The Contribution of the Publication of 2 Manuscripts of the 15th and the 18th C. to the Science of the History of Mathematics

Maria Chalkou

Review of the National Center for Digitization, Tome 45 (2024), p. 12

Résumé

The paper concerns topics of arithmetic, algebra and geometry which are included in the publication of the Codex Vindobonensis phil. Gr. 65 ff. (11r-126r) of the 15th c. (Chalkou, 2006), and of the manuscript 72 of the 18th c. of the historical Library of Demetsana (Chalkou, 2009). During the study of the 2 manuscripts the interest mainly focused on the mathematical analysis of the methods of the authors, and their significance in the development of the History of Mathematics. The paper also aims to highlight the necessity of easier and broader access to the Sources of Cultural Heritage and the value of digitizing its archives. We attempt to briefly describe the time the 2 codes were written, the language, the influences and the mathematical fields which comprise their content. We make known the findings which consolidated the view that the Byzantine manuscripts the Mathematical Encyclopedia of the Byzantines, while the manuscript 72 of the 18th c. is one of the first texts with non-elementary Mathematics during Ottoman rule, and it includes Euclidean Geometry by Nikephoros Theotokes, topics of algebra but also the commercial Mathematics of the Byzantines. From the ‘Mathemataria’ which were found in the School of Demetsana it is evident that the students were taught, among other things, theoretical and practical arithmetic as well as Euclidean geometry from the manuscript 72, which covered syllabus of today’s junior and senior high school. The School was considered higher, and certain manuscripts which were found in its library contain material which is basic but of university level. The anonymous author of Codex 65 writes that his main source is the work of Greek scholars, and that he has been influenced by the Hindus, the Chinese and the Persians through the Latin scholars due to the commercial transactions between the Byzantines and the West. In the Codex 65we discovered categories of problems whose solution is achieved through methods unknown to this day. During the research we studied reliable sources of the History of Mathematics in which no data related to these methods were found (Loria and Kovaios, 1972) and (Heath, 1921) and (Smith, 1958). Then certain methods led us to formulate and prove new mathematical propositions in the field of number theory.

Détail

Keywords: Byzantine Mathematics, number theory, Mathematics of the 18th c. in the Greek schools, geometry by Nikephoros Theotokes