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Headword: Tetraktus
Adler number: tau,394
Translated headword: tetraktys, tetraktus
Vetting Status: high
[Meaning] the tetrads: or rather the fourth [sc. triangular number].[1]
[Note] that the Pythagoreans used to call every number by a name. The number adds up to 10, the tenth [sc. number is] a composition of the 4. And because of this they used to call the whole [nature of] number tetraktys.[2]
The same men [i.e. the Pythagoreans] also used to revere the tetrads, because of the four phases of the moon; for [they are] new-born, crescent-shaped, gibbous, and full-moon.[3]
Greek Original:
Tetraktus: hoi tessares: êgoun hê tetras. hoti hoi Puthagoreioi panta arithmon prosêgoreuon. ho de arithmos sumplêroutai tois i#, ho de dekatos sunthesis tôn d#. kai dia touto ton arithmon panta tetraktun elegon. hoi autoi etimôn kai ta tessara, dia tas tessaras tês selênês morphas: artitokos gar, mênoeidês, amphikurtos kai panselênos.
See LSJ s.v. tetraktu/s, I, for the Pythagorean sense of this headword. (Sense II, with various subsets, relates to musical intervals.) See also tau 481.
[1] The headword is identically glossed in the Synagoge (tau121), Photius' Lexicon (tau194 Theodoridis) and Lexica Segueriana 385.21; cf. Hesychius (tau625) and Photius, Bibliotheca 439a 5-8. The tetraktys represents the summation 1+2+3+4=10 geometrically -- typically with pebbles, dots, or alphas -- as one item centered above a pair, three underneath those, and a base of four, thereby forming an equilateral triangle (Ross, pp. 145-6; Annas, p. 54-5). The sums of successive levels comprise the triangular numbers: 1, 3, 6, 10, and so forth (Burnet, pp. 113-4; Thomas, pp. 86-91).
[2] The preceding three sentences also appear, approximately, at alpha 3880 (end). Number naming traditions varied. Parts of one can be gleaned from Aristotle's extant works and the commentary on the Metaphysics by Alexander of Aphrodisias, the latter evidently working from Aristotle's lost work on the Pythagoreans. For example, the number one is mind and being; two is opinion; three -- comprising beginning, middle, and end -- is the whole; and four represents both justice and, as the tetraktys itself, the whole nature of number (Burkert, p. 467; Ross, p. 144-5).
[3] Swearing their oaths upon it (Ross, p. 146), the Pythagoreans considered the tetraktys perfect; cf. epsiloniota 29 notes. Other Suda passages devoted to Pythagoras include pi 3120, pi 3121, pi 3123, and pi 3124.
W.D. Ross, Aristotle's Metaphysics, vol. I, Oxford: Oxford University Press, 1924
J. Annas, Aristotle's Metaphysics Books M and N, Oxford: Oxford University Press, 1976
J. Burnet, Early Greek Philosophy, 2nd edn., London: Adam and Charles Black, 1908
I. Thomas, trans., Greek Mathematics: From Thales to Euclid, vol. I, Cambridge, MA: Harvard University Press, 2002
W. Burkert, Lore and Science in Ancient Pythagoreanism, trans. E.L. Minar, Jr., Cambridge, MA: Harvard University Press, 1972
Keywords: daily life; definition; ethics; imagery; law; mathematics; philosophy; religion; science and technology
Translated by: Ronald Allen on 3 July 2008@19:50:24.
Vetted by:
David Whitehead (added primary note; tweaks and cosmetics) on 4 July 2008@03:12:59.
Catharine Roth (tweaked translation) on 7 July 2008@00:38:17.
David Whitehead on 9 January 2014@06:03:54.
David Whitehead (codings) on 27 May 2016@11:34:32.


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