The First Treatise on Mathematics Written in Anatolia: Amīn-al-Dīn al-Abhari’s (d. 1333) Work Entitled Fuṣūl Kāfīya fī Ḥisāb at-Taḫt wa-’l-Mīl / Anadolu’da Yazılan İlk Matematik Risâlesi: Emînüddin Ebherî’nin Fuṣūl Kāfīye fī Ḥisābi’t- Taḫt ve’l-Mīl Adlı Eseri

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Baga E.

1. Uluslararası Prof. Dr. Fuat Sezgin İslâm Bilim Tarihi Sempozyumu, İstanbul, Turkey, 13 - 15 June 2019, pp.231-246

  • Publication Type: Conference Paper / Full Text
  • Doi Number: 10.26650/pb/aa08.2020.001
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.231-246


Mathematics is one of the sciences that have received remarkable interest and then soared with quick acceleration since the very beginning of the
tradition of science in Islamic civilization. While one justification for this relevance is that mathematics was viewed superior in terms of not being
dependent on any one science with many sciences dependent on it, another justification is that, because it is a tool of science, the simplification
and perfection of work done or knowledge produced both theoretically as well as pragmatically in every field, the authenticity, and the accuracy
depend on mathematics. In this interval after the great Turkification and Islamization of Anatolian lands in the 13th century, math books began to
be produced and educational activities carried out through these books in Anatolia as well, just as in other regions of the Islamic geography. The
earliest recorded surviving mathematics book produced in Anatolia, according to recent research, is the work, Fuṣūl Kāfīya fī Ḥisāb at-Taḫt wa-
’l-Mīl [Sufficient Chapters for Arithmetic using a Board and Stick (with Sharp End)/ فصول كافية في حساب التخت والميل ], which was probably compiled
in the first quarter of the 14th century in Arabic by Amīn-al-Dīn al-Abharī (d. 1333 CE), born in Sivas and the grandson of Athīr-al-Dīn al-Abharī
(d. 1265 CE). The text constructed in the first 10 chapters on the patterns and placement of numbers, doubling, halving, adding, subtracting,
multiplying, dividing, finding the square root, finding the cube root, and proving arithmetic operations is based on the Indian (Hindu, 10-base
number system) and sexagesimal (Babylonian, 60-base number system) arithmetic from the Indian, Hawai (mental arithmetic), and sexagesimal
types of arithmetic. The treatise in this context can be said to represent the starting point in the Anatolian geography for being able to recognize,
disseminate, and reproduce in accordance with the changing needs the 10-base and 60-base number systems and all arithmetic operations done
with respect to these systems. Owing to all this importance and the justifications in this treatise, its role in the formation and development of the
Ottoman mathematics tradition will be discussed by introducing the first mathematics book written in Anatolia.
Keywords: History of mathematics, İslamic mathematics, Mathematics in Medieval, Anatolia Amīn-al-Dīn al-Abharī, Fuṣūl Kāfīya fī Ḥisāb at-Taḫt