Bostanîzâde Mehmet Tahir Pasha his work titled Usûl-i Jabr

The subject of our thesis is the transliteration, simplification and content analysis of the mathematical work Usûl-i Cebr written by Bostanîzâde Mehmet Tahir Pasha, one of the mathematicians who lived in the Ottoman Empire in the 19th century. "Usûl-i Cebr" means the principles on which the science of algebra is based and the methods of teaching it. Usūl al-Jabr, which was taught as a textbook in military schools, presents both the principles of algebra and teaching methods together. After briefly reviewing the scientific life of the Ottoman Empire in the classical period and the works on the science of algebra, we will discuss the developments in Ottoman algebra education and the formation of the Ottoman algebra tradition, especially the works of scholars from the Samarkand school. In addition to bibliographic data on the algebra chapters in the calculus books written in the classical Ottoman period, the works written in the classical style during the transition from the classical period to the modern period are discussed under headings. After briefly touching upon the changes in Ottoman education and science, attention is drawn to the place of Bostanizade Mehmet Tahir Pasha's Usûl-i Cebr in algebra education at the Mekteb-i Harbiye, which was founded in 1834. This chapter also examines the scope, nature and importance of algebra education, one of the main branches of mathematics at the Mekteb-i Harbiye established in 1834 and emphasizes the place of algebra education in modern education. In Chapter One, Bostanîzâde Mehmet Tahir Pasha's life, education, career and other works are discussed under separate headings. Mehmet Tahir was one of the first students sent abroad during the reign of Sultan Mahmud II (1808-1839). Mehmed Tahir studied in England, probably in Cambridge, and after returning home, he worked as a teacher and lecturer at the Harbiye Mektebi for many years. Mehmed Tahir Pasha preferred to compose a direct work on 'algebra', which he felt was lacking in education, rather than translating it. Among the students trained by Tahir Pasha was Vidinli Hüseyin Tevfik Pasha, the author of Linear El-Cebra. Since Vidinli Tevfik Pasha made an addendum to his teacher's book Usul-i Jabr, we had to partially mention his work. The main body of our thesis is the transliteration of Usûl-i Jabr. Naturally, before the simplification, the transliteration of the work -except for the studies- was done and placed in the third chapter of this thesis. Only after an intensive and sensitive studying on this work, a mathematical evaluation was possible. Usûl-i Cebr is a book that deals with the basic concepts and problems of algebra, emphasizes the importance of algebra in mathematics education and research of the period, and is quite comprehensive. The work consists of a total of 186 articles under 37 topics and an introduction. In the introduction, the author explains the reason for writing the work after the hamdele, salvala and prayers that are found in the classical Ottoman scientific literature. When I was appointed as a lecturer at the Mekteb-i Harbiye-i Şahane, I had prepared retail notes for the students through translations from foreign languages. Subsequently, since it was inevitable that these notes would be scattered and used for other works, I was determined to bring these scattered notes together. Tahir Pasha pointed out that the first volume of the Mecmua-i Ulum-ı Riyaziye, written by Hacı Hafız İshak Efendi, the former head teacher of the Mühendishane-i Berri-i Hümayun, contained some rules on algebra, and that there were a few other treatises on the subject translated from European languages, the translators of which were unknown, but all of these were quite inadequate and remained at an elementary level. However, according to the author, the science of algebra encompasses many methods and rules and requires a specialized education in its application. Considering all this, Tahir Pasha finally found the opportunity to complete his work, which had been a longtime ambition of his, during the reign of Sultan Abdülmecid Khan. He named it "Usul-i Cebr". In our thesis, the algebra courses at Mekteb-i Harbiye, the professors who taught algebra, the books on algebra written by these people and their contents were also investigated. First of all, the curriculum of Mekteb-i Harbiye was analyzed and the relevant data were identified. Finally, the transliteration, simplification and content analysis of Tahir Pasha's Usûl-i Cebr were analyzed. At the end of the thesis, a glossary of the mathematical terms in the work was prepared and presented to the readers.