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Abū al-Ḥassan, Aḥmad Ibn Ibrāhīm, al-Uqlīdisī (Arabic: أبو الحسن أحمد بن ابراهيم الإقليدسي, fl. 952) was a mathematician of the Islamic Golden Age, possibly from Damascus, who wrote the earliest surviving book on the use of decimal fractions with Hindu–Arabic numerals, Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī (The Book of Chapters on Hindu Arithmetic), in Arabic in 952. The book is well preserved in a single 12th century manuscript, but other than the author's name, original year of publication (341 AH, 952/3 AD) and the place (Damascus) we know nothing else about the author: after an extensive survey of extant reference material, mathematical historian Ahmad Salīm Saʿīdān, who discovered the manuscript in 1960, could find no other mention of him. His nickname al-Uqlīdisī ("the Euclidean") was commonly given to people who sold manuscript copies of Euclid's Elements.

In the introductory remarks to his Arithmetic, Al-Uqlīdisī claims that he traveled to confer with every arithmetic expert he knew of, and read every previous book he could find, and comprehensively synthesized this previous work while adding his own ideas. The Arithmetic describes the main calculation methods of medieval Islamic arithmetic, including finger reckoning, the Greco-Babylonian sexagesimal system commonly used for astronomy, calculations with fractions, and positional decimal calculations using the Hindu–Arabic system performed using the dust board and stylus. It is especially notable for its treatment of decimal fractions, and for showing how to calculate using pen and paper rather than an erasable dust board.

While the Persian mathematician Jamshīd al-Kāshī claimed to have discovered decimal fractions himself in the 15th century, J. Lennart Berggren notes that he was mistaken, as decimal fractions were first used five centuries before him by al-Uqlidisi as early as the 10th century.

A. S. Saidan who studied al-Uqlidisi's mathematical treatise in detail wrote:

The most remarkable idea in this work is that of decimal fraction. Al-Uqlidisi uses decimal fractions as such, appreciates the importance of a decimal sign, and suggests a good one. Not al-Kashi (d. 1436/7) who treated decimal fractions in his "Miftah al-Hisab", but al-Uqlidisi, who lived five centuries earlier, is the first Muslim mathematician so far known to write about decimal fractions.

Notes

1. ^ Saidan 1978.
2. MS 802 at Yeni Cami Library, Istanbul, written in 582 AH (1186 AD)
3. Berggren 2007.
4. O'Connor & Robertson 1999.

References

• Berggren, J. Lennart (2007). "Mathematics in Medieval Islam". The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook. Princeton University Press. p. 518. ISBN 978-0-691-11485-9.
• Brentjes, Sonja (2005). "Uqlidisi, Al-". In Glick, Thomas; Livesey, Steven John; Wallis, Faith (eds.). Medieval Science, Technology, and Medicine: An Encyclopedia. Routledge. p. 499. ISBN 978-0-415-96930-7.
• O'Connor, John J.; Robertson, Edmund F. (1999). "Abu'l Hasan Ahmad ibn Ibrahim Al-Uqlidisi". MacTutor History of Mathematics Archive. University of St Andrews.
• Saidan, A. S. (1966). "The Earliest Extant Arabic Arithmetic: Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī of Abū al-Ḥassan, Aḥmad Ibn Ibrāhim, al-Uqlīdisī". Isis. 57 (4): 475–490. JSTOR 228518.
• Saidan, A. S. (1976). "Al-Uqlīdisī, Abu'l-Ḥasan Aḥmad Ibn Ibrāhīm". In Gillispie, Charles C. (ed.). Dictionary of Scientific Biography. Vol. 13 – Staudinger–Veronese. New York: Charles Scribner's Sons / American Council of Learned Societies. pp. 544–546. ISBN 0-684-12925-6.
• Saidan, A. S., ed. (1978). The Arithmetic of Al-Uqlīdisī: The Story of Hindu–Arabic Arithmetic as told in the Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Dordrecht: D. Reidel. doi:10.1007/978-94-009-9772-1. ISBN 978-94-009-9774-5.

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

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