Abu al-Hasan ibn Ali al-Qalasadi
Encyclopedia
Abū al-Ḥasan ibn ʿAlī ibn Muḥammad ibn ʿAlī al-Qalaṣādī (1412–1486) was a Muslim mathematician
from Al-Andalus
specializing in Islamic inheritance jurisprudence
. Al-Qalaṣādī is known for being one of the most influential voices in algebraic notation
since antiquity and for taking "the first steps toward the introduction of algebra
ic symbolism." He wrote numerous books on arithmetic
and algebra, including al-Tabsira fi'lm al-hisab ( "Clarification of the science of arithmetic").
, an outpost of the Emirate of Granada
. He received education in Granada
, but continued to support his family in Baza. He published many works and eventually retired to his native Baza. He spent seven years living in Tlemcen
, where he studied under the local Berber scholars, the most important of which was a man named Ibn Zaghu.
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
forces of Ferdinand
and Isabella
, "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
, Tunisia
, where he died in 1486. Baza was eventually besieged by the forces of Ferdinand and Isabella and its inhabitants sacked.
. Certainly these symbols were not the invention of al-Qalaṣādī. The same ones had been used by other Muslim mathematicians in North Africa 100 years earlier, just like Diophantus
and Brahmagupta
in ancient times. Al-Qalaṣādī represented mathematical symbols
using characters from the Arabic alphabet
, where:
As an example, the equation
would have been written using his notation as:
2ﻙ ﻭ 3ﻡ ﻻ 4ﺵ ﻭ 5 ﻝ 0
Islamic mathematics
In the history of mathematics, mathematics in medieval Islam, often termed Islamic mathematics or Arabic mathematics, covers the body of mathematics preserved and developed under the Islamic civilization between circa 622 and 1600...
from Al-Andalus
Andalusia
Andalusia is the most populous and the second largest in area of the autonomous communities of Spain. The Andalusian autonomous community is officially recognised as a nationality of Spain. The territory is divided into eight provinces: Huelva, Seville, Cádiz, Córdoba, Málaga, Jaén, Granada and...
specializing in Islamic inheritance jurisprudence
Islamic inheritance jurisprudence
Islamic Inheritance jurisprudence is a field of Islamic Jurisprudence 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 known as ʿulm al-farāʾiḍ...
. Al-Qalaṣādī is known for being one of the most influential voices in algebraic notation
Mathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...
since antiquity and for taking "the first steps toward the introduction of algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
ic symbolism." He wrote numerous books on arithmetic
Arithmetic
Arithmetic or arithmetics is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. It involves the study of quantity, especially as the result of combining numbers...
and algebra, including al-Tabsira fi'lm al-hisab ( "Clarification of the science of arithmetic").
Early life
Al-Qalaṣādī was born in BazaBaza, Granada
Baza is a town in the province of Granada in southern Spain. It has 21,000 inhabitants . It is situated at 844 m above sea level, in the Hoya de Baza, a valley of the Sierra Nevada, not far from the Gallego River. This town gives its name to the Sierra de Baza...
, an outpost of the Emirate of Granada
Emirate of Granada
The Emirate of Granada , also known as the Nasrid Kingdom of Granada , was an emirate established in 1238 following the defeat of Muhammad an-Nasir of the Almohad dynasty by an alliance of Christian kingdoms at the Battle of Las Navas de Tolosa in 1212...
. He received education in Granada
Granada
Granada is a city and the capital of the province of Granada, in the autonomous community of Andalusia, Spain. Granada is located at the foot of the Sierra Nevada mountains, at the confluence of three rivers, the Beiro, the Darro and the Genil. It sits at an elevation of 738 metres above sea...
, but continued to support his family in Baza. He published many works and eventually retired to his native Baza. He spent seven years living in Tlemcen
Tlemcen
Tlemcen is a town in Northwestern Algeria, and the capital of the province of the same name. It is located inland in the center of a region known for its olive plantations and vineyards...
, where he studied under the local Berber scholars, the most important of which was a man named Ibn Zaghu.
In 1480 the Christian
Christian
A Christian is a person who adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus of Nazareth as recorded in the Canonical gospels and the letters of the New Testament...
forces of Ferdinand
Ferdinand II of Aragon
Ferdinand the Catholic was King of Aragon , Sicily , Naples , Valencia, Sardinia, and Navarre, Count of Barcelona, jure uxoris King of Castile and then regent of that country also from 1508 to his death, in the name of...
and Isabella
Isabella I of Castile
Isabella I was Queen of Castile and León. She and her husband Ferdinand II of Aragon brought stability to both kingdoms that became the basis for the unification of Spain. Later the two laid the foundations for the political unification of Spain under their grandson, Charles V, Holy Roman Emperor...
, "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
Beja is a town in Tunisia, Africa. It is the capital of the Béja Governorate. It is located 105 km from Tunis, between the Medjerdah River and the Mediterranean, against the foothills of the Khroumire, the town of Beja is situated on the sides of Djebel Acheb, facing the greening meadows,...
, Tunisia
Tunisia
Tunisia , officially the Tunisian RepublicThe long name of Tunisia in other languages used in the country is: , is the northernmost country in Africa. It is a Maghreb country and is bordered by Algeria to the west, Libya to the southeast, and the Mediterranean Sea to the north and east. Its area...
, 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 made attempts at creating an algebraic notationMathematical notation
Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...
. Certainly these symbols were not the invention of al-Qalaṣādī. The same ones had been used by other Muslim mathematicians in North Africa 100 years earlier, just like Diophantus
Diophantus
Diophantus of Alexandria , sometimes called "the father of algebra", was an Alexandrian Greek mathematician and the author of a series of books called Arithmetica. These texts deal with solving algebraic equations, many of which are now lost...
and Brahmagupta
Brahmagupta
Brahmagupta was an Indian mathematician and astronomer who wrote many important works on mathematics and astronomy. His best known work is the Brāhmasphuṭasiddhānta , written in 628 in Bhinmal...
in ancient times. Al-Qalaṣādī represented mathematical symbols
Table of mathematical symbols
This is a listing of common symbols found within all branches of mathematics. Each symbol is listed in both HTML, which depends on appropriate fonts being installed, and in , as an image.-Symbols:-Variations:...
using characters from the Arabic alphabet
Arabic alphabet
The Arabic alphabet or Arabic abjad is the Arabic script as it is codified for writing the Arabic language. It is written from right to left, in a cursive style, and includes 28 letters. Because letters usually stand for consonants, it is classified as an abjad.-Consonants:The Arabic alphabet has...
, where:
- ﻭ (waWaw (letter)Waw is the sixth letter of the Northwest Semitic family of scripts, including Phoenician, Aramaic, Hebrew, Syriac, and Arabic ....
) means "and" for additionAdditionAddition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
(+) - ﻻ (illaIlla (Arabic)The Arabic word illa is a negative word corresponding to the English except, only and but.-Use:It is an often reacurring phrase in the Qur'an, often used to give strength to statements by first negating all possibilities, and then referring to a subject...
) means "less" for subtractionSubtractionIn arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
(-) - ف (fi) means "times" for multiplicationMultiplicationMultiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
(*) - ة (ala) means "over" for divisionDivision (mathematics)right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
(/) - ﺝ (jGIMGIM or Gim may refer to:*Generation Investment Management, a London-based investment management firm*Goa Institute of Management, a business school*Gruppe Internationale Marxisten, a Trotskyist group...
) represents jadah meaning "root" - ﺵ (shShin (letter)Shin literally means "Sharp" ; It is the twenty-first letter in many Semitic abjads, including Phoenician , Aramaic/Hebrew , and Arabic ....
) represents shay meaning "thing" for a variableVariable (mathematics)In mathematics, a variable is a value that may change within the scope of a given problem or set of operations. In contrast, a constant is a value that remains unchanged, though often unknown or undetermined. The concepts of constants and variables are fundamental to many areas of mathematics and...
(x) - ﻡ (mMîmMîm is a fictional character in J. R. R. Tolkien's fictional universe of Middle-earth. He is introduced in The Silmarillion as the last of the Petty-dwarves....
) represents mal for a square (x2) - ﻙ (k) represents kab for a cube (x3)
- ﻝ (lLam-Lam:*Mor lam, an ancient Lao form of song in Laos and Isan*Lam saravane, a music genre*Lam luang, a music genre*Lam, Germany, a town in Bavaria-LAM:*Lactational amenorrhea method, a contraceptive method...
) represents yadilu for equality (=)
As an example, the equation
would have been written using his notation as:2ﻙ ﻭ 3ﻡ ﻻ 4ﺵ ﻭ 5 ﻝ 0