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Abū'l-Ḥasan ʿAlī ibn Muḥammad ibn ʿAlī al-Qurashī al-Qalaṣādī (Arabic: أبو الحسن علي بن محمد بن علي القرشي البسطي; 1412–1486) was a Muslim Arab mathematician from Al-Andalus specializing in Islamic inheritance jurisprudence. Franz Woepcke 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 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").

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.

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 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 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 then 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, these symbols had actually been used by other mathematicians in North Africa 100 years earlier. Al-Qalaṣādī represented mathematical symbols using characters from the Arabic alphabet, where:

• ﻭ (wa) means "and" for addition (+)
• إلا (illa) literally, "except"; means "less" for subtraction (−)
• في (fi) literally, "in"; means "times" for multiplication (*)
• على (ala) means "over" for division (/)
• ﺝ (j) represents jadah meaning "root"
• ﺵ (sh) represents shay' meaning "thing" for a variable (x)
• ﻡ (m) represents maal for a square (x)
• ﻙ (k) represents moka'aab for a cube (x)
• ﻝ (l) represents ya'adilu for equality (=)

See also

• Islamic mathematics
• List of Muslim scientists

Notes

1. ^ O'Connor, John J.; Robertson, Edmund F., "Abu'l Hasan ibn Ali al Qalasadi", MacTutor History of Mathematics Archive, University of St Andrews
2. Karpinski, Louis Charles (1965). The history of arithmetic. Russell & Russell. ISBN 9780846206316.

References

• Rebstock, Ulrich (1990). "Arabic Mathematical Manuscripts in Mauretania". Bulletin of the School of Oriental and African Studies. 52 (3): 429–441. doi:10.1017/s0041977x0015133x. JSTOR 618117. S2CID 162679825.
• Boyer, Carl B. (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 978-0-471-54397-8.

External links

• Saidan, A. S. (2008) . "Al-Qalaṣādī (or Al-Qalaṣādī), Abu 'L-Ḥasan 'Alī Ibn Muḥammad Ibn 'Alī". Complete Dictionary of Scientific Biography. Encyclopedia.com.

v t e Mathematics in the medieval Islamic world
Mathematicians	9th century 'Abd al-Hamīd ibn Turk Sanad ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Qusta ibn Luqa Al-Mahani al-Dinawari Banū Mūsā brothers Hunayn ibn Ishaq Al-Khwarizmi Yusuf al-Khuri Ishaq ibn Hunayn Na'im ibn Musa Thābit ibn Qurra al-Marwazi Abu Said Gorgani 10th century Abu al-Wafa al-Khazin Al-Qabisi Abu Kamil Ahmad ibn Yusuf Aṣ-Ṣaidanānī Sinān ibn al-Fatḥ al-Khojandi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus al-Uqlidisi Al-Battani Sinan ibn Thabit Ibrahim ibn Sinan Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud Al-Sijzi Al-Karaji al-Majriti al-Jabali 11th century Abu Nasr Mansur Alhazen Kushyar Gilani Al-Biruni Ibn al-Samh Abu Mansur al-Baghdadi Avicenna al-Jayyānī al-Nasawī al-Zarqālī ibn Hud Al-Isfizari Omar Khayyam Muhammad al-Baghdadi 12th century Jabir ibn Aflah Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi al-Hassar Sharaf al-Din al-Tusi Ibn al-Yasamin 13th century Ibn al‐Ha'im al‐Ishbili Ahmad al-Buni Ibn Munim Alam al-Din al-Hanafi Ibn Adlan al-Urdi Nasir al-Din al-Tusi al-Abhari Muhyi al-Din al-Maghribi al-Hasan al-Marrakushi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Ibn al-Banna' Kamāl al-Dīn al-Fārisī 14th century Nizam al-Din al-Nisapuri Ibn al-Shatir Ibn al-Durayhim Al-Khalili al-Umawi 15th century Ibn al-Majdi al-Rūmī al-Kāshī Ulugh Beg Ali Qushji al-Wafa'i al-Qalaṣādī Sibt al-Maridini Ibn Ghazi al-Miknasi 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi
Mathematical works	The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Book on the Measurement of Plane and Spherical Figures Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij
Concepts	Alhazen's problem Islamic geometric patterns
Centers	Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi ad-Din Madrasa Maragheh observatory University of al-Qarawiyyin
Influences	Babylonian mathematics Greek mathematics Indian mathematics
Influenced	Byzantine mathematics European mathematics Indian mathematics
Related	Hindu–Arabic numeral system Arabic numerals (Eastern Arabic numerals, Western Arabic numerals) Trigonometric functions History of trigonometry History of algebra

• 1412 births
• 1486 deaths
• 15th-century Arab people
• People from the Province of Granada
• Mathematicians from al-Andalus
• 15th-century mathematicians
• Jurisprudence academics
• Mathematicians who worked on Islamic inheritance
• Scholars of the Nasrid period
• 15th-century Spanish mathematicians