Instruct: Given a question, retrieve passages that can help answer the question.
Query: When were Arabic numerals introduced to Europe?
From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo. Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th  century. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's "Liber Abaci" of 1201. In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.
The first mentions of the numerals in the West are found in the "Codex Vigilanus" of 976.
Nicomachus' treatises were well known in Greek, Latin and the Arabic worlds. In the 1st century an Arabic translation of Nicomachus’ "Introduction to Arithmetic" was published. The Arabic translations of Nicomachus' treatises were in turn translated into Latin by Gerard of Cremona, making them part of the Latin tradition of numerology. The Pythagorean theorem was referenced in Arabic manuscripts. Scholars in the Arabic world displayed a strong interest in Pythagorean concepts. In the 1st century Abu al-Wafa' Buzjani discussed multiplication and division in a treatise on arithmetic for business administrators in reference to Nicomachus. However, the primary interest of Islamic arithmeticians was in solving practical problems, such as taxation, measurement, the estimation of agricultural values and business applications for the buying and selling of goods. There was little interest for the Pythagorean numerology that developed in the Latin world. The primary arithmetical system used by Islamic mathematicians was based on Hindu arithmetic, which rejected the notion that the relations between numbers and geometrical forms were symbolic.
The decimal Hindu–Arabic numeral system with zero was developed in India by around AD 700. The development was gradual, spanning several centuries, but the decisive step was probably provided by Brahmagupta's formulation of zero as a number in AD 628. The system was revolutionary by including zero in positional notation, thereby limiting the number of individual digits to ten. It is considered an important milestone in the development of mathematics. One may distinguish between this positional "system", which is identical throughout the family, and the precise glyphs used to write the numerals, which varied regionally.
Adelard of Bath (; 1080 1152 AD) was a 12th-century English natural philosopher. He is known both for his original works and for translating many important Arabic and Greek scientific works of astrology, astronomy, philosophy and mathematics into Latin from Arabic versions, which were then introduced to Western Europe. He is known as one of the first to introduce the Arabic numeral system to Europe. He stands at the convergence of three intellectual schools: the traditional learning of French schools, the Greek culture of Southern Italy, and the Arabic science of the East.
Evidence for more complex mathematics does not appear until around 3000 BC, when the Babylonians and Egyptians began using arithmetic, algebra and geometry for taxation and other financial calculations, for building and construction, and for astronomy. The most ancient mathematical texts from Mesopotamia and Egypt are from 2000–1800 BC. Many early texts mention Pythagorean triples and so, by inference, the Pythagorean theorem seems to be the most ancient and widespread mathematical development after basic arithmetic and geometry. It is in Babylonian mathematics that elementary arithmetic (addition, subtraction, multiplication and division) first appear in the archaeological record. The Babylonians also possessed a place-value system, and used a sexagesimal numeral system, still in use today for measuring angles and time.
Cyrillic numerals were a numbering system derived from the Cyrillic alphabet, used by South and East Slavic peoples. The system was used in Russia as late as the early 18th century when Peter the Great replaced it with Arabic numerals.
Many numbers include hundreds, units and tens. The Roman numeral system being basically decimal, each power of ten is added in descending sequence from left to right, as with Arabic numerals. For example:As each power of ten (or "place") has its own notation there is no need for place keeping zeros, so "missing places" are ignored, as in Latin (and English) speech, thus:Roman numerals for large numbers are nowadays seen mainly in the form of year numbers (other uses are detailed later in this article), as in these examples:The "standard" forms described above reflect typical modern usage rather than an unchanging and universally accepted convention. Usage in ancient Rome varied greatly and remained inconsistent in medieval times. There is still no official "binding" standard, which makes the elaborate "rules" used in some sources to distinguish between "correct" and "incorrect" forms highly problematic.Although Roman numerals came to be written with letters of the Roman alphabet, they were originally independent symbols. The Etruscans, for example, used , , , , , and for , , , , , and , of which only and happened to be letters in their alphabet.
In print, Arabic numerals are employed in Modern Hebrew for most purposes. Hebrew numerals are used nowadays primarily for writing the days and years of the Hebrew calendar; for references to traditional Jewish texts (particularly for Biblical chapter and verse and for Talmudic folios); for bulleted or numbered lists (similar to "A", "B", "C", "etc.", in English); and in numerology (gematria).
Algebra was also pioneered by Persian Scientist Muhammad ibn Mūsā al-Khwārizmī during this time in his landmark text, Kitab al-Jabr wa-l-Muqabala, from which the term algebra is derived. He is thus considered to be the father of algebra. The terms algorism and algorithm are also derived from the name of al-Khwarizmi, who was responsible for introducing the Arabic numerals and Hindu-Arabic numeral system beyond the Indian Subcontinent.
Writing was introduced by the Greeks and from there also brought to the Romans (6th century BC). There are five alphabets in regular use in the areas generally considered Europe. The Latin alphabet was developed into several scripts. In the early years of Europe, the Carolingian minuscules were the most important variety of the Latin script. From this two branches developed, the Gothic/Fracture/German tradition, which Germans used well into the 20th century, and the Italian/Italic/Antiqua/Latin tradition, still used. For some nations the integration into Europe meant giving up older scripts, e.g. the Germanic gave up the runes (Futhark) (3rd to 17th centuries), the Irish the Ogham script (4th to 7th centuries). The Cyrillic script is the second most widespread alphabet in Europe, and was developed in the 9th century under the influence of the Greek, Latin and Glagolitic alphabets. Both the Latin and Cyrillic alphabets are used for multiple languages in multiple states, both inside and outside Europe. As well as these two, there are three alphabets used primarily for a single language, although they are occasionally applied to minority languages in the states from which they originate. The oldest of these alphabets is the Greek alphabet, which could be considered the progenitor of all the surviving alphabets of Europe, with the earliest recorded inscriptions appearing in the 9th century BC. The other two are both found in the Caucasus, both originating in the 5th century. The Georgian alphabet is used primarily to write Georgian, though it is also used to write the other Kartvelian languages, Svan, Mingrelian and Laz, all of which are found largely within the borders of Georgia. The Armenian alphabet is used to write the Armenian language, which has two dialects, and has been used to write Turkish in the past.
Al-Karkhi (953–1029), also known as Al-Karaji, was the successor of Abū al-Wafā' al-Būzjānī (940–998) and he discovered the first numerical solution to equations of the form ax + bx = c. Al-Karkhi only considered positive roots. Al-Karkhi is also regarded as the first person to free algebra from geometrical operations and replace them with the type of arithmetic operations which are at the core of algebra today. His work on algebra and polynomials, gave the rules for arithmetic operations to manipulate polynomials. The historian of mathematics F. Woepcke, in "Extrait du Fakhri, traité d'Algèbre par Abou Bekr Mohammed Ben Alhacan Alkarkhi" (Paris, 1853), praised Al-Karaji for being "the first who introduced the theory of algebraic calculus". Stemming from this, Al-Karaji investigated binomial coefficients and Pascal's triangle.
For central Arabia, especially Mecca, there is a lack of epigraphical evidence but details are found in the writings of Muslim authors of the Abbasid era. Inscriptions of the ancient South Arabian calendars reveal the use of a number of local calendars. At least some of these South Arabian calendars followed the lunisolar system. Both al-Biruni and al-Mas'udi suggest that the ancient Arabs used the same month names as the Muslims, though they also record other month names used by the pre-Islamic Arabs.
Like other European languages, English contains many words derived from Arabic, often through other European languages, especially Spanish. Among them is every-day vocabulary like "sugar" ("sukkar"), "cotton" ("quṭn") or "magazine" (""). More recognizable are words like "algebra" ("al-jabr"), "alcohol" ("al-kuhūl"), "alchemy" ("al-kimiya"), "alkali", "cypher" and "zenith" (see list of English words of Arabic origin).
During 1909 and 1910 there were movements by Young Turks supporters to adopt an Arabic alphabet, as they considered the Latin script to be un-Islamic. In Elbasan, Muslim clerics led a demonstration for the Arabic script, telling their congregations that using the Latin script would make them infidels. In 1911, the Young Turks dropped their opposition to the Latin script, and the Latin alphabet was invented. In order to eliminate ambiguity in the pronunciation of the Arabic script, Rexhep Voka developed a customized Arabic alphabet consisting of 44 consonants and vowels, which he published in 1911. However, it was hardly used anymore due to the Congress of Monastir. Tiranli Fazli then used this script to publish a thirty-two page grammar. Only one Albanian newspaper at the time ever appeared in Arabic script, and it lasted a brief period. Regardless of what script appeared, such material raised Albanian national consciousness.
Al-Khwarizmi's popularizing treatise on algebra ("The Compendious Book on Calculation by Completion and Balancing", c. 813–833 CE) presented the first systematic solution of linear and quadratic equations. One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications. Because he was the first 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 term "algebra" itself comes from the title of his book (specifically the word "al-jabr" meaning "completion" or "rejoining"). His name gave rise to the terms "algorism" and "algorithm". His name is also the origin of (Spanish) "guarismo" and of (Portuguese) "algarismo", both meaning digit.
Musical notation was developed before parchment or paper were used for writing. The earliest form of musical notation can be found in a cuneiform tablet that was created at Nippur, in Sumer (today's Iraq) in about 2,000 BC. The tablet represents fragmentary instructions for performing music, that the music was composed in harmonies of thirds, and that it was written using a diatonic scale.
The currency was introduced in non-physical form (traveller's cheques, electronic transfers, banking, etc.) at midnight on 1 January 1999, when the national currencies of participating countries (the eurozone) ceased to exist independently. Their exchange rates were locked at fixed rates against each other. The euro thus became the successor to the European Currency Unit (ECU). The notes and coins for the old currencies, however, continued to be used as legal tender until new euro notes and coins were introduced on 1 January 2002.
The currency was introduced in non-physical form (traveller's cheques, electronic transfers, banking, etc.) at midnight on 1 January 1999, when the national currencies of participating countries (the eurozone) ceased to exist independently in that their exchange rates were locked at fixed rates against each other, effectively making them mere non-decimal subdivisions of the euro. The euro thus became the successor to the European Currency Unit (ECU). The notes and coins for the old currencies, however, continued to be used as legal tender until new notes and coins were introduced on 1 January 2002 (having been distributed in small amounts in the previous December). Beginning on 1 January 1999, all bonds and other forms of government debt by eurozone nations were denominated in euros.
The similarity of the Hebrew, Arabic and Aramaic languages was accepted by Jewish and Islamic scholars since medieval times. The languages were familiar to Western European scholars due to historical contact with neighbouring Near Eastern countries and through Biblical studies, and a comparative analysis of Hebrew, Arabic, and Aramaic was published in Latin in 1538 by Guillaume Postel. Almost two centuries later, Hiob Ludolf described the similarities between these three languages and the Ethiopian Semitic languages. However, neither scholar named this grouping as "Semitic".
The euro was founded on 1 January 1999, when it became the currency of over 300 million people in Europe. For the first three years of its existence it was an invisible currency, only used in accountancy. Euro cash was not introduced until 1 January 2002, when it replaced the national banknotes and coins of the countries in eurozone 12, such as the French franc and the Spanish peseta.
The European acceptance of the numerals was accelerated by the invention of the printing press, and they became widely known during the 15th century. Early evidence of their use in Britain includes: an equal hour horary quadrant from 1396, in England, a 1445 inscription on the tower of Heathfield Church, Sussex; a 1448 inscription on a wooden lych-gate of Bray Church, Berkshire; and a 1487 inscription on the belfry door at Piddletrenthide church, Dorset; and in Scotland a 1470 inscription on the tomb of the first Earl of Huntly in Elgin Cathedral. (See G.F. Hill, "The Development of Arabic Numerals in Europe" for more examples.) In central Europe, the King of Hungary Ladislaus the Posthumous, started the use of Arabic numerals, which appear for the first time in a royal document of 1456. By the mid-16th century, they were in common use in most of Europe. Roman numerals remained in use mostly for the notation of anno Domini years, and for numbers on clockfaces.
Arabic numerals were introduced to China during the Yuan Dynasty (1271–1368) by the Muslim Hui people. In the early 17th century, European-style Arabic numerals were introduced by Spanish and Portuguese Jesuits.
In Christian Europe, the first mention and representation of Hindu-Arabic numerals (from one to nine, without zero), is in the ", an illuminated compilation of various historical documents from the Visigothic period in Spain, written in the year 976 by three monks of the Riojan monastery of San Martín de Albelda.
Between 967 and 969, Gerbert of Aurillac discovered and studied Arab science in the Catalan abbeys. Later he obtained from these places the book " ("On multiplication and division"). After becoming Pope Sylvester II in the year 999, he introduced a new model of abacus, the so-called Abacus of Gerbert, by adopting tokens representing Hindu-Arab numerals, from one to nine.
Leonardo of Pisa, now known as Fibonacci, serendipitously learned about the Hindu–Arabic numerals on a trip to what is now Béjaïa, Algeria with his merchant father. (Europe was still using Roman numerals.) There, he observed a system of arithmetic (specifically algorism) which due to the positional notation of Hindu–Arabic numerals was much more efficient and greatly facilitated commerce. Leonardo wrote "Liber Abaci" in 1202 (updated in 1254) introducing the technique to Europe and beginning a long period of popularizing it. The book also brought to Europe what is now known as the Fibonacci sequence (known to Indian mathematicians for hundreds of years before that) which was used as an unremarkable example within the text.