Euclid (EN)

Euclid, Eukleídes, ca. 3rd/4th century BC, Greek mathematician. He worked in Alexandria. Author of Stoicheía geometrías (‘elements of geometry’), which was the standard geometry textbook until the time of Descartes. The musical treatise Katatomé kanónos (‘divisions of the monochord’), traditionally attributed to him, falls within the scope of Pythagorean science. Euclid expressed musical intervals in numerical ratios. He used numerical proportions as a criterion for distinguishing between consonances and dissonances. Katatomé kanónos is the oldest source of data on the monochord and the Greek sound system. It also contains important information on acoustics based on the observation of string vibrations. Euclid’s division of the monochord became a model for Nicomachus, Theon of Smyrna, Aristides Quintilianus, and Ptolemy. The treatise Eisagogé harmoniké (‘harmonic introduction’), attributed to Euclid, was probably written by Cleonides. 

Literature: L. S. Wantzloeben Das Monochord…, Halle 1911; Árpád Szabó The beginnings of Greek Mathematics, Budapest 1978; A.C. Bowen Euclid’s Sectio canonis and the History of Pythagoreanism, “Science and Philosophy in Classical Greece” (New York, 1991); A.M. Laskowska Euklidesowy traktat Podział kanonu i pitagorejska harmonika, “Argument. Biannual Philosophical Journal” 11, 2/2021, ibid. Polish translation.