420: The coefficient of the square and using the two operations al-jabr ( Arabic : الجبر "restoring" or "completion") and al-muqābala ("balancing"). Al-jabr is the process of removing negative units, roots and squares from the equation by adding the same quantity to each side. For example, x = 40 x − 4 x is reduced to 5 x = 40 x . Al-muqābala is the process of bringing quantities of
5278-466: The destruction were arrested, and families who refused to leave their homes were beaten. In the Libyan Civil War , Toubou tribespeople in Libya sided with the rebel anti-Gaddafi forces and participated in the Fezzan campaign against forces loyal to Muammar Gaddafi , briefly capturing the town of Qatrun and claiming to capture Murzuk for the rebel movement a month later. In March 2012, bloody clashes broke out between Toubou and Arab tribesmen in
5369-418: The eldest of the three Banū Mūsā brothers . Al-Khwārizmī's contributions to mathematics, geography, astronomy, and cartography established the basis for innovation in algebra and trigonometry . His systematic approach to solving linear and quadratic equations led to algebra , a word derived from the title of his book on the subject, Al-Jabr . On the Calculation with Hindu Numerals, written about 820,
5460-465: The emancipation of all slaves and suppressed the use of captives in the Borkou region, while slaves from the contiguous regions, such as Tibesti and Ennedi, uncovered the liberation center situated in Borkou. Several of these slaves escaped and sought refuge in Borkou under the protection of the Kamaya canton and they were subsequently emancipated by the esteemed chief, Al-Haj Kellei Chahami, who granted them land that enabled them to settle, and this district
5551-409: The expression "Kama-dro-yédé". This expression pertains to the inhabitant of the Faya oasis in the accent of Kanem Dazaga, where "Kama" describes a valley, "dro" implies interior, and "yédé" denotes an occupant. In this context, "yé" indicates the act of dwelling, while "dé" stands as the indicator of a singular form. Thus, the expression "Kama-dro-yédé" may be interpreted as "the individual who dwells in
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#17330848190565642-429: The freed captives' people led them to assume this title. However, once the descendants of freed slaves embrace this belief and depart, the Teda proceed to use insulting terms such as "blind," "stupid," and "unintelligent," as well as other terms that are demeaning. The term "Kamadja" is a mispronunciation of Kamaya, and the Teda are grudgingly attempting to sabotage the Toubou Gorane Kamaya clans' federation reputation since
5733-419: The last fraction of the Kamaya canton thus was established. Not only the captives were attached to the Kamaya canton, but along with all foreigners who resided in Faya, including Fezzanais (Libyan refugees who fled Italian brutality in 1929 before the Italian colonialists' progression into southern Libya, the Fezzan region), Ouadaens from the Chad's Waddai region, prostitutes, blacksmiths etc, were also attached to
5824-446: The longitudes and latitudes of cities and localities. He further produced a set of astronomical tables and wrote about calendric works, as well as the astrolabe and the sundial . Al-Khwarizmi made important contributions to trigonometry , producing accurate sine and cosine tables and the first table of tangents . Few details of al-Khwārizmī's life are known with certainty. Ibn al-Nadim gives his birthplace as Khwarazm , and he
5915-535: The mean motions in the tables of al-Khwarizmi are derived from those in the "corrected Brahmasiddhanta" ( Brahmasphutasiddhanta ) of Brahmagupta . The work contains tables for the movements of the sun , the moon and the five planets known at the time. This work marked the turning point in Islamic astronomy . Hitherto, Muslim astronomers had adopted a primarily research approach to the field, translating works of others and learning already discovered knowledge. The original Arabic version (written c. 820 )
6006-437: The moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts. In modern notation this process, with x
6097-408: The name of Kitāb al-jabr wal-muqābala , including Abū Ḥanīfa Dīnawarī , Abū Kāmil , Abū Muḥammad al-'Adlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk , Sind ibn 'Alī , Sahl ibn Bišr , and Sharaf al-Dīn al-Ṭūsī . Solomon Gandz has described Al-Khwarizmi as the father of Algebra: Al-Khwarizmi's algebra is regarded as the foundation and cornerstone of the sciences. In a sense, al-Khwarizmi
6188-458: The natives of the valley that is situated in the palm grove of Faya oasis. In Dazaga, the community is called "Kama-yanga" which means the Kamaya canton and together with the suffix "ga" implies the dialect spoken by the Dazagada. In the linguistic context under consideration, the citizens of the aforementioned canton are referred to as "Kamay" in the singular form for males, while the singular form for females may be either "Kamaydo" or "Kamayro", with
6279-407: The one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less a thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots;
6370-433: The parental clan, it provides ties. The third factor is protective relationships at the primary residence. Despite shared linguistic heritage, few institutions among the Toubou generate a broader sense of identity than the clan. Regional divisions do exist, however. During the colonial period (and since independence in 1960), Chadian administrations have conferred legality and legitimacy on these regional groupings by dividing
6461-559: The personality of al-Khwārizmī, occasionally even the origins of his knowledge, had not been made. Recently, G.J. Toomer ... with naive confidence constructed an entire fantasy on the error which cannot be denied the merit of amusing the reader. On the other hand, David A. King affirms his nisba to Qutrubul, noting that he was called al-Khwārizmī al-Qutrubbulli because he was born just outside of Baghdad. Regarding al-Khwārizmī's religion, Toomer writes: Another epithet given to him by al-Ṭabarī, "al-Majūsī," would seem to indicate that he
6552-514: The phoneme represented by the letter "y" in the alphabet. As a replacement, they frequently resorted to apply the phonetic sounds of "dj" or "j". Moreover, the explorers who visited Borkou before the French colonization made contributions to the misinterpretation of various expressions, as evidenced by Gustav Nichtigal's works. These inaccuracies include referring to the Yira clan as Jira, the Yenoa clans as Jenoa,
6643-544: The political class of Chad are drawn from Dazzaga. During the First Chadian Civil War (1966–1979), the derde came to occupy a more important position. In 1965 the Chadian government assumed direct authority over the Tibesti Mountains, sending a military garrison and administrators to Bardaï , the capital of Tibesti Sub-prefecture. Within a year, abuses of authority had roused considerable opposition among
6734-531: The same type to the same side of the equation. For example, x + 14 = x + 5 is reduced to x + 9 = x . The above discussion uses modern mathematical notation for the types of problems that the book discusses. However, in al-Khwārizmī's day, most of this notation had not yet been invented , so he had to use ordinary text to present problems and their solutions. For example, for one problem he writes, (from an 1831 translation) If some one says: "You divide ten into two parts: multiply
6825-410: The scattered oases where they cultivate dates , grain and legumes . Their herds include dromedaries , goats, cattle, donkeys and sheep. Livestock is a major part of their wealth, and trade. Livestock is also used as a part of dowry payment during marriage, either as one where the groom's family agrees to pay to the bride's family in exchange for the bride, or it is given by the bride's kin to supply
6916-431: The second degree, and discussed the fundamental method of "reduction" and "balancing", referring to the transposition of terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation. Al-Khwārizmī's method of solving linear and quadratic equations worked by first reducing the equation to one of six standard forms (where b and c are positive integers) by dividing out
7007-551: The short-hand title of his aforementioned treatise ( الجبر Al-Jabr , transl. "completion" or "rejoining" ). His name gave rise to the English terms algorism and algorithm ; the Spanish, Italian, and Portuguese terms algoritmo ; and the Spanish term guarismo and Portuguese term algarismo , both meaning ' digit '. In the 12th century, Latin translations of al-Khwarizmi's textbook on Indian arithmetic ( Algorithmo de Numero Indorum ), which codified
7098-464: The slaves ( Agara ). Slaves entered the Toubou Teda and Daza societies from raids and warfare on other ethnic groups in lands to their south. All slaves were the property of their masters, their caste was endogamous, and their status was inherited by birth. In the year 1953, Al-Haj Kellei Chahami, a highly esteemed privileged chieftain of the Kamaya canton, an agreement with the French colonizers decreed
7189-475: The southern city of Sabha, Libya . In response, Issa Abdel Majid Mansour, the leader of the Toubou tribes in Libya threatened a separatist bid, decrying what he saw as "ethnic cleansing" against Toubou and declaring "We announce the reactivation of the Toubou Front for the Salvation of Libya to protect the Toubou people from ethnic cleansing." The TFSL was the opposition group active in the unrest of 2007–2008 that
7280-460: The square , for which he provided geometric justifications. Because al-Khwarizmi was the first person to treat algebra as an independent discipline and introduced the methods of "reduction" and "balancing" (the transposition of subtracted terms to the other side of an equation, that is, the cancellation of like terms on opposite sides of the equation), he has been described as the father or founder of algebra. The English term algebra comes from
7371-452: The translation of Greek and Sanskrit scientific manuscripts. He was also a historian who is cited by the likes of al-Tabari and Ibn Abi Tahir . During the reign of al-Wathiq , he is said to have been involved in the first of two embassies to the Khazars . Douglas Morton Dunlop suggests that Muḥammad ibn Mūsā al-Khwārizmī might have been the same person as Muḥammad ibn Mūsā ibn Shākir,
7462-518: The two Northeastern Sub-Saharan samples, this Western Eurasian ancestry in their Toubou sample was 31.4%, and it was 14.9% for the East African Bantu. The Toubou also maintained similar genetic distance to other Sub-Saharan samples, but was also genetically close to North African and non-African samples. The Eurasian component in the North African individuals was present at high rates of 84.9% for
7553-468: The valley" of the palm grove situated in the Faya oasis. The ancient designation for the clans of Kamaya was "Kamayada", with "ya" denoting habitation and "da" indicating plurality. Conversely, "Kamayédé" is the singular and authentic noun used to refer to an occupant of the Faya palm grove oasis valley, since the suffix "dé" is appended to the solitary form of "yé". Therefore, the designation "Kamaya" refers to
7644-536: The various Indian numerals , introduced the decimal -based positional number system to the Western world . Likewise, Al-Jabr , translated into Latin by the English scholar Robert of Chester in 1145, was used until the 16th century as the principal mathematical textbook of European universities . Al-Khwarizmi revised Geography , the 2nd-century Greek-language treatise by the Roman polymath Claudius Ptolemy , listing
7735-470: The vocalization of the suffix varying across specific regions and individuals' accents, ranging from "do" to "ro" which is only the "d" and "r". The plural form of the female noun may be expressed as either "Kamayda" or "Kamayra", whereas the plural form for males and as a general reference is "Kamaya". The Teda, in particular, forbids marriage between cousins, up to 9 generations unrelated, a tradition prevalent with many Muslim ethnic groups in Africa, however,
7826-405: The young couple with economic resources in order to start a family. In a few places, the Toubou also mine salt and natron , a salt-like substance which is essential in nearly all components of Toubou life from medicine, as a mixture in chewing tobacco, preservation, tanning, soap production, textiles and for livestock. Literacy rates among the Toubou are quite low. Many Toubou people still follow
7917-513: Was "ruthlessly persecuted" by the Gaddafi government. Tebu languages Tebu is a small family of two Saharan languages , consisting of Daza and Teda . It is spoken by the two groups of Toubou people , the Daza and Teda . Tebu is predominantly spoken in Chad and in southern Libya by around 580,000 people. Daza and Teda have an estimated 537,000 and 42,500 speakers, respectively. This Nilo-Saharan languages –related article
8008-430: Was an adherent of the old Zoroastrian religion . This would still have been possible at that time for a man of Iranian origin, but the pious preface to al-Khwārizmī's Algebra shows that he was an orthodox Muslim , so al-Ṭabarī's epithet could mean no more than that his forebears, and perhaps he in his youth, had been Zoroastrians. Ibn al-Nadīm 's Al-Fihrist includes a short biography on al-Khwārizmī together with
8099-515: Was formerly referred to as "Ni-Agaranga" in Dazaga, which literally translates to "country of slaves" in the Faya-Largeau city. However, the Borkou municipality opted to rechristen it as "Quartier Huit" (Eighth Quarter) as a euphemistic expression. After the abolition of slavery in 1953, the chief Kellei Chahami admitted the descendants of former captives to the canton, where they were recognized as full members and can move around freely and in this way,
8190-486: Was on the subject of arithmetic, which survived in Latin translations but is lost in the original Arabic. His writings include the text kitāb al-ḥisāb al-hindī ('Book of Indian computation' ), and perhaps a more elementary text, kitab al-jam' wa'l-tafriq al-ḥisāb al-hindī ('Addition and subtraction in Indian arithmetic'). These texts described algorithms on decimal numbers ( Hindu–Arabic numerals ) that could be carried out on
8281-547: Was principally responsible for spreading the Hindu–Arabic numeral system throughout the Middle East and Europe. When the work was translated into Latin in the 12th century as Algoritmi de numero Indorum (Al-Khwarizmi on the Hindu art of reckoning), the term "algorithm" was introduced to the Western world. Some of his work was based on Persian and Babylonian astronomy, Indian numbers , and Greek mathematics . Al-Khwārizmī systematized and corrected Ptolemy 's data for Africa and
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