106-505: Al-Jabr ( Arabic : الجبر ), also known as 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-Muqābalah ; or Latin : Liber Algebræ et Almucabola ), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath Al-Khwarizmi . It
212-470: A + b ) 2 = a 2 + 2 a b + b 2 . {\displaystyle (a+b)^{2}=a^{2}+2ab+b^{2}.} Furthermore, there are also geometric solutions given to many equations. For instance, proposition 6 of Book II gives the solution to the quadratic equation a x + x 2 = b 2 , {\displaystyle ax+x^{2}=b^{2},} and proposition 11 of Book II gives
318-575: A collection of related dialects that constitute the precursor of Arabic, first emerged during the Iron Age . Previously, the earliest attestation of Old Arabic was thought to be a single 1st century CE inscription in Sabaic script at Qaryat al-Faw , in southern present-day Saudi Arabia. However, this inscription does not participate in several of the key innovations of the Arabic language group, such as
424-435: A corpus of poetic texts, in addition to Qur'an usage and Bedouin informants whom he considered to be reliable speakers of the ʿarabiyya . Arabic spread with the spread of Islam . Following the early Muslim conquests , Arabic gained vocabulary from Middle Persian and Turkish . In the early Abbasid period , many Classical Greek terms entered Arabic through translations carried out at Baghdad's House of Wisdom . By
530-436: A deficient quantity from one side of the equation to the other side. In an al-Khwarizmi's example (in modern notation), " x = 40 x − 4 x " is transformed by al-Jabr into "5 x = 40 x ". Repeated application of this rule eliminates negative quantities from calculations. Al-Muqābala ( المقابله , "balancing" or "corresponding") means subtraction of the same positive quantity from both sides: " x + 5 = 40 x + 4 x "
636-1081: A dialect of Arabic and written in the Latin alphabet . The Balkan languages, including Albanian, Greek , Serbo-Croatian, and Bulgarian , have also acquired many words of Arabic origin, mainly through direct contact with Ottoman Turkish . Arabic has influenced languages across the globe throughout its history, especially languages where Islam is the predominant religion and in countries that were conquered by Muslims. The most markedly influenced languages are Persian , Turkish , Hindustani ( Hindi and Urdu ), Kashmiri , Kurdish , Bosnian , Kazakh , Bengali , Malay ( Indonesian and Malaysian ), Maldivian , Pashto , Punjabi , Albanian , Armenian , Azerbaijani , Sicilian, Spanish, Greek, Bulgarian, Tagalog , Sindhi , Odia , Hebrew and African languages such as Hausa , Amharic , Tigrinya , Somali , Tamazight , and Swahili . Conversely, Arabic has borrowed some words (mostly nouns) from other languages, including its sister-language Aramaic, Persian, Greek, and Latin and to
742-487: A lesser extent and more recently from Turkish, English, French, and Italian. Arabic is spoken by as many as 380 million speakers, both native and non-native, in the Arab world, making it the fifth most spoken language in the world, and the fourth most used language on the internet in terms of users. It also serves as the liturgical language of more than 2 billion Muslims . In 2011, Bloomberg Businessweek ranked Arabic
848-558: A matrix) and performing column reducing operations on the magic square. The earliest known magic squares of order greater than three are attributed to Yang Hui (fl. c. 1261 – 1275), who worked with magic squares of order as high as ten. Ssy-yüan yü-chien 《四元玉鑒》, or Precious Mirror of the Four Elements , was written by Chu Shih-chieh in 1303 and it marks the peak in the development of Chinese algebra. The four elements , called heaven, earth, man and matter, represented
954-690: A millennium before the modern period . Early lexicographers ( لُغَوِيُّون lughawiyyūn ) sought to explain words in the Quran that were unfamiliar or had a particular contextual meaning, and to identify words of non-Arabic origin that appear in the Quran. They gathered shawāhid ( شَوَاهِد 'instances of attested usage') from poetry and the speech of the Arabs—particularly the Bedouin ʾaʿrāb [ ar ] ( أَعْراب ) who were perceived to speak
1060-401: A parabola, the equation y 2 = l x {\displaystyle y^{2}=lx} holds, where l {\displaystyle l} is a constant called the latus rectum , although he was not aware of the fact that any equation in two unknowns determines a curve. He apparently derived these properties of conic sections and others as well. Using this information it
1166-507: A process that they invented, known as "the application of areas". "The application of areas" is only a part of geometric algebra and it is thoroughly covered in Euclid 's Elements . An example of geometric algebra would be solving the linear equation a x = b c . {\displaystyle ax=bc.} The ancient Greeks would solve this equation by looking at it as an equality of areas rather than as an equality between
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#17327653672801272-631: A rectangular hyperbola and a parabola. This was related to a problem in Archimedes ' On the Sphere and Cylinder . Conic sections would be studied and used for thousands of years by Greek, and later Islamic and European, mathematicians. In particular Apollonius of Perga 's famous Conics deals with conic sections, among other topics. Chinese mathematics dates to at least 300 BC with the Zhoubi Suanjing , generally considered to be one of
1378-594: A result, many European languages have borrowed words from it. Arabic influence, mainly in vocabulary, is seen in European languages (mainly Spanish and to a lesser extent Portuguese , Catalan , and Sicilian ) owing to the proximity of Europe and the long-lasting Arabic cultural and linguistic presence, mainly in Southern Iberia, during the Al-Andalus era. Maltese is a Semitic language developed from
1484-462: A script derived from ASA attest to a language known as Hasaitic . On the northwestern frontier of Arabia, various languages known to scholars as Thamudic B , Thamudic D, Safaitic , and Hismaic are attested. The last two share important isoglosses with later forms of Arabic, leading scholars to theorize that Safaitic and Hismaic are early forms of Arabic and that they should be considered Old Arabic . Linguists generally believe that "Old Arabic",
1590-470: A single language, despite mutual incomprehensibility among differing spoken versions. From a linguistic standpoint, it is often said that the various spoken varieties of Arabic differ among each other collectively about as much as the Romance languages . This is an apt comparison in a number of ways. The period of divergence from a single spoken form is similar—perhaps 1500 years for Arabic, 2000 years for
1696-633: A solution to a x + x 2 = a 2 . {\displaystyle ax+x^{2}=a^{2}.} Data is a work written by Euclid for use at the schools of Alexandria and it was meant to be used as a companion volume to the first six books of the Elements . The book contains some fifteen definitions and ninety-five statements, of which there are about two dozen statements that serve as algebraic rules or formulas. Some of these statements are geometric equivalents to solutions of quadratic equations. For instance, Data contains
1802-877: A table of Pythagorean triples and represents some of the most advanced mathematics prior to Greek mathematics. Babylonian algebra was much more advanced than the Egyptian algebra of the time; whereas the Egyptians were mainly concerned with linear equations the Babylonians were more concerned with quadratic and cubic equations . The Babylonians had developed flexible algebraic operations with which they were able to add equals to equals and multiply both sides of an equation by like quantities so as to eliminate fractions and factors. They were familiar with many simple forms of factoring , three-term quadratic equations with positive roots, and many cubic equations, although it
1908-507: A type of Arabic. Cypriot Arabic is recognized as a minority language in Cyprus. The sociolinguistic situation of Arabic in modern times provides a prime example of the linguistic phenomenon of diglossia , which is the normal use of two separate varieties of the same language, usually in different social situations. Tawleed is the process of giving a new shade of meaning to an old classical word. For example, al-hatif lexicographically means
2014-507: A variety of regional vernacular Arabic dialects , which are not necessarily mutually intelligible. Classical Arabic is the language found in the Quran , used from the period of Pre-Islamic Arabia to that of the Abbasid Caliphate . Classical Arabic is prescriptive, according to the syntactic and grammatical norms laid down by classical grammarians (such as Sibawayh ) and the vocabulary defined in classical dictionaries (such as
2120-440: 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. The book was a compilation and extension of known rules for solving quadratic equations and for some other problems, and considered to be the foundation of algebra, establishing it as an independent discipline. The word algebra
2226-476: A wider audience." In the wake of the industrial revolution and European hegemony and colonialism , pioneering Arabic presses, such as the Amiri Press established by Muhammad Ali (1819), dramatically changed the diffusion and consumption of Arabic literature and publications. Rifa'a al-Tahtawi proposed the establishment of Madrasat al-Alsun in 1836 and led a translation campaign that highlighted
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#17327653672802332-737: Is a Central Semitic language of the Afroasiatic language family spoken primarily in the Arab world . The ISO assigns language codes to 32 varieties of Arabic , including its standard form of Literary Arabic, known as Modern Standard Arabic , which is derived from Classical Arabic . This distinction exists primarily among Western linguists; Arabic speakers themselves generally do not distinguish between Modern Standard Arabic and Classical Arabic, but rather refer to both as al-ʿarabiyyatu l-fuṣḥā ( اَلعَرَبِيَّةُ ٱلْفُصْحَىٰ "the eloquent Arabic") or simply al-fuṣḥā ( اَلْفُصْحَىٰ ). Arabic
2438-472: Is a collection of 6 1 4 {\displaystyle 6{\tfrac {1}{4}}} object of one kind with 25 object of second kind which lack 9 objects of third kind with no operation present. Similar to medieval Arabic algebra Diophantus uses three stages to solve a problem by Algebra: 1) An unknown is named and an equation is set up 2) An equation is simplified to a standard form( al-jabr and al-muqābala in arabic) 3) Simplified equation
2544-590: Is a minimum level of comprehension between all Arabic dialects, this level can increase or decrease based on geographic proximity: for example, Levantine and Gulf speakers understand each other much better than they do speakers from the Maghreb. The issue of diglossia between spoken and written language is a complicating factor: A single written form, differing sharply from any of the spoken varieties learned natively, unites several sometimes divergent spoken forms. For political reasons, Arabs mostly assert that they all speak
2650-559: Is a sister language rather than their direct ancestor. Arabia had a wide variety of Semitic languages in antiquity. The term "Arab" was initially used to describe those living in the Arabian Peninsula , as perceived by geographers from ancient Greece . In the southwest, various Central Semitic languages both belonging to and outside the Ancient South Arabian family (e.g. Southern Thamudic) were spoken. It
2756-478: Is believed that the ancestors of the Modern South Arabian languages (non-Central Semitic languages) were spoken in southern Arabia at this time. To the north, in the oases of northern Hejaz , Dadanitic and Taymanitic held some prestige as inscriptional languages. In Najd and parts of western Arabia, a language known to scholars as Thamudic C is attested. In eastern Arabia, inscriptions in
2862-565: Is built of exponentiation, scalar multiplication, addition, and subtraction. The algebra of Diophantus, similar to medieval arabic algebra is an aggregation of objects of different types with no operations present For example, in Diophantus a polynomial "6 4 ′ inverse Powers, 25 Powers lacking 9 units", which in modern notation is 6 1 4 x − 1 + 25 x 2 − 9 {\displaystyle 6{\tfrac {1}{4}}x^{-1}+25x^{2}-9}
2968-408: Is credited with establishing the rules of Arabic prosody . Al-Jahiz (776–868) proposed to Al-Akhfash al-Akbar an overhaul of the grammar of Arabic, but it would not come to pass for two centuries. The standardization of Arabic reached completion around the end of the 8th century. The first comprehensive description of the ʿarabiyya "Arabic", Sībawayhi's al - Kitāb , is based first of all upon
3074-472: Is credited with standardizing Arabic grammar , or an-naḥw ( النَّحو "the way" ), and pioneering a system of diacritics to differentiate consonants ( نقط الإعجام nuqaṭu‿l-i'jām "pointing for non-Arabs") and indicate vocalization ( التشكيل at-tashkīl ). Al-Khalil ibn Ahmad al-Farahidi (718–786) compiled the first Arabic dictionary, Kitāb al-'Ayn ( كتاب العين "The Book of the Letter ع "), and
3180-400: Is derived from the name of one of the basic operations with equations described in this book, following its Latin translation by Robert of Chester . The book classifies quadratic equations to one of the six basic types and provides algebraic and geometric methods to solve the basic ones. Historian Carl Boyer notes the following regarding the lack of modern abstract notations in the book: ...
3286-611: Is found through the use of proportions. In some of the problems the author "checks" his solution, thereby writing one of the earliest known simple proofs. It is sometimes alleged that the Greeks had no algebra, but this is disputed. By the time of Plato , Greek mathematics had undergone a drastic change. The Greeks created a geometric algebra where terms were represented by sides of geometric objects, usually lines, that had letters associated with them, and with this new form of algebra they were able to find solutions to equations by using
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3392-530: Is not known if they were able to reduce the general cubic equation. Ancient Egyptian algebra dealt mainly with linear equations while the Babylonians found these equations too elementary, and developed mathematics to a higher level than the Egyptians. The Rhind Papyrus, also known as the Ahmes Papyrus, is an ancient Egyptian papyrus written c. 1650 BC by Ahmes, who transcribed it from an earlier work that he dated to between 2000 and 1800 BC. It
3498-574: Is not present in the spoken varieties, but deletes Classical words that sound obsolete in MSA. In addition, MSA has borrowed or coined many terms for concepts that did not exist in Quranic times, and MSA continues to evolve. Some words have been borrowed from other languages—notice that transliteration mainly indicates spelling and not real pronunciation (e.g., فِلْم film 'film' or ديمقراطية dīmuqrāṭiyyah 'democracy'). The current preference
3604-855: Is official in Mali and recognized as a minority language in Morocco, while the Senegalese government adopted the Latin script to write it. Maltese is official in (predominantly Catholic ) Malta and written with the Latin script . Linguists agree that it is a variety of spoken Arabic, descended from Siculo-Arabic , though it has experienced extensive changes as a result of sustained and intensive contact with Italo-Romance varieties, and more recently also with English. Due to "a mix of social, cultural, historical, political, and indeed linguistic factors", many Maltese people today consider their language Semitic but not
3710-406: Is referred to as "aha" or heap, is the unknown. The solutions were possibly, but not likely, arrived at by using the "method of false position", or regula falsi , where first a specific value is substituted into the left hand side of the equation, then the required arithmetic calculations are done, thirdly the result is compared to the right hand side of the equation, and finally the correct answer
3816-547: Is remembered for his great explanatory skills. The Elements is not, as is sometimes thought, a collection of all Greek mathematical knowledge to its date; rather, it is an elementary introduction to it. The geometric work of the Greeks, typified in Euclid's Elements , provided the framework for generalizing formulae beyond the solution of particular problems into more general systems of stating and solving equations. Book II of
3922-572: Is the third most widespread official language after English and French, one of six official languages of the United Nations , and the liturgical language of Islam . Arabic is widely taught in schools and universities around the world and is used to varying degrees in workplaces, governments and the media. During the Middle Ages , Arabic was a major vehicle of culture and learning, especially in science, mathematics and philosophy. As
4028-531: Is the most extensive ancient Egyptian mathematical document known to historians. The Rhind Papyrus contains problems where linear equations of the form x + a x = b {\displaystyle x+ax=b} and x + a x + b x = c {\displaystyle x+ax+bx=c} are solved, where a , b , {\displaystyle a,b,} and c {\displaystyle c} are known and x , {\displaystyle x,} which
4134-590: Is the variety used in most current, printed Arabic publications, spoken by some of the Arabic media across North Africa and the Middle East, and understood by most educated Arabic speakers. "Literary Arabic" and "Standard Arabic" ( فُصْحَى fuṣḥá ) are less strictly defined terms that may refer to Modern Standard Arabic or Classical Arabic. Some of the differences between Classical Arabic (CA) and Modern Standard Arabic (MSA) are as follows: MSA uses much Classical vocabulary (e.g., dhahaba 'to go') that
4240-413: Is to avoid direct borrowings, preferring to either use loan translations (e.g., فرع farʻ 'branch', also used for the branch of a company or organization; جناح janāḥ 'wing', is also used for the wing of an airplane, building, air force, etc.), or to coin new words using forms within existing roots ( استماتة istimātah ' apoptosis ', using the root موت m/w/t 'death' put into
4346-613: Is turned into "5 = 40 x + 3 x ". Repeated application of this rule makes quantities of each type ("square"/"root"/"number") appear in the equation at most once, which helps to see that there are only 6 basic solvable types of the problem, when restricted to positive coefficients and solutions. Subsequent parts of the book do not rely on solving quadratic equations. The second chapter of the book catalogues methods of finding area and volume . These include approximations of pi (π), given three ways, as 3 1/7, √10, and 62832/20000. This latter approximation, equalling 3.1416, earlier appeared in
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4452-524: Is used to denote concepts that have arisen in the industrial and post-industrial era , especially in modern times. Due to its grounding in Classical Arabic, Modern Standard Arabic is removed over a millennium from everyday speech, which is construed as a multitude of dialects of this language. These dialects and Modern Standard Arabic are described by some scholars as not mutually comprehensible. The former are usually acquired in families, while
4558-445: The Lisān al-ʻArab ). Modern Standard Arabic (MSA) largely follows the grammatical standards of Classical Arabic and uses much of the same vocabulary. However, it has discarded some grammatical constructions and vocabulary that no longer have any counterpart in the spoken varieties and has adopted certain new constructions and vocabulary from the spoken varieties. Much of the new vocabulary
4664-520: The Babylonian tablets , but also from the Diophantus ' Arithmetica . It no longer concerns a series of problems to be resolved, 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
4770-493: The Elements contains fourteen propositions, which in Euclid's time were extremely significant for doing geometric algebra. These propositions and their results are the geometric equivalents of our modern symbolic algebra and trigonometry. Today, using modern symbolic algebra, we let symbols represent known and unknown magnitudes (i.e. numbers) and then apply algebraic operations on them, while in Euclid's time magnitudes were viewed as line segments and then results were deduced using
4876-489: The Elements the commutative and associative laws for multiplication are demonstrated. Many basic equations were also proved geometrically. For instance, proposition 5 in Book II proves that a 2 − b 2 = ( a + b ) ( a − b ) , {\displaystyle a^{2}-b^{2}=(a+b)(a-b),} and proposition 4 in Book II proves that (
4982-568: The Xth form , or جامعة jāmiʻah 'university', based on جمع jamaʻa 'to gather, unite'; جمهورية jumhūriyyah 'republic', based on جمهور jumhūr 'multitude'). An earlier tendency was to redefine an older word although this has fallen into disuse (e.g., هاتف hātif 'telephone' < 'invisible caller (in Sufism)'; جريدة jarīdah 'newspaper' < 'palm-leaf stalk'). Colloquial or dialectal Arabic refers to
5088-485: The intersection of a cone with a plane . There are three primary types of conic sections: ellipses (including circles ), parabolas , and hyperbolas . The conic sections are reputed to have been discovered by Menaechmus (c. 380 BC – c. 320 BC) and since dealing with conic sections is equivalent to dealing with their respective equations, they played geometric roles equivalent to cubic equations and other higher order equations. Menaechmus knew that in
5194-494: The northern Hejaz . These features are evidence of common descent from a hypothetical ancestor , Proto-Arabic . The following features of Proto-Arabic can be reconstructed with confidence: On the other hand, several Arabic varieties are closer to other Semitic languages and maintain features not found in Classical Arabic, indicating that these varieties cannot have developed from Classical Arabic. Thus, Arabic vernaculars do not descend from Classical Arabic: Classical Arabic
5300-419: The "learned" tradition (Classical Arabic). This variety and both its classicizing and "lay" iterations have been termed Middle Arabic in the past, but they are thought to continue an Old Higazi register. It is clear that the orthography of the Quran was not developed for the standardized form of Classical Arabic; rather, it shows the attempt on the part of writers to record an archaic form of Old Higazi. In
5406-865: The "purest," most eloquent form of Arabic—initiating a process of jamʿu‿l-luɣah ( جمع اللغة 'compiling the language') which took place over the 8th and early 9th centuries. Kitāb al-'Ayn ( c. 8th century ), attributed to Al-Khalil ibn Ahmad al-Farahidi , is considered the first lexicon to include all Arabic roots ; it sought to exhaust all possible root permutations —later called taqālīb ( تقاليب ) — calling those that are actually used mustaʿmal ( مستعمَل ) and those that are not used muhmal ( مُهمَل ). Lisān al-ʿArab (1290) by Ibn Manzur gives 9,273 roots, while Tāj al-ʿArūs (1774) by Murtada az-Zabidi gives 11,978 roots. History of algebra Algebra can essentially be considered as doing computations similar to those of arithmetic but with non-numerical mathematical objects. However, until
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#17327653672805512-454: The 11th and 12th centuries in al-Andalus , the zajal and muwashah poetry forms developed in the dialectical Arabic of Cordoba and the Maghreb. The Nahda was a cultural and especially literary renaissance of the 19th century in which writers sought "to fuse Arabic and European forms of expression." According to James L. Gelvin , " Nahda writers attempted to simplify the Arabic language and script so that it might be accessible to
5618-441: The 19th century, algebra consisted essentially of the theory of equations . For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging to algebra (in fact, every proof must use the completeness of the real numbers , which is not an algebraic property). This article describes the history of the theory of equations, referred to in this article as "algebra", from
5724-571: The 4th to the 6th centuries, the Nabataean script evolved into the Arabic script recognizable from the early Islamic era. There are inscriptions in an undotted, 17-letter Arabic script dating to the 6th century CE, found at four locations in Syria ( Zabad , Jebel Usays , Harran , Umm el-Jimal ). The oldest surviving papyrus in Arabic dates to 643 CE, and it uses dots to produce the modern 28-letter Arabic alphabet. The language of that papyrus and of
5830-834: The 8th century, knowledge of Classical Arabic had become an essential prerequisite for rising into the higher classes throughout the Islamic world, both for Muslims and non-Muslims. For example, Maimonides , the Andalusi Jewish philosopher, authored works in Judeo-Arabic —Arabic written in Hebrew script . Ibn Jinni of Mosul , a pioneer in phonology , wrote prolifically in the 10th century on Arabic morphology and phonology in works such as Kitāb Al-Munṣif , Kitāb Al-Muḥtasab , and Kitāb Al-Khaṣāʾiṣ [ ar ] . Ibn Mada' of Cordoba (1116–1196) realized
5936-634: The Circle Measurements , is a collection of some 170 problems written by Li Zhi (or Li Ye) (1192 – 1279 AD). He used fan fa , or Horner's method , to solve equations of degree as high as six, although he did not describe his method of solving equations. Shu-shu chiu-chang , or Mathematical Treatise in Nine Sections , was written by the wealthy governor and minister Ch'in Chiu-shao (c. 1202 – c. 1261). With
6042-460: The Hindus, did not deal with negative numbers at all; hence an equation like bx + c = 0 does not appear in the classification, because it has no positive solutions if all the coefficients are positive. Similarly equation types 4, 5 and 6, which look equivalent to the modern eye, were distinguished because the coefficients must all be positive. Al-Jabr ("forcing", "restoring") operation is moving
6148-679: The Indian Āryabhaṭīya (499 CE). Al-Khwārizmī explicates the Jewish calendar and the 19-year cycle described by the convergence of lunar months and solar years. About half of the book deals with Islamic rules of inheritance , which are complex and require skill in first-order algebraic equations. Arabic Arabic (endonym: اَلْعَرَبِيَّةُ , romanized : al-ʿarabiyyah , pronounced [al ʕaraˈbijːa] , or عَرَبِيّ , ʿarabīy , pronounced [ˈʕarabiː] or [ʕaraˈbij] )
6254-412: The Middle East and North Africa have become a badge of sophistication and modernity and ... feigning, or asserting, weakness or lack of facility in Arabic is sometimes paraded as a sign of status, class, and perversely, even education through a mélange of code-switching practises." Arabic has been taught worldwide in many elementary and secondary schools, especially Muslim schools. Universities around
6360-690: The Qur'an is referred to by linguists as "Quranic Arabic", as distinct from its codification soon thereafter into " Classical Arabic ". In late pre-Islamic times, a transdialectal and transcommunal variety of Arabic emerged in the Hejaz , which continued living its parallel life after literary Arabic had been institutionally standardized in the 2nd and 3rd century of the Hijra , most strongly in Judeo-Christian texts, keeping alive ancient features eliminated from
6466-576: The Romance languages. Also, while it is comprehensible to people from the Maghreb , a linguistically innovative variety such as Moroccan Arabic is essentially incomprehensible to Arabs from the Mashriq , much as French is incomprehensible to Spanish or Italian speakers but relatively easily learned by them. This suggests that the spoken varieties may linguistically be considered separate languages. With
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#17327653672806572-647: The algebra of al-Khwarizmi is thoroughly rhetorical, with none of the syncopation (see History of algebra ) found in the Greek Arithmetica or in Brahmagupta 's work. Even the numbers were written out in words rather than symbols! Thus the equations are verbally described in terms of "squares" (what would today be " x "), "roots" (what would today be " x ") and "numbers" ("constants": ordinary spelled out numbers, like 'forty-two'). The six types, with modern notations, are: Islamic mathematicians, unlike
6678-479: The ancient Babylonians , who developed a positional number system that greatly aided them in solving their rhetorical algebraic equations. The Babylonians were not interested in exact solutions, but rather approximations, and so they would commonly use linear interpolation to approximate intermediate values. One of the most famous tablets is the Plimpton 322 tablet , created around 1900–1600 BC, which gives
6784-497: The axioms or theorems of geometry. Many basic laws of addition and multiplication are included or proved geometrically in the Elements . For instance, proposition 1 of Book II states: But this is nothing more than the geometric version of the (left) distributive law , a ( b + c + d ) = a b + a c + a d {\displaystyle a(b+c+d)=ab+ac+ad} ; and in Books V and VII of
6890-488: The beginning and, one could say, in 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. J. J. O'Connor and E. F. Robertson wrote in 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
6996-532: 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 a whole new development path so much broader in concept to that which had existed before, and provided
7102-574: The conversion of Semitic mimation to nunation in the singular. It is best reassessed as a separate language on the Central Semitic dialect continuum. It was also thought that Old Arabic coexisted alongside—and then gradually displaced— epigraphic Ancient North Arabian (ANA), which was theorized to have been the regional tongue for many centuries. ANA, despite its name, was considered a very distinct language, and mutually unintelligible, from "Arabic". Scholars named its variant dialects after
7208-587: The emergence of Central Semitic languages, particularly in grammar. Innovations of the Central Semitic languages—all maintained in Arabic—include: There are several features which Classical Arabic, the modern Arabic varieties, as well as the Safaitic and Hismaic inscriptions share which are unattested in any other Central Semitic language variety, including the Dadanitic and Taymanitic languages of
7314-728: The eve of the conquests: Northern and Central (Al-Jallad 2009). The modern dialects emerged from a new contact situation produced following the conquests. Instead of the emergence of a single or multiple koines, the dialects contain several sedimentary layers of borrowed and areal features, which they absorbed at different points in their linguistic histories. According to Veersteegh and Bickerton, colloquial Arabic dialects arose from pidginized Arabic formed from contact between Arabs and conquered peoples. Pidginization and subsequent creolization among Arabs and arabized peoples could explain relative morphological and phonological simplicity of vernacular Arabic compared to Classical and MSA. In around
7420-530: The extended rectangle so as to find the side of the rectangle that is the solution. Iamblichus in Introductio arithmatica says that Thymaridas (c. 400 BC – c. 350 BC) worked with simultaneous linear equations. In particular, he created the then famous rule that was known as the "bloom of Thymaridas" or as the "flower of Thymaridas", which states that: If the sum of n {\displaystyle n} quantities be given, and also
7526-607: The fact that they participate in the innovations common to all forms of Arabic. The earliest attestation of continuous Arabic text in an ancestor of the modern Arabic script are three lines of poetry by a man named Garm(')allāhe found in En Avdat, Israel , and dated to around 125 CE. This is followed by the Namara inscription , an epitaph of the Lakhmid king Imru' al-Qays bar 'Amro, dating to 328 CE, found at Namaraa, Syria. From
7632-415: The first six have survived. Arithmetica is the earliest extant work present that solve arithmetic problems by algebra. Diophantus however did not invent the method of algebra, which existed before him. Algebra was practiced and diffused orally by practitioners, with Diophantus picking up techniques to solve problems in arithmetic. In modern algebra a polynomial is a linear combination of variable x that
7738-519: The form x 2 + p x + q = 0 , {\displaystyle x^{2}+px+q=0,} with p {\displaystyle p} and q {\displaystyle q} positive, have no positive roots . In between the rhetorical and syncopated stages of symbolic algebra, a geometric constructive algebra was developed by classical Greek and Vedic Indian mathematicians in which algebraic equations were solved through geometry. For instance, an equation of
7844-457: The form x 2 = A {\displaystyle x^{2}=A} was solved by finding the side of a square of area A . {\displaystyle A.} In addition to the three stages of expressing algebraic ideas, some authors recognized four conceptual stages in the development of algebra that occurred alongside the changes in expression. These four stages were as follows: The origins of algebra can be traced to
7950-540: The four unknown quantities in his algebraic equations. The Ssy-yüan yü-chien deals with simultaneous equations and with equations of degrees as high as fourteen. The author uses the method of fan fa , today called Horner's method , to solve these equations. The Precious Mirror opens with a diagram of the arithmetic triangle ( Pascal's triangle ) using a round zero symbol, but Chu Shih-chieh denies credit for it. A similar triangle appears in Yang Hui's work, but without
8056-510: The fourth most useful language for business, after English, Mandarin Chinese , and French. Arabic is written with the Arabic alphabet , an abjad script that is written from right to left . Arabic is usually classified as a Central Semitic language . Linguists still differ as to the best classification of Semitic language sub-groups. The Semitic languages changed between Proto-Semitic and
8162-415: The fundamental concept of "reduction" and "balancing" (which the term al-jabr originally referred to), the transposition of subtracted terms to the other side of an equation, i.e. the cancellation of like terms on opposite sides of the equation. Mathematics historian Victor J. Katz regards Al-Jabr as the first true algebra text that is still extant. Translated into Latin by Robert of Chester in 1145, it
8268-597: The inclusion of new words into their published standard dictionaries. They also publish old and historical Arabic manuscripts. In 1997, a bureau of Arabization standardization was added to the Educational, Cultural, and Scientific Organization of the Arab League . These academies and organizations have worked toward the Arabization of the sciences, creating terms in Arabic to describe new concepts, toward
8374-514: The introduction of a method for solving simultaneous congruences , now called the Chinese remainder theorem , it marks the high point in Chinese indeterminate analysis . The earliest known magic squares appeared in China. In Nine Chapters the author solves a system of simultaneous linear equations by placing the coefficients and constant terms of the linear equations into a magic square (i.e.
8480-613: The language. Software and books with tapes are an important part of Arabic learning, as many of Arabic learners may live in places where there are no academic or Arabic language school classes available. Radio series of Arabic language classes are also provided from some radio stations. A number of websites on the Internet provide online classes for all levels as a means of distance education; most teach Modern Standard Arabic, but some teach regional varieties from numerous countries. The tradition of Arabic lexicography extended for about
8586-604: The late 6th century AD, a relatively uniform intertribal "poetic koine" distinct from the spoken vernaculars developed based on the Bedouin dialects of Najd , probably in connection with the court of al-Ḥīra . During the first Islamic century, the majority of Arabic poets and Arabic-writing persons spoke Arabic as their mother tongue. Their texts, although mainly preserved in far later manuscripts, contain traces of non-standardized Classical Arabic elements in morphology and syntax. Abu al-Aswad al-Du'ali ( c. 603 –689)
8692-420: The latter is taught in formal education settings. However, there have been studies reporting some degree of comprehension of stories told in the standard variety among preschool-aged children. The relation between Modern Standard Arabic and these dialects is sometimes compared to that of Classical Latin and Vulgar Latin vernaculars (which became Romance languages ) in medieval and early modern Europe. MSA
8798-883: The many national or regional varieties which constitute the everyday spoken language. Colloquial Arabic has many regional variants; geographically distant varieties usually differ enough to be mutually unintelligible , and some linguists consider them distinct languages. However, research indicates a high degree of mutual intelligibility between closely related Arabic variants for native speakers listening to words, sentences, and texts; and between more distantly related dialects in interactional situations. The varieties are typically unwritten. They are often used in informal spoken media, such as soap operas and talk shows , as well as occasionally in certain forms of written media such as poetry and printed advertising. Hassaniya Arabic , Maltese , and Cypriot Arabic are only varieties of modern Arabic to have acquired official recognition. Hassaniya
8904-782: The need for a lexical injection in Arabic, to suit concepts of the industrial and post-industrial age (such as sayyārah سَيَّارَة 'automobile' or bākhirah باخِرة 'steamship'). In response, a number of Arabic academies modeled after the Académie française were established with the aim of developing standardized additions to the Arabic lexicon to suit these transformations, first in Damascus (1919), then in Cairo (1932), Baghdad (1948), Rabat (1960), Amman (1977), Khartum [ ar ] (1993), and Tunis (1993). They review language development, monitor new words and approve
9010-555: The oldest Chinese mathematical documents. Chiu-chang suan-shu or The Nine Chapters on the Mathematical Art , written around 250 BC, is one of the most influential of all Chinese math books and it is composed of some 246 problems. Chapter eight deals with solving determinate and indeterminate simultaneous linear equations using positive and negative numbers, with one problem dealing with solving four equations in five unknowns. Ts'e-yuan hai-ching , or Sea-Mirror of
9116-424: The one whose sound is heard but whose person remains unseen. Now the term al-hatif is used for a telephone. Therefore, the process of tawleed can express the needs of modern civilization in a manner that would appear to be originally Arabic. In the case of Arabic, educated Arabs of any nationality can be assumed to speak both their school-taught Standard Arabic as well as their native dialects, which depending on
9222-454: The origins to the emergence of algebra as a separate area of mathematics . The word "algebra" is derived from the Arabic word الجبر al-jabr , and this comes from the treatise written in the year 830 by the medieval Persian mathematician, Al-Khwārizmī , whose Arabic title, Kitāb al-muḫtaṣar fī ḥisāb al-ğabr wa-l-muqābala , can be translated as The Compendious Book on Calculation by Completion and Balancing . The treatise provided for
9328-549: The overhaul of Arabic grammar first proposed by Al-Jahiz 200 years prior. The Maghrebi lexicographer Ibn Manzur compiled Lisān al-ʿArab ( لسان العرب , "Tongue of Arabs"), a major reference dictionary of Arabic, in 1290. Charles Ferguson 's koine theory claims that the modern Arabic dialects collectively descend from a single military koine that sprang up during the Islamic conquests; this view has been challenged in recent times. Ahmad al-Jallad proposes that there were at least two considerably distinct types of Arabic on
9434-428: The ratios a : b {\displaystyle a:b} and c : x . {\displaystyle c:x.} The Greeks would construct a rectangle with sides of length b {\displaystyle b} and c , {\displaystyle c,} then extend a side of the rectangle to length a , {\displaystyle a,} and finally they would complete
9540-410: The region may be mutually unintelligible. Some of these dialects can be considered to constitute separate languages which may have "sub-dialects" of their own. When educated Arabs of different dialects engage in conversation (for example, a Moroccan speaking with a Lebanese), many speakers code-switch back and forth between the dialectal and standard varieties of the language, sometimes even within
9646-458: The same sentence. The issue of whether Arabic is one language or many languages is politically charged, in the same way it is for the varieties of Chinese , Hindi and Urdu , Serbian and Croatian , Scots and English, etc. In contrast to speakers of Hindi and Urdu who claim they cannot understand each other even when they can, speakers of the varieties of Arabic will claim they can all understand each other even when they cannot. While there
9752-458: The sole example of Medieval linguist Abu Hayyan al-Gharnati – who, while a scholar of the Arabic language, was not ethnically Arab – Medieval scholars of the Arabic language made no efforts at studying comparative linguistics, considering all other languages inferior. In modern times, the educated upper classes in the Arab world have taken a nearly opposite view. Yasir Suleiman wrote in 2011 that "studying and knowing English or French in most of
9858-399: The solutions to the equations d x 2 − a d x + b 2 c = 0 {\displaystyle dx^{2}-adx+b^{2}c=0} and the familiar Babylonian equation x y = a 2 , x ± y = b . {\displaystyle xy=a^{2},x\pm y=b.} A conic section is a curve that results from
9964-563: The standardization of these new terms throughout the Arabic-speaking world, and toward the development of Arabic as a world language . This gave rise to what Western scholars call Modern Standard Arabic. From the 1950s, Arabization became a postcolonial nationalist policy in countries such as Tunisia, Algeria, Morocco, and Sudan. Arabic usually refers to Standard Arabic, which Western linguists divide into Classical Arabic and Modern Standard Arabic. It could also refer to any of
10070-1761: The sum of every pair containing a particular quantity, then this particular quantity is equal to 1 / ( n − 2 ) {\displaystyle 1/(n-2)} of the difference between the sums of these pairs and the first given sum. or using modern notation, the solution of the following system of n {\displaystyle n} linear equations in n {\displaystyle n} unknowns, x + x 1 + x 2 + ⋯ + x n − 1 = s {\displaystyle x+x_{1}+x_{2}+\cdots +x_{n-1}=s} x + x 1 = m 1 {\displaystyle x+x_{1}=m_{1}} x + x 2 = m 2 {\displaystyle x+x_{2}=m_{2}} ⋮ {\displaystyle \vdots } x + x n − 1 = m n − 1 {\displaystyle x+x_{n-1}=m_{n-1}} is, x = ( m 1 + m 2 + . . . + m n − 1 ) − s n − 2 = ( ∑ i = 1 n − 1 m i ) − s n − 2 . {\displaystyle x={\cfrac {(m_{1}+m_{2}+...+m_{n-1})-s}{n-2}}={\cfrac {(\sum _{i=1}^{n-1}m_{i})-s}{n-2}}.} Iamblichus goes on to describe how some systems of linear equations that are not in this form can be placed into this form. Euclid ( Greek : Εὐκλείδης )
10176-423: The systematic solution of linear and quadratic equations . According to one history, "[i]t is not certain just what the terms al-jabr and muqabalah mean, but the usual interpretation is similar to that implied in the previous translation. The word 'al-jabr' presumably meant something like 'restoration' or 'completion' and seems to refer to the transposition of subtracted terms to the other side of an equation;
10282-501: The towns where the inscriptions were discovered (Dadanitic, Taymanitic, Hismaic, Safaitic). However, most arguments for a single ANA language or language family were based on the shape of the definite article, a prefixed h-. It has been argued that the h- is an archaism and not a shared innovation, and thus unsuitable for language classification, rendering the hypothesis of an ANA language family untenable. Safaitic and Hismaic, previously considered ANA, should be considered Old Arabic due to
10388-432: 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. Algebra did not always make use of the symbolism that is now ubiquitous in mathematics; instead, it went through three distinct stages. The stages in the development of symbolic algebra are approximately as follows: Equally important as the use or lack of symbolism in algebra
10494-547: The word 'muqabalah' is said to refer to 'reduction' or 'balancing'—that is, the cancellation of like terms on opposite sides of the equation. Arabic influence in Spain long after the time of al-Khwarizmi is found in Don Quixote , where the word 'algebrista' is used for a bone-setter, that is, a 'restorer'." The term is used by al-Khwarizmi to describe the operations that he introduced, " reduction " and "balancing", referring to
10600-451: The world have classes that teach Arabic as part of their foreign languages , Middle Eastern studies , and religious studies courses. Arabic language schools exist to assist students to learn Arabic outside the academic world. There are many Arabic language schools in the Arab world and other Muslim countries. Because the Quran is written in Arabic and all Islamic terms are in Arabic, millions of Muslims (both Arab and non-Arab) study
10706-463: The zero symbol. There are many summation equations given without proof in the Precious mirror . A few of the summations are: Diophantus was a Hellenistic mathematician who lived c. 250 AD, but the uncertainty of this date is so great that it may be off by more than a century. He is known for having written Arithmetica , a treatise that was originally thirteen books but of which only
10812-555: Was a Greek mathematician who flourished in Alexandria , Egypt , almost certainly during the reign of Ptolemy I (323–283 BC). Neither the year nor place of his birth have been established, nor the circumstances of his death. Euclid is regarded as the "father of geometry ". His Elements is the most successful textbook in the history of mathematics . Although he is one of the most famous mathematicians in history there are no new discoveries attributed to him; rather he
10918-432: Was a landmark work in the history of mathematics , with its title being the ultimate etymology of the word "algebra" itself, later borrowed into Medieval Latin as algebrāica . Al-Jabr provided an exhaustive account of solving for the positive roots of polynomial equations up to the second degree. It was the first text to teach elementary algebra , and the first to teach algebra for its own sake. It also introduced
11024-401: Was now possible to find a solution to the problem of the duplication of the cube by solving for the points at which two parabolas intersect, a solution equivalent to solving a cubic equation. We are informed by Eutocius that the method he used to solve the cubic equation was due to Dionysodorus (250 BC – 190 BC). Dionysodorus solved the cubic by means of the intersection of
11130-438: Was the degree of the equations that were addressed. Quadratic equations played an important role in early algebra; and throughout most of history, until the early modern period, all quadratic equations were classified as belonging to one of three categories. where p {\displaystyle p} and q {\displaystyle q} are positive. This trichotomy comes about because quadratic equations of
11236-438: Was used until the sixteenth century as the principal mathematical textbook of European universities. Several authors have also published texts under this name, including Abu Hanifa Dinawari , Abu Kamil , Abū Muḥammad al-ʿAdlī, Abū Yūsuf al-Miṣṣīṣī, 'Abd al-Hamīd ibn Turk , Sind ibn ʿAlī, Sahl ibn Bišr, and Šarafaddīn al-Ṭūsī . R. Rashed and Angela Armstrong write: Al-Khwarizmi's text can be seen to be distinct not only from
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