The euclidean sectio canonis

Although a work of several hands, rather then of Euclid (active around 300 BCE), this short treatise (an introduction and 20 propositions formulated in the manner of theorems, preserved independently and, partially and slightly differently, in Porphyry and Boethius), is counted among the most important writings on ancient mathematical harmonics. The central part of the treatise could indeed be written by the great mathematician himself, undoubtedly, on the basis of the works of early authors, such as Archytas, while the rest, esp. the introduction, is admittedly a later addition. Despite few logical incontinences, the treatise as a whole is a unique early attempt at the composing of a systematic mathematical harmonics, based both on the empirical observations and an intrinsic logic of the division of the musical kanon. The treatise is translated into the Russian for the first time.