Abstracts
Abstract
A new interpretation is proposed of the crucial expression «ἑνὶ ὀνόματι» (“in one name”) as applied to ratios of the musical concords in the preface of the Sectio canonis ascribed to Euclid. A link is also established with the name of one of the irrational lines introduced by Euclid in Elements 10. Past interpretations of the expression are discussed and shown to be inadequate.
Keywords:
- Greek harmonic science,
- Concordance,
- Euclid,
- Sectio canonis,
- ἑνὶ ὀνόματι
Appendices
Bibliography
- Acerbi, F. 2008. “In What Proof Would a Geometer Use the ποδιαία?” Classical Quarterly 58:120–126.
- Acerbi, F. and B. Vitrac. 2014. edd. Héron d’Alexandrie, Metrica. Mathematica Graeca Antiqua 4. Pisa/Rome.
- Barbera, A. 1991. The Euclidean Division of the Canon: Greek and Latin Sources. Lincoln, NB/London.
- Barker, A. 1981. “Methods and Aims in the Euclidean Sectio Canonis”. Journal of Hellenic Studies 101: 1–16.
- Barker, A. 1984–1989. Greek Musical Writings. 2 vols. Cambridge, UK.
- Barker, A. 1994. “Ptolemy’s Pythagoreans, Archytas, and Plato’s Conception of Mathematics”. Phronesis 39: 113–135.
- Barker, A. 2000. Scientific Method in Ptolemy’s Harmonics. Cambridge, UK.
- Bonitz, H. 1849. Commentarius in Aristotelis metaphysicam. Bonn.
- Bowen, A. C. 1991. “Euclid’s Sectio canonis and the History of Pythagoreanism”. Pp. 164–187 in A. C. Bowen ed. Science and Philosophy in Classical Greece. New York/London.
- Burkert, W. 1972. Lore and Science in Ancient Pythagoreanism. Cambridge, MA.
- Cathala, M.-R. 1935. ed. S. Thomae Aquinatis doctoris angelici O. P. in metaphysicam Aristotelis commentaria. Torino.
- Düring, I. 1930. ed. Die Harmonielehre des Klaudios Ptolemaios. Göteborg.
- Düring, I. 1932. ed. Porphyrios Kommentar zur Harmonielehre des Ptolemaios. Göteborg.
- Fowler, D. H. 1999. The Mathematics of Plato’s Academy. 2nd edn. Oxford.
- Friedlein, G. 1867. ed. De institutione arithmetica libri duo, De institutione musica libri quinque. Accedit geometria quae fertur Boetii. Leipzig.
- Hayduck, M. 1891. ed. Alexandri Aphrodisiensis in Aristotelis metaphysica commentaria. Commentaria in Aristotelem Graeca 1. Berlin.
- Heath, T. L. 1949. Mathematics in Aristotle. Oxford.
- Heiberg, J. L. 1910–1915. ed. Archimedis opera omnia cum commentariis Eutocii. 3 vols. Leipzig.
- Heiberg, J. L. and Stamatis, E. S. 1969–1977. edd. Euclidis elementa. 5 vols. Leipzig.
- Hiller, E. 1878. ed. Theonis Smyrnaei philosophi platonici expositio rerum mathematicarum ad legendum Platonem utilium. Leipzig.
- Jan, C. 1895. ed. Musici scriptores graeci. Leipzig.
- Junge, G. and W. Thomson. 1930. edd. and trans. Pappus: Commentary on Book X of Euclid’s Elements. Cambridge, MA.
- Laloy, L. 1900. “Un passage d’Euclide mal interprété”. Revue de philologie, de littérature et d’histoire ancienne 24: 236–241.
- Liddell, H. G.; H. R. Scott; and H. S. Jones. 1968. A Greek-English Lexicon. Oxford.
- Lippmann, E. A. 1964. Musical Thought in Ancient Greece. New York/ London.
- Mathiesen, T. 1975. An Annotated Translation of Euclid’s Division of a Monochord. Journal of Music Theory 19: 236–258.
- Menge, H. 1916. ed. Euclidis phaenomena et scripta musica. In J. L. Heiberg and H. Menge edd. Euclidis opera omnia. vol. 8. Leipzig.
- Ross, W. D. 1924. ed. Aristotle’s Metaphysics. Oxford.
- Ruelle, C. E. 1906. “Sur l’authenticité probable de la Division du canon musical attribuée à Euclide”. Revue des études grecques 19: 318–320.
- Smyth, H. W. 1920. Greek Grammar. Cambridge, MA.
- Tannery, P. 1893–1895. ed. Diophanti Alexandrini opera omnia cum graecis commentariis. Leipzig.
- Tannery, P. 1904. “Inauthenticité de la “Division du Canon” attribuée à Euclide”. Comptes rendus des séances de l’Académie des Inscriptions et Belles Lettres 4: 439–445. Repr. pp. 213–219 in J. L. Heiberg and H. G. Zeuthen edd. Paul Tannery. Mémoires scientifiques. vol. 3. 1915. Paris.
- Vitrac, B. 1990–2001. trans. and comm. Euclide d’Alexandrie, Les Éléments. 4 vols. Paris.
- Zanoncelli, L. 1990. La manualistica musicale greca. Milan.