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# Abū al-Ḥasan ibn ʿAlī al-Qalaṣādī

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 algebraic symbolism." He wrote numerous books on arithmetic and algebra, including al-Tabsira fi'lm al-hisab (Arabic: التبصير في علم الحساب "Clarification of the science of arithmetic").[1]

Early life

Al-Qalaṣādī was born in Baza, 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.

Historic map of 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 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.

Symbolic algebra

Like his predecessors al-Qalaṣādī made attempts at creating an algebraic notation. 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,[1] just like Diophantus and Brahmagupta in ancient times. Al-Qalaṣādī represented mathematical symbols using characters from the Arabic alphabet, where:[1]

ﻭ (wa) means "and" for addition (+)

ﻻ (illa) means "less" for subtraction (-)

ف (fi) means "times" for multiplication (*)

ة (ala) means "over" for division (/)

ﺝ (j) represents jadah meaning "root"

ﺵ (sh) represents shay meaning "thing" for a variable (x)

ﻡ (m) represents mal for a square (\( x^2 \))

ﻙ (k) represents kab for a cube (\( x^3 \))

ﻝ (l) represents yadilu for equality (=)

As an example, the equation \( 2x^3 + 3x^2 - 4x + 5 = 0 \) would have been written using his notation as:

2ﻙ ﻭ 3ﻡ ﻻ 4ﺵ ﻭ 5 ﻝ 0

See also

Islamic mathematics

Notes

^ a b c O'Connor, John J.; Robertson, Edmund F., "Abu'l Hasan ibn Ali al Qalasadi", MacTutor History of Mathematics archive, University of St Andrews.

References

Rebstock, Ulrich (1990). "Arabic Mathematical Manuscripts in Mauretania". Bulletin of the School of Oriental and African Studies (University of London) 52 (3): 429–441. JSTOR 618117.

Boyer, Carl B. (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc.. ISBN 0-471-54397-7.

External links

Saidan, A. S. (2008) [1970-80]. "Al-Qalaṣādī (or Al-Qalaṣādī), Abu ’L-Ḥasan ‘Alī Ibn Muḥammad Ibn ‘Alī". Complete Dictionary of Scientific Biography. Encyclopedia.com.

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