Propositions VIII.4–5 of Euclid's Elements and the compounding of ratios on the monochord

Bibliography

• Ps Aristotle, ‘Problems Book XIX’, in Andrew Barker, Greek musical writings I, Cambridge: Cambridge University Press, 1984, 190–204.
   Google Scholar
• Artmann, Benno, Euclid–The creation of mathematics, New York: Springer-Verlag, 1999.
   Google Scholar
• Barker, Andrew, Greek musical writings II, Cambridge: Cambridge University Press, 1989.
   Google Scholar
• Barker, Andrew, Scientific method in Ptolemy's harmonics, Cambridge: Cambridge University Press, 2000.
   Google Scholar
• Barker, Andrew, Euterpe. Ricerche sulla musica greca e romana, Pisa: Edizioni Ets, 2002.
   Google Scholar
• Barker, Andrew, Psicomusicolgia nella Grecia antica, Napoli: Alfredo Guida Editore, 2005.
   Google Scholar
• Barker, Andrew, The science of harmonics in classical Greece, Cambridge: Cambridge University Press, 2007.
   Google Scholar
• Barbera, Andre, The Euclidean division of the canon: Greek and Latin sources, Lincoln: University of Nebraska Press, 1991.
   Google Scholar
• Bellissima, Fabio, ‘La Sectio canonis di Euclide e il suo errore logico’, Bollettino di Storia delle Scienze Matematiche, 23(1) (2003), 5–45.
   Google Scholar
• Bellissima, Fabio, ‘Arithmetic, geometric and harmonic means in music theory’, Bollettino di Storia delle Scienze Matematiche, 34(2) (2014), 181–223.
   Google Scholar
• Bowen, Alan C, ‘Euclid's Sectio canonis and the history of Pythagoreanism’, in Science and philosophy in classical Greece, New York and London: Garland P I, 1991, 164–188.
   Google Scholar
• Burkert, Walter, Lore and science in ancient Pythagoreanism, Cambridge, MA: Harvard University Press, 1972.
   Google Scholar
• Creese, David, The monochord in ancient Greek harmonic science, Cambridge: Cambridge University Press, 2010.
   Google Scholar
• Euclide, Les Éléments (French trans Bernard Vitrac), Paris: Presses Universitaires de France, 1994.
   Google Scholar
• Fowler, D H, The mathematics of Plato's Academy: a new reconstruction, Oxford: Clarendon Press, 1987.
   Google Scholar
• Heat, Thomas L, A history of Greek mathematics, Oxford: Clarendon Press, 1921.
   Google Scholar
• Heat, Thomas L, The thirteen books of Euclid's Elements, New York: Dover Publications, 1956.
   Google Scholar
• Horky, Phillip S, Plato and Pythagoreanism, Oxford: Oxford University Press, 2013.
   Google Scholar
• Huffman, Carl A, Philolaus: Pythagorean and Presocratic, Cambridge: Cambridge University Press, 1993.
   Google Scholar
• Huffman, Carl A, ‘The Pythagorean tradition’, in A A Long (ed), The Cambridge companion to early Greek philosophy, Cambridge: Cambridge University Press, 1999.
   Google Scholar
• Huffman, Carl A, Archytas of Tarentum: Pythagorean, philosopher and mathematician king, Cambridge: Cambridge University Press, 2005.
   Google Scholar
• Kahn, Charles H, Pythagoras and the Pythagoreans: a brief history, Indianapolis and Cambridge: Hackett Publishing Company Inc, 2001.
   Google Scholar
• Knorr, Wilbur R, The evolution of the Euclidean elements, Dordrecht: D Reidel Publishing Company, 1975.
   Google Scholar
• Michel, Paul H, Contribution a l’Histoire des Mathématiquess Préeuclidiennes, Paris: Les Belles Lettres, 1950.
   Google Scholar
• Mueller, Ian, Philosophy of mathematics and deductive structure in Euclid's Elements, Cambridge, MA: The Massachusetts Institute of Technology Press, 1981.
   Google Scholar
• Nicomachus of Gerasa, Introduction to arithmetic (trans Martin L D’ooge), New York: The Macmillan Company, 1926.
   Google Scholar
• Nicomachus of Gerasa, ‘Enchiridion’, in Andrew Barker, Greek musical writings II, Cambridge: Cambridge University Press, 1989, 247–269.
   Google Scholar
• Ps Plutarch, ‘De Musica’, in Andrew Barker, Greek musical writings I, Cambridge: Cambridge University Press, 1984, 205–249.
   Google Scholar
• Porphyry, ‘Harmonica Ptolomaei commentarius’, in John Wallis, Opera Mathematica III, Oxford: e theatro Sheldoniano, 1699 (reprinted by G Olms, 1972).
   Google Scholar
• Proclus, A commentary on the first book of Euclid's Elements (trans G M Morrow), Princeton: Princeton University Press, 1992.
   Google Scholar
• Ptolemy, ‘Harmonics’, in Andrew Barker, Greek musical writings II, Cambridge: Cambridge University Press, 1989, 275–391.
   Google Scholar
• Szabó, Árpád, The beginnings of Greek mathematics, Dordrecht: D Reidel Publishing Company, 1978.
   Google Scholar
• Tannery, Paul, ‘Du rôle de la musique grecque dans le développment de la mathématique pure’, Bibliotheca Mathematica, 3 (1902), 161–175 (also in Mémories Scientifiques de Paul Tannery, III, 68–89).
   Google Scholar
• Tannery, Paul, ‘Inautenticité de la division du canon attribuéè à Euclide’, Comptes rendus de l’Académie des Inscriptions ed Belles Lettres, (1904), 439–445 (also in Mémories Scientifiques de Paul Tannery, III, 213–219).
   Google Scholar
• Theon of Smyrna, Exposition des connaissance mathématiques utiles pour la lecture de Platon (French trans J Dupuis), Paris: Librairie Hachette, 1892.
   Google Scholar
• van der Waerden, Bartel L, ‘Die Hermonielehre der Pythagoreer’, Hermes, 78 (1943), 163–199.
   Google Scholar
• van der Waerden, Bartel L, Science awakening, Dordrecht: Kluver Academic Publishers, 1954.
   Google Scholar
• Zarlino, Gioseffo, Le Istitutioni Harmoniche, Venezia, 1561 (reprinted by Arnaldo Forni Editore, 2008).
   Google Scholar
• Zarlino, Gioseffo, Dimostrationi Harmoniche, Venezia, 1571.
   Google Scholar