Abū'l-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qurashī al-Qalaṣādī ( ar, أبو الحسن علي بن محمد بن علي القرشي البسطي; 1412–1486) was a

Muslim Muslims ( ar, المسلمون, , ) are people who adhere to Islam, a monotheistic religion belonging to the Abrahamic tradition. They consider the Quran, the foundational religious text of Islam, to be the verbatim word of the God of Abrah ...

Arab The Arabs (singular: Arab; singular ar, عَرَبِيٌّ, DIN 31635: , , plural ar, عَرَب, DIN 31635: , Arabic pronunciation: ), also known as the Arab people, are an ethnic group mainly inhabiting the Arab world in Western Asia, ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

from

Al-Andalus Al-Andalus DIN 31635, translit. ; an, al-Andalus; ast, al-Ándalus; eu, al-Andalus; ber, ⴰⵏⴷⴰⵍⵓⵙ, label=Berber languages, Berber, translit=Andalus; ca, al-Àndalus; gl, al-Andalus; oc, Al Andalús; pt, al-Ândalus; es, ...

specializing in

Islamic inheritance jurisprudence Islamic Inheritance jurisprudence is a field of Islamic jurisprudence ( ar, فقه) that deals with inheritance, a topic that is prominently dealt with in the Qur'an. It is often called ''Mīrāth'', and its branch of Islamic law is technically ...

Franz Woepcke Franz Woepcke (6 May 1826 – 25 March 1864) was a historian, Orientalist and mathematician. He is remembered for publishing editions and translations of medieval Arabic mathematical manuscripts and for his research on the propagation of the H ...

stated that al-Qalaṣādī was known as one of the most influential voices in algebraic notation for taking "the first steps toward the introduction of

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

ic symbolism''. He wrote numerous books on

arithmetic Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

and algebra, including ''al-Tabsira fi'lm al-hisab'' ( ar, التبصير في علم الحساب "''Clarification of the science of arithmetic''").

Early life

Al-Qalaṣādī was born in Baza, an outpost of the

Emirate of Granada The Emirate of Granada ( ar, إمارة غرﻧﺎﻃﺔ, Imārat Ġarnāṭah), also known as the Nasrid Kingdom of Granada ( es, Reino Nazarí de Granada), was an Emirate, Islamic realm in southern Iberia during the Late Middle Ages. It was the ...

. He received education in

Granada Granada (,, DIN 31635, DIN: ; grc, Ἐλιβύργη, Elibýrgē; la, Illiberis or . ) is the capital city of the province of Granada, in the autonomous communities of Spain, autonomous community of Andalusia, Spain. Granada is located at the fo ...

, but continued to support his family in Baza. He published many works and eventually retired to his native Baza. Granada by Piri Reis

His works dealt with Algebra and contained the precise mathematical answers to problems in everyday life, such as the composition of medicaments, the calculation of the drop of irrigation canals and the explanation of frauds linked to instruments of measurement. The second part belongs to the already ancient tradition of judicial and cultural mathematics and joins a collection of little arithmetical problems presented in the form of poetical riddles In 1480 the

Christian Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ. The words ''Christ'' and ''Christian'' derive from the Koine Greek title ''Christós'' (Χρι ...

forces of

Ferdinand Ferdinand is a Germanic name composed of the elements "protection", "peace" (PIE "to love, to make peace") or alternatively "journey, travel", Proto-Germanic , abstract noun from root "to fare, travel" (PIE , "to lead, pass over"), and "co ...

and

Isabella Isabella may refer to: People and fictional characters * Isabella (given name), including a list of people and fictional characters * Isabella (surname), including a list of people Places United States * Isabella, Alabama, an unincorpor ...

, "The Catholic Monarchs", raided and often pillaged the city, al-Qalasādī himself served in the mountain citadels which were erected in the vicinity of Baza. al-Qalasādī eventually left his homeland and took refuge with his family in

Béja Béja ( ar, باجة ') is a city in Tunisia. It is the capital of the Béja Governorate. It is located from Tunis, between the Medjerdah River and the Mediterranean, against the foothills of the Khroumire, the town of Béja is situated on the ...

Tunisia ) , image_map = Tunisia location (orthographic projection).svg , map_caption = Location of Tunisia in northern Africa , image_map2 = , capital = Tunis , largest_city = capital , ...

, where he died in 1486. Baza was eventually besieged by the forces of Ferdinand and Isabella and its inhabitants sacked.

Symbolic algebra

Like his predecessors, al-Qalaṣādī used an algebraic notation. While the 19th century writer Franz Woepcke believed that this algebraic symbolism was created by al-Qalaṣādī himself, these symbols had actually been used by other mathematicians in North Africa 100 years earlier. Al-Qalaṣādī represented

mathematical symbols A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. ...

using characters from the Arabic alphabet, where: *ﻭ ('' wa'') means "and" for

addition Addition (usually signified by the Plus and minus signs#Plus sign, plus symbol ) is one of the four basic Operation (mathematics), operations of arithmetic, the other three being subtraction, multiplication and Division (mathematics), division. ...

(+) *إلا ('' illa'') literally, "except"; means "less" for

subtraction Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Subtraction is signified by the minus sign, . For example, in the adjacent picture, there are peaches—meaning 5 peaches with 2 taken ...

(-) *في (''fi'') literally, "in"; means "times" for

multiplication Multiplication (often denoted by the cross symbol , by the mid-line dot operator , by juxtaposition, or, on computers, by an asterisk ) is one of the four elementary mathematical operations of arithmetic, with the other ones being additi ...

(*) *على (''ala'') means "over" for

division Division or divider may refer to: Mathematics *Division (mathematics), the inverse of multiplication *Division algorithm, a method for computing the result of mathematical division Military *Division (military), a formation typically consisting ...

(/) *ﺝ ('' j'') represents ''jadah'' meaning "

root In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often below the sur ...

" *ﺵ ('' sh'') represents ''shay meaning "thing" for a

variable Variable may refer to: * Variable (computer science), a symbolic name associated with a value and whose associated value may be changed * Variable (mathematics), a symbol that represents a quantity in a mathematical expression, as used in many ...

(x) *ﻡ ('' m'') represents ''morabba'a'' for a

square In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length adj ...

(x²) *ﻙ ('' k'') represents ''moka'aab'' for a

cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. The cube is the only r ...

(x³) *ﻝ ('' l'') represents ''ya'adilu'' for

equality Equality may refer to: Society * Political equality, in which all members of a society are of equal standing ** Consociationalism, in which an ethnically, religiously, or linguistically divided state functions by cooperation of each group's elite ...

(=) As an example, the equation

2x^3 + 3x^2 - 4x + 5 = 0

would have been written using his notation as: ٢ في ش^ك ﻭ ٣ في ش^ﻡ إﻻ ٤ في ﺵ ﻭ ٥ ﻝ ٠

Notes

References

* *

External links

* {{DEFAULTSORT:Qalasadi, Abu Hasan Ali 1412 births 1486 deaths 15th-century Arabs People from the Province of Granada Mathematicians of Al-Andalus 15th-century mathematicians Jurisprudence academics Mathematicians who worked on Islamic inheritance Scholars of the Nasrid period 15th-century Spanish mathematicians

Early life

Symbolic algebra

See also

Notes

References

External links