Pir Mahmud Sıdkı Edirnevi’s Double False Position Method in the Traditional Period of Ottoman Mathematics

Abstract

Beyond the operations with known numbers, even the operations with unknown numbers date back to ancient times. One of the remarkable of these operations is the “false position” method. This method has been preferred for centuries, since it simplifies the solution of the problems, when some arithmetical and algebraic methods make the operations complicated. The method which is known to be treated intensely in both Eastern and Wastern civilization in the Middle Ages, was also adopted by Ottoman mathematicians. It is not neglected to explain this method in the arithmetical texts which increased in number, in the traditional period. So the method has become an integral part of the arithmetical texts which is used by both in madrasah and in accounting bureaucracy.

In fact, this method which is two type as single and double false, is treated under the title of ‘Hata’eyn (double false) in these arithmetical texts, based on the importance of the double false position method. The double false position method is much more emphasized in these texts, as it is far beyond a simple proportion as in the single false method. 151 

Some of the first mathematical texts in the traditional period of Ottomans are not only Ali Qushji’s el-Muhammediyye fî el-Hisâb which was adopted in madrasahas (at the end of the 15^th century) and Hadji Atmaca el-Katib’s Mecma el-Kavâid fî Beyâni Muntehâb el-Fevâid which was adopted among the accounters (at the end of the 15^th century), but also Hayrettin Halil bin İbrahim’s Persian text titled Miftâh-ı Künûz-ı Erbâb-ı Kalem ve Misbâh-ı Rumûz-ı Ashâb-ı Rakam (at the end of the 15^th century) and its Turkish translation made by Pir Mahmud Sıdkı Edirnevî (at the beginning of 16^th century). In this study, it is aimed to reveal the contributions to Ottoman mathematics at the end of the 15^th century and the beginning of the 16^th century by analyzing Pir Mahmud Sıdkı Edirnevi’s “double false position” method, in the seventh chapter of his arithmetical text written for accountants. In this context, after mentioning the historical background of the subject, the examined text were handled, briefly. Then, mathematical content and analysis of the text were presented. Thus, it was discussed how the Ottomans evaluated this method, through the findings about the problems in the text and also it is tried to be determined how it is seen on practical mathematics with its effects.