Calculation in the Ottoman Classical Period and Dervish Bin Lutfi’s ApproachTuba Oğuz Ceyhan, Halime Mücella Demirhan Çavuşoğlu
Books and treatises on calculation written during the Ottoman classical period, which handled the operations between numbers and their properties, benefited from Mashrik, Maghreb, and Mamluk mathematical traditions. The Ottomans combined these traditions with their own contributions and produced texts in different genres, such as commentaries, translations, and original works. One of the most important of these works is the supplementary translation (translation with commentary) of the Mamluk mathematician Garseddin ibn Nakib’s book titled Kitâbü’t-Tezkire fî İlmi’lHisâb into Turkish by his former student and mathematician Dervish bin Lutfi. Dervish bin Lutfi seems to have included a considerable amount of information in his translation, which is not found in the original work and is rarely found in other Ottoman calculation books. Furthermore, he aimed at a larger target audience. Our study evaluates Dervish bin Lutfi’s translation by combining the historical method, conducted with the help of primary and secondary sources, and the mathematical analysis method.
Osmanlı Klasik Döneminde Hesap ve Derviş Bin Lütfi’nin YaklaşımıTuba Oğuz Ceyhan, Halime Mücella Demirhan Çavuşoğlu
Sayılar arasındaki işlemler ve özelliklerini konu edinen “hesap” disipliniyle ilgili pek çok kitabın telif edildiği Osmanlı klasik döneminde, Maşrik, Mağrip ve Memlük matematik geleneklerinden yararlanılmıştır. Hatta Osmanlılar, bu gelenekleri kendi katkılarıyla mezcetmiş ve bazen yeni telif, bazen şerh, bazen ihtisar, bazen tercüme gibi farklı yazım türlerinde metinler kaleme almışlardır. Bunların en önemlilerinden biri, Derviş bin Lütfi’nin hocası Memlük matematikçisi Garseddin ibn Nakib’in Kitâbü’t-Tezkire fî İlmi’l-Hisâb isimli eserinden yaptığı ilaveli Türkçe tercümedir. Bu tercümede, eserin orijinalinde olmayan hatta diğer hesap kitaplarında nadir olarak rastlanan malumata yer verildiği ve hedef kitlenin genişletildiği anlaşılmıştır. Çalışmamızda, birincil ve ikincil kaynaklar yardımıyla takip edilen tarihsel yöntem, matematiksel analiz yöntemiyle birleştirilerek eserin değerlendirilmesi yapılmıştır.
Following the conquest of Istanbul, the Ottomans enjoyed a lively period regarding studies on mathematics with contributions initially from scholars from other lands (i.e., Ilkhanids or Mamluks) and later from scholars who were native to the Ottoman Realm. Arguably, the most productive contributions occurred in the field of “calculation” during the 16th century when the compilation of new texts in this context reached a remarkable degree of quality. Some of these works, which are significant for providing information on the level attained by the Ottomans in mathematics at that time, are still waiting to be thoroughly examined from the perspective of the history of Ottoman mathematics. Among them is a Turkish translation (1574) of the Arabic book on calculation titled Kitâbü’t-Tezkire fî İlmi’l-Hisâb, written by Garseddin Ahmed bin İbrahim bin el-Nakib el-Halebî, who arrived in Istanbul in the retinue of Yavuz Sultan Selim following the Ottomans’ military expeditions to the Mamluk realm. The book was translated by el- Halebî’s student Dervish bin Lutfi. It is, however, not a simple translation but a Turkish redaction, which was written in the same outline as Kitâbü’tTezkire fî İlmi’l-Hisâb while the content was greatly expanded. Therefore, it can be accepted as a “supplementary translation” (translation with commentary). Dervish bin Lutfi treated the text with contributions from Ottoman mathematicians in order to obtain more precise results rapidly. This is one piece of evidence showing that the Ottomans were adopting the mathematical traditions of various regions. Therefore, dervish bin Lutfi’s work stands out as a noteworthy example of Ottoman reception of the classical era’s calculation.
This study, which is based on a classical text, aims to examine Dervish bin Lutfi’s way of handling the “calculation” directly with this text’s accurate manuscript. First of all, the content of the text was introduced. Then, prominent issues in the text are mentioned in the footnotes, with their being quoted and their representations in modern mathematics. In conclusion, similarities or differences and superiority or weaknesses compared to the original book and other general calculation books from the Ottoman classical era were all considered during the evaluation of the text. For this purpose, the findings inferred from the manuscript copy -which is thought to be suitable and reliable- were analyzed by integrating them with information from other sources.
Findings indicate that the features and parts of the numbers, which are mentioned at the end of the preface of the text, are not always included in general calculation books in Ottomans or need to be adequately detailed. When it comes to Dervish bin Lutfi’s second article, which evidently distinguishes with his own contributions, and the way he covers the subject of fractions is entirely distinctive, it differs from the original of the text with the operations with “akche,” “cantar,” “zira,” “mud,” “mitgal” and their decimal fractions. In this second article, most problems are solved by the proportion method. Some notable ones are trading, inverse and compound proportion, inverse operation, and transforming a cubeshaped object into a sphere by eliminating its corners, work, pool, and “cumel calculation” (hesab-ı cumel) problems. The epilogue of the text is allocated to the subject of “mesaha”. It is understood that the author made a great effort to handle this subject. Here, it is possible to find traces of the definition of the mesaha and the historical background of the value of the number pi.
To sum up, the field of “calculation”, which was progressed by being integrated with algebra and geometry, had been used in practice for all operations related to the state and the community. Many books were compiled in the Ottoman classical period to teach the mathematical skills required to meet the needs of the state and community. These books contain knowledge from all Mashrik, Maghreb, and Egyptian mathematical traditions. In this regard, Dervish bin Lutfi’s work goes far beyond the original text of Garseddin ibn Nakib in terms of its scope. This is because both the article about fractional numbers and the chapter on “mesaha,” where many contributions can be observed, make the text useful in many professions and arts, such as law, bureaucracy, or architecture. It is essential to point out that although algebra is not treated in the work, on rare occasions, algebraic procedures are used to solve problems. This shows the advanced level of mathematics in the text and how competent and skillful the author and other Ottoman scholars were in this field. Thus, it is clear that the text examined here, which is a translation with commentary, holds a prominent place among general calculation books in the Ottoman period.