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Bilinen niceliklerle yapılan işlemlerin ötesinde, bilinmeyen niceliklerle yapılan işlemlerin dahi arka planı, eski çağ uygarlıklarına kadar dayanır. Bu işlemlerden dikkat çekici olanlardan birisi de “yanlış yolu ile çözüm” metodudur. Esas prensibi rastgele bir tahmine dayanan “yanlış yolu ile çözüm”, cebirsel ifadeler veyahut bayağı kesirlerden doğacak muhtemel zorluklara hiç fırsat verilmeden, bilinmeyen niceliklerle oldukça hızlı ve basit işlemler yapılmasını sağlayan en yaygın metotlardan biridir. Avrupa’da da uzun yıllar kullanılan “yanlış yolu ile çözüm”e, Osmanlıların hem medrese kitaplarında, hem de muhasebe kaleminin (bürokrasinin) kaynak olarak kullandığı matematik kitaplarında yer verilmesi, bu hususta bir gelenek oluşturmuş ve bu metot, klasik dönem Osmanlı matematiğinde hesap ilminin ayrılamaz bir parçası haline gelmiştir. Aslında tek yanlış ve çift yanlış olmak üzere iki tür olan bu metot, bu dönemdeki eserlerde, çift yanlış metodunun önemine binaen “Hata’eyn (Çift yanlış)” başlığı altında işlenir. Çünkü, tek yanlış metodu, ax=b tipinde bir denklemi temsil eden problemlerde uygulandığı için esasında basit bir orantıya dayalıdır. Yanlışların aynı veya farklı işarette bulunmasına göre iki alt türe ayrılan çift yanlış metodu ise, “genellikle” ax+b=c tipindeki denklemleri temsil eden problemlerde, cebirsel işlemlere başvurmaksızın uygulanabildiği için daha fazla vurgulanmıştır. Klasik dönem Osmanlı matematiğini biçimlendiren ilk metinlerden bazıları, eğitim kurumlarında benimsenen Ali Kuşçu’nun el- Muhammediyye fî el-Hisâb’ı (15. asrın sonu) ve muhasebeciler arasında benimsenen Hacı Atmaca el-Kâtib’in Mecmaʻu’l-Kavâid fî Beyâni Müntehâbi’l-Fevâid’inin (15. asrın sonu) yanı sıra, Fatih Sultan Mehmed dönemine ait olan Hayrettin Halil bin İbrahim’in Miftâh-ı Künûz-ı Erbâb-ı Kalem ve Misbâh-ı Rumûz-ı Ashâb-ı Rakam isimli Farsça eseri (15. asrın sonu) ile bunun Pir Mahmud Sıdkı Edirnevî (16. asrın başı) tarafından yapılan tercümesidir. Çalışmamızda, Edirnevî’nin tercümesi üzerinden, çift yanlış yoluyla çözüm metodunu analiz etmek suretiyle, 15. asrın sonu ve 16. asrın başında Osmanlı matematiğine yapılan katkıları ortaya çıkarmak amaçlanmıştır. Bu eserler özellikle muhasebecilere hitap etmekte olduğu için muhasebe kaleminin kendine özgü uygulamaları göz önünde bulundurularak metin ele alınmıştır. Konunun tarihsel arka planından bahsedildikten sonra, eser ve incelenen metne temas edilmiştir. Daha sonra, metnin matematiksel içeriğine yer verilmiştir. Böylece, metindeki çözümlü problemlerle ilgili en önemli tespitler sunularak, aritmetikte son derece gözde bir konuma getirilen bu metoda Osmanlıların nasıl ve ne ölçüde yer verdiği değerlendirilmiş ve metodun uygulamalı bir matematik anlayışına yansıması belirlenmeye çalışılmıştır.
Beyond the processes made with known quantities, even the background of the processes made with unknown quantities stands up to ancient civilizations. One of these processes is the “solution by the wrong way” method. Basic principle is one of the most common methods to make processes very fast and simple with unknown amounts, without giving any opportunity to the potential challenges that will arise from misleading expressions, or considerable cuts. The "solution by the wrong way" used for many years in Europe, the place of the Ottomans in both the medrese books and the mathematical books in which the accounting pen (the bureaucracy) is used as a source, has created a tradition in this regard, and this method has become an inseparable part of accounting science in the classical period of Ottomans mathematics. In fact, this method, which is two types, one wrong and double wrong, is processed under the title "Hata'eyn (Double wrong)" based on the importance of the double wrong method in the works of this period. Because the only wrong method is based on a simple proportion because it is applied in problems that represent an equation in the ax=b type. If the double error method, which is divided into two subtypes according to the same or different signals, is more emphasized because it can be applied without reference to gaps in the problems that represent the equations of the "usually" ax+b=c type. For example, in the first half of the century, there was a number of different types of mathematics, such as mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics, mathematics and mathematics. The translation is made by the head. In our study, through the translation of Edirnevî, by analyzing the method of solution by double errors, it is intended to reveal the contributions made to Ottoman mathematics in the late 15th and early 16th centuries. These works are especially addressed to accountants, and the text has been addressed taking into account the own practices of the accounting pen. After discussing the historical background of the subject, the work and the text being studied were contacted. Then, the mathematical content of the text was placed. Thus, by submitting the most important findings regarding the solved problems in the text, this method, which has been put to a highly popular position in the arithmetic, has been tried to determine how and to what extent the Ottomans are involved and how the method is reflected in a practical mathematical understanding.
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. 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 15th 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 15th 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 15th century) and its Turkish translation made by Pir Mahmud Sıdkı Edirnevî (at the beginning of 16th century). In this study, it is aimed to reveal the contributions to Ottoman mathematics at the end of the 15th century and the beginning of the 16th 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.
Alan : Güzel Sanatlar; Sosyal, Beşeri ve İdari Bilimler
Dergi Türü : Ulusal
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