Quests for a General Method to Solve the Equations of High Degree in the History of Islamic Mathematics: The Case of Irshad al-tullab ila ‘ilm al-hisab


This article introduces a book titled Irshād al-tullāb ilā ‘ilm al-hisāb, written by an anonymous author who most probably lived in Ottoman lands, presented the book to Ottoman Sultan Bayezid II. In the epilogue of the book, the author presents an equation solving method, unknown up to its period according to our research, which he used to solve third, fourth, fifth and sixth degree equations whose degrees of variables are successively ordered. Following a short introduction on the subject, I first summarize the history of solving methods for third and higher degree equations, and then I examine the mathematical analysis of the book’s epilogue. After a short conclusion, I present the Arabic text of the manuscript and its Turkish translation.


Equations of High Degree Algebra in the Ottomans Mathematics in the Ottomans Equations Solving Methods Irshād al-tullāb