|
| 1 | += Nichomachus of Gerasa |
| 2 | + |
| 3 | +#set quote(block: true) |
| 4 | + |
| 5 | +Nicomachus of Gerasa hailed from Roman Syria(now Jerash, Jordan), born in the year 60 CE. It must be recalled in the centuries after Plato there had come into fashion a tendency to herald Plato and Aristotle as not only harmonious and united in overall aim, but also to see them as merely refining the treasured insight of Pythagoras. So Nicomachus is remembered as a Pythagorean, and he wrote about the mystical nature of number and set about exploring a theory of music and harmony. In an Era where Arithmetic was philosophy, Nicomachus set the standard for later Neoplatonic schooling in the Late Antique World, and this central status led Boethius to paraphrase Nicomachus into Latin, preserving him as a standard in medieval schooling[^1]. With humor we may regard Boethius as having released a language model compression of the Philsopher of Arithmetic for Latin. |
| 6 | + |
| 7 | + |
| 8 | +#quote(attribution: [wikipedia[1]])[ |
| 9 | + Historians consider Nicomachus a Neopythagorean based on his tendency to view numbers as having mystical properties rather than their mathematical properties,^[3]^[4] citing an extensive amount of Pythagorean literature in his work, including works by Philolaus, Archytas, and Androcydes.^[1] He writes extensively on numbers, especially on the significance of prime numbers and perfect numbers and argues that arithmetic is ontologically prior to the other mathematical sciences (music, geometry, and astronomy), and is their cause. Nicomachus distinguishes between the wholly conceptual immaterial number, which he regards as the 'divine number', and the numbers which measure material things, the 'scientific' number.^[2] Nicomachus provided one of the earliest Greco-Roman multiplication tables; the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum).^[5] |
| 10 | +] |
| 11 | + |
| 12 | +#quote(attribution: [wikipedia[1]])[ |
| 13 | + Although Nicomachus is considered a Pythagorean, John M. Dillon says that Nicomachus's philosophy "fits comfortably within the spectrum of contemporary Platonism."^[6] In his work on arithmetic, Nicomachus quotes from Plato's Timaeus^[7] to make a distinction between the intelligible world of Forms and the sensible world, however, he also makes more Pythagorean distinctions, such as between Odd and even numbers.^[6] Unlike many other Neopythagoreans, such as Moderatus of Gades, Nicomachus makes no attempt to distinguish between the Demiurge, who acts on the material world, and The One which serves as the supreme first principle.^[6] For Nicomachus, God as the supreme first principle is both the demiurge and the Intellect (nous), which Nicomachus also equates to being the monad, the potentiality from which all actualities are created.^[6] |
| 14 | +] |
| 15 | + |
| 16 | +#quote(attribution: [wikipedia[1]])[ |
| 17 | + Two of Nicomachus' works, the Introduction to Arithmetic and the Manual of Harmonics are extant in a complete form, and two others, a work on Theology of Arithmetic and a Life of Pythagoras survive in fragments, epitomes, and summaries by later authors.^[1] The Theology of Arithmetic (Ancient Greek Θεολογούμενα ἀριθμητικῆς), on the Pythagorean mystical properties of numbers in two books is mentioned by Photius. There is an extant work sometimes attributed to Iamblichus under this title written two centuries later which contains a great deal of material thought to have been copied or paraphrased from Nicomachus' work. Nicomachus's Life of Pythagoras was one of the main sources used by Porphyry and Iamblichus, for their (extant) Lives of Pythagoras.^[1] An Introduction to Geometry, referred to by Nicomachus himself in the Introduction to Arithmetic,^[8] has not survived.^[1] Among his known lost work is another larger work on music, promised by Nicomachus himself, and apparently^[citation needed] referred to by Eutocius in his comment on the sphere and cylinder of Archimedes. |
| 18 | +] |
| 19 | + |
| 20 | +#quote(attribution: [wikipedia[1]])[ |
| 21 | + The work of Boethius on arithmetic and music was a core part of the Quadrivium liberal arts and had a great diffusion during the Middle Ages. |
| 22 | +] |
| 23 | + |
| 24 | +Nichomachus of Gerasa is the source of the sieve of Eratosthenes, which was used by Euler in his proof of the product for of the Zeta function. |
| 25 | + |
| 26 | +#quote(attribution: [wikipedia[2]])[ |
| 27 | + The earliest known reference to the sieve (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) is in Nicomachus of Gerasa's Introduction to Arithmetic,[3] an early 2nd cent. CE book which attributes it to Eratosthenes of Cyrene, a 3rd cent. BCE Greek mathematician, though describing the sieving by odd numbers instead of by primes. |
| 28 | +] |
| 29 | + |
| 30 | + |
| 31 | +== Citation Chain |
| 32 | + |
| 33 | +[1]: https://en.wikipedia.org/wiki/Nicomachus |
| 34 | + |
| 35 | + 1. ^ ^a ^b ^c ^d ^e ^f ^g ^h Dillon 1996, pp. 352–353. |
| 36 | + |
| 37 | + 2. ^ ^a ^b ^c ^d Midonick 1965, pp. 15–16. |
| 38 | + |
| 39 | + 3. ^ Eric Temple Bell (1940), The development of mathematics, page 83. |
| 40 | + |
| 41 | + 4. ^ Frank J. Swetz (2013), The European Mathematical Awakening, page 17, Courier |
| 42 | + |
| 43 | + 5. ^ David E. Smith (1958), History of Mathematics, Volume I: General Survey of the History of Elementary Mathematics, New York: Dover Publications (a reprint of the 1951 publication), ISBN 0-486-20429-4, pp 58, 129. |
| 44 | + |
| 45 | + 6. ^ ^a ^b ^c ^d Dillon 1996, pp. 353–358. |
| 46 | + |
| 47 | + 7. ^ Plato, Timaeus 27D |
| 48 | + |
| 49 | + 8. ^ Nicomachus, Arithmetica, ii. 6. 1. |
| 50 | + |
| 51 | + 9. ^ Heath, Thomas (1921). A History of Greek Mathematics. Vol. 1. pp. 97–98. |
| 52 | + |
| 53 | + 10. ^ Levin, Flora R. (2001). "Nicomachus [Nikomachos] of Gerasa". Grove Music Online. Oxford: Oxford University Press. doi:10.1093/gmo/9781561592630.article.19911. ISBN 978-1-56159-263-0. Retrieved 25 September 2021. (subscription or UK public library membership required) |
| 54 | + |
| 55 | + 11. ^ Edward Grant (1974). A Source Book in Medieval Science. Source books in the history of the sciences. Vol. 13. Harvard University Press. p. 17. ISBN 9780674823600. ISSN 1556-9063. OCLC 1066603. |
| 56 | + |
| 57 | + 12. ^ Arnold, Jonathan; Bjornlie, Shane; Sessa, Kristina (April 18, 2016). A Companion to Ostrogothic Italy. Brill's Companions to European History. Brill. p. 332. ISBN 9789004315938. OCLC 1016025625. Retrieved May 16, 2021. |
| 58 | + |
| 59 | + 13. ^ Ivor Bulmer-Thomas (April 1, 1985). "Boethian Number Theory - Michael Masi: Boethian Number Theory: A Translation of the De Institutione Arithmetica (with Introduction and Notes)". The Classical Review. 35 (1). The Classical Association, Harvard University Press: 86–87. doi:10.1017/S0009840X00107462. S2CID 125741349. |
| 60 | + |
| 61 | + 14. ^ Pengelley, David (2002), "The bridge between continuous and discrete via original sources", Study the Masters: The Abel-Fauvel Conference (PDF), National Center for Mathematics Education, Univ. of Gothenburg, Sweden |
| 62 | + |
| 63 | + Bibliography |
| 64 | + |
| 65 | + Editions and translations |
| 66 | + |
| 67 | + Introduction to Arithmetic |
| 68 | + |
| 69 | + • Nicomachus, of Gerasa; Hoche, Richard Gottfried (1866). Nicomachi Geraseni |
| 70 | + Pythagorei Introductionis arithmeticae libri II (in Ancient Greek). |
| 71 | + Lipsiae : in aedibvs B.G. Teubneri. Retrieved 16 April 2023. |
| 72 | + • D'Ooge, Martin Luther; Robbins, Frank Egleston; Karpinski, Louis Charles |
| 73 | + (1926). Nicomachus' Introduction to Arithmetic. Macmillan. Retrieved 16 |
| 74 | + April 2023. |
| 75 | + |
| 76 | + Manual of Harmonics |
| 77 | + |
| 78 | + • Jan, Karl von; Nicomachus (1895). Musici scriptores graeci. Aristoteles, |
| 79 | + Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum |
| 80 | + quidquid exstat (in Ancient Greek). Lipsiae, in aedibus B. G. Teubneri. |
| 81 | + pp. 209–282. Retrieved 16 April 2023. |
| 82 | + • Andrew Barker, editor, Greek Musical Writings vol 2: Harmonic and Acoustic |
| 83 | + Theory (Cambridge: Cambridge University Press, 1989), pp. 245–69. |
| 84 | + |
| 85 | + Primary sources |
| 86 | + |
| 87 | + • Iamblichus (January 1989). Gillian Clark (ed.). On the Pythagorean Life. |
| 88 | + Liverpool University Press. ISBN 9780853233268. |
| 89 | + • Photius, Bibliotheca |
| 90 | + • Anonymous, Theology of Arithmetic |
| 91 | + • Boethius (1488). De institutione arithmetica (in Latin). Erhard Ratdolt. |
| 92 | + p. 110. Archived from the original on May 16, 2021 – via Internet Archive. |
| 93 | + |
| 94 | + References |
| 95 | + |
| 96 | + • Dillon, John M. (1996). "Nicomachus of Gerasa". The Middle Platonists, 80 |
| 97 | + B.C. to A.D. 220. Cornell University Press. pp. 352–361. ISBN |
| 98 | + 978-0-8014-8316-5. Retrieved 16 April 2023. |
| 99 | + • Midonick, Henrietta O. (1965). The treasury of mathematics: a collection of |
| 100 | + source material in mathematics edited and presented with introductory |
| 101 | + biographical and historical sketches. Philosophical Library. pp. 15–16. |
| 102 | + |
| 103 | +[2]: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes |
| 104 | + |
| 105 | + 3. ^ Hoche, Richard, ed. (1866), Nicomachi Geraseni Pythagorei Introductionis arithmeticae libri II, chapter XIII, 3, Leipzig: B.G. Teubner, p. 30 |
| 106 | + 4. ^ Nicomachus of Gerasa (1926), Introduction to Arithmetic; translated into English by Martin Luther D'Ooge; with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski, chapter XIII, 3, New York: The Macmillan Company, p. 204 |
0 commit comments