ʿAbd al-Qāhir al-Baghdādī

Abū Mansūr ʿAbd al-Qāhir ibn Tāhir al-Baghdādī ( Arabic أبو منصور عبدالقاهر ابن طاهر البغدادي, DMG Abū Manṣūr ʿAbd al-Qāhir ibn Ṭāhir al-Baġdādī ; born around 980; died 1037 ) was an Arab Muslim theologian and mathematician from Baghdad who belongs to the Shafi'ite school of law .

His name affix al-Shafi'i indicated the religious school to which he belonged and al-Tamimi the tribe. He grew up in Baghdad and went to Nishapur with his father . He spent part of his large private fortune on scholars and studies. After riots broke out in Nishapur, he went to the quieter town of Asfirayin. He is said to have taught there free of charge for several years in the mosque and was considered an important theologian.

While his treatise on the measurement of lengths, areas and volumes (Kitab fi'l misaha) is of little importance, his treatise al-Tamila fi'l Hisab has significance for the history of mathematics. There he deals with various computing systems, preferring the Indian numerals and arithmetic methods based on them, including the use of the abacus. Finger counting methods and the hexagesimal system , fractions and irrational numbers as well as commercial arithmetic are also discussed, including problems relating to entertainment mathematics. It contains references to a lost work by Al-Khwarizmi that is not based on the Indian decimal system, but based on finger counting methods. He also dealt with series of polygonal numbers .

He dealt with friendly numbers (previously Thabit ibn Qurra ), perfect numbers , deficient numbers and abundant numbers . In doing so, he corrected some of the claims made by Nicomachus of Gerasa about perfect numbers. He gave 945 as the smallest odd abundant number, which was rediscovered in the west by Bachet . He was the first to discuss equivalent numbers where the sum of the real divisors is equal.

Works

• Uṣūl ad-Dīn , systematic treatise on the foundations of the Islamic religion. Digitized version of the Istanbul 1928 print edition
• al-Farq baina l-firaq , work on the different schools of law ( Madhhab ) and the history of sects in Islam , which was translated into English by Kate Chambers Seelye under the title Moslem Schisms and Sects . Digitized
• al-Nāsiḫ wa-l-mansūḫ , Treatise on Abrogation . Ed. Ḥilmī Kāmil Asʿad ʿAbd al-Hādī. Amman 1987. Digitized
• al-Takmila fī l-ḥisāb , treatise containing results on arithmetic and number theory and comments on works by al-Chwarizmi that are no longer extant .
• Kitāb fī l-Misah , Treatise on Geometric Measures

literature

• AS Saidan: Al-Baghdadi, Abu Mansur 'Abd al-Quahir ibn Tahir ibn Muhammad ibn' Abdallah, Al-Tamimi, Al-Shafi'i , Dictionary of Scientific Biography , Volume 15, pp. 9-10

Web links

• O'Connor, John J .; Robertson, Edmund F. , Abu Mansur ibn Tahir al-Baghdadi , MacTutor History of Mathematics archive, University of St Andrews.
• at-tawhid.net: Biography of Imam al Baghdadi
• Literature by and about ʿAbd al-Qāhir al-Baghdādī in the catalog of the German National Library