Instruct: Given a question, retrieve relevant documents that answer the question.
Query: When were Arabic numerals introduced to Europe?
The first mentions of the numerals in the West are found in the Codex Vigilanus of 976.[22]
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.
Before the discovery of Hindu–Arabic numeral system, which was introduced in Europe during the 13th century by Fibonacci, division was extremely difficult, and only the best mathematicians were able to do it. In fact, the long division algorithm requires this notation.
The "Western Arabic" numerals as they were in common use in Europe since the Baroque period have secondarily found worldwide use together with the Latin alphabet, and even significantly beyond the contemporary spread of the Latin alphabet, intruding into the writing systems in regions where other variants of the Hindu–Arabic numerals had been in use, but also in conjunction with Chinese and Japanese writing (see Chinese numerals, Japanese numerals).
The 1228 edition, first section introduces the Hindu-Arabic numeral system and compares the system with other systems, such as Roman numerals, and methods to convert the other numeral systems into Hindu-Arabic numerals. Replacing the Roman numeral system, its ancient Egyptian multiplication method, and using an abacus for calculations, with a Hindu-Arabic numeral system was an advance in making business calculations easier and faster, which led to the growth of banking and accounting in Europe.
Following the first wave of Arabic interest during the Renaissance of the 12th century, which saw numerous Arabic texts being translated into Latin, there was a 'second wave' of interest in the study of Arabic literature, Arabic science and Islamic philosophy in 16th-century France and 17th-century England.
Together with the development of the Franco-Ottoman alliance, cultural and scientific exchanges between France and the Ottoman Empire flourished. French scholars such as Guillaume Postel or Pierre Belon were able to travel to Asia Minor and the Middle East to collect information.
Scientific exchange is thought to have occurred, as numerous works in Arabic, especially pertaining to astronomy were brought back, annotated and studied by scolars such as Guillaume Postel. Transmission of scientific knowledge, such as the Tusi-couple, may have occurred on such occasions, at the time when Copernicus was establishing his own astronomical theories.
Historically the grid calculation (tweaked slightly) was the basis of a method called lattice multiplication, which was the standard method of multiple-digit multiplication developed in medieval Arabic and Hindu mathematics. Lattice multiplication was introduced into Europe by Fibonacci at the start of the thirteenth century along with the so-called Arabic numerals themselves; although, like the numerals also, the ways he suggested to calculate with them were initially slow to catch on. Napier's bones were a calculating help introduced by the Scot John Napier in 1617 to assist lattice method calculations.
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.
In the 7th century, Brahmagupta identified the Brahmagupta theorem, Brahmagupta's identity and Brahmagupta's formula, and for the first time, in Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu–Arabic numeral system.[134] It was from a translation of this Indian text on mathematics (c. 770) that Islamic mathematicians were introduced to this numeral system, which they adapted as Arabic numerals. Islamic scholars carried knowledge of this number system to Europe by the 12th century, and it has now displaced all older number systems throughout the world. Various symbol sets are used to represent numbers in the Hindu–Arabic numeral system, all of which evolved from the Brahmi numerals. Each of the roughly dozen major scripts of India has its own numeral glyphs. In the 10th century, Halayudha's commentary on Pingala's work contains a study of the Fibonacci sequence and Pascal's triangle, and describes the formation of a matrix.
During the early medieval era, Roman numerals were used in Europe to represent numbers, but the Arabs represented numbers using the Hindu numeral system, a positional notation that used ten symbols. In about 1202, Fibonacci published his book "Liber Abaci" (Book of Calculation) which introduced the concept of positional notation into Europe. These symbols evolved into the numerals "0", "1", "2" etc. At that time there was dispute regarding the difference between rational numbers and irrational numbers and there was no consistency in the way in which decimal fractions were represented.
Stefan of Pise translated into Latin around 1127 an Arab manual of medical theory. The method of algorism for performing arithmetic with Indian-Arabic numerals was developed by the Persian al-Khwarizmi in the 9th century, and introduced in Europe by Leonardo Fibonacci (1170–1250). A translation by Robert of Chester of the "Algebra" by al-Kharizmi is known as early as 1145. Ibn al-Haytham (Alhazen, 980–1037) compiled treatises on optical sciences, which were used as references by Newton and Descartes. Medical sciences were also highly developed in Islam as testified by the Crusaders, who relied on Arab doctors on numerous occasions. Joinville reports he was saved in 1250 by a “Saracen” doctor.
Leonardo Fibonacci brought this system to Europe. His book Liber Abaci introduced Arabic numerals, the use of zero, and the decimal place system to the Latin world. The numeral system came to be called "Arabic" by the Europeans. It was used in European mathematics from the 12th century, and entered common use from the 15th century to replace Roman numerals.[13][14]
By the 11th century, Arabic numerals had been introduced into Europe from al-Andalus, by way of Arab traders and arithmetic treatises. Roman numerals, however, proved very persistent, remaining in common use in the West well into the 14th and 15th centuries, even in accounting and other business records (where the actual calculations would have been made using an abacus). Replacement by their more convenient "Arabic" equivalents was quite gradual, and Roman numerals are still used today in certain contexts. A few examples of their current use are:
In the "Liber Abaci" (1202), Fibonacci introduced the so-called "modus Indorum" (method of the Indians), today known as the Hindu–Arabic numeral system. The book advocated numeration with the digits 0–9 and place value. The book showed the practical use and value of the new Hindu-Arabic numeral system by applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing, and other applications. The book was well-received throughout educated Europe and had a profound impact on European thought. No copies of the 1202 edition are known to exist.
Suzhou numerals were used as shorthand in number-intensive areas of commerce such as accounting and bookkeeping. At the same time, standard Chinese numerals were used in formal writing, akin to spelling out the numbers in English. Suzhou numerals were once popular in Chinese marketplaces, such as those in Hong Kong along with local transportation before the 1990s, but they have gradually been supplanted by Arabic numerals. This is similar to what had happened in Europe with Roman numerals used in ancient and medieval Europe for mathematics and commerce. Nowadays, the Suzhou numeral system is only used for displaying prices in Chinese markets or on traditional handwritten invoices.
During the Ming and Qing dynasties (after Arabic numerals were introduced into China), some Chinese mathematicians used Chinese numeral characters as positional system digits. After the Qing period, both the Chinese numeral characters and the Suzhou numerals were replaced by Arabic numerals in mathematical writings.
The widespread Western "Arabic numerals" used with the Latin, Cyrillic, and Greek alphabets in the table, descended from the "West Arabic numerals" which were developed in al-Andalus and the Maghreb (there are two typographic styles for rendering western Arabic numerals, known as lining figures and text figures). The "Arabic–Indic" or "Eastern Arabic numerals" used with Arabic script, developed primarily in what is now Iraq. A variant of the Eastern Arabic numerals is used in Persian and Urdu. The Indian numerals in use with scripts of the Brahmic family in India and Southeast Asia. Each of the roughly dozen major scripts of India has its own numeral glyphs (as one will note when perusing Unicode character charts).
The reason the digits are more commonly known as "Arabic numerals" in Europe and the Americas is that they were introduced to Europe in the 10th century by Arabic-speakers of North Africa, who were then using the digits from Libya to Morocco. Arabs, on the other hand, call the base-10 system (not just these digits) "Hindu numerals",[23][24] referring to their origin in India. This is not to be confused with what the Arabs call the "Hindi numerals", namely the Eastern Arabic numerals (٠‎ - ١‎ - ٢‎ - ٣‎ -٤‎ - ٥‎ - ٦‎ - ٧‎ - ٨‎ - ٩‎) used in the Middle East, or any of the numerals currently used in Indian languages (e.g. Devanagari: ०.१.२.३.४.५.६.७.८.९).[17]
These symbol sets can be divided into three main families: Western Arabic numerals used in the Greater Maghreb and in Europe, Eastern Arabic numerals (also called "Indic numerals") used in the Middle East, and the Indian numerals used in the Indian subcontinent.
Although various scholars had mentioned about numerations in the Sinhala language in their writing on Sinhala language, a systematic study had not been conducted up to now on numerals and numerations found in Sinhala right before British occupation of Kandy. In modern Sinhala, Arabic numerals, which were introduced by Portuguese, Dutch and English, is used for writing numbers and carrying out calculations. Roman numerals are used for writing dates and for listing items or words in Sinhala though at present, Roman numerals are not commonly used and they were also introduced by Westerners who invaded Sri Lanka. It is accepted that Arabic numerals had evolved from Brahmi numerals. It had also been discovered by Sri Lankan archeologists that Brahmi numerals were used in the ancient Sri Lanka and it may have evolved into two sets of numerals which were known as archaic Sinhala numerals and Lith Illakkum which were found in the Kandyan period. This paper mainly covers numerals and numerations in Sri Lanka at the time of British occupation of the Kandyan Kingdom and their evolution to the forms which were found in 1815, the year the British occupied the whole of Sri Lanka. This article will also touch upon Brahmi numerals, which were found in Sri Lanka.
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.
Sacrobosco's "Algorismus" aka "De Arte Numerandi" is thought to have been his first work, and the date is estimated at about 1225, and before 1230. The Hindu–Arabic methods of numerical calculation had arrived in Latin Europe during the previous fifty years but had not been disseminated on a wide scale. Sacrobosco's "Algorismus" was the first text to introduce Hindu–Arabic numerals and procedures into the European university curriculum. 
The Abjad numerals ( ) are a decimal numeral system in which the 28 letters of the Arabic alphabet are assigned numerical values. They have been used in the Arabic-speaking world since before the eighth century when Arabic numerals were adopted. In modern Arabic, the word "" () means 'alphabet' in general.
Pickover states, “The Latin translation [of Al-Khuwarizmi's Algebra] introduced the decimal positional number system to Europe” (84). Later, Pickover writes that Fibonacci's Liber Abaci "introduced the Hindu-Arabic numerals and decimal system to Western Europe" (100). 
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,[25] 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.[26] By the mid-16th century, they were in common use in most of Europe.[27] Roman numerals remained in use mostly for the notation of anno Domini years, and for numbers on clockfaces.