Μόνον καὶ ἓν διαφέρει

monad and one differ

Translated by Ronald Allen3 Jan 2009Vetting: high6 revisions

2 notes · 44 words
"[...] the monad [is] that which exists in things noetic, but the one [is that which exists] among the sensible numbers.1 And while the monad is apprehended in accordance with equality and proportion, the dyad [sc. is taken] in accordance with excess and deficiency."2

Greek original · Adler’s text

Μόνον καὶ ἓν διαφέρει· μονὰς ἡ ἐν τοῖς νοητοῖς οὖσα, ἓν δὲ τὸ ἐν τοῖς αἰσθητοῖς ἀριθμοῖς. καὶ ἡ μὲν μονὰς κατὰ τὴν ἰσότητα καὶ μέτρον λαμβάνεται, ἡ δὲ δυὰς καθ' ὑπερβολὴν καὶ ἔλλειψιν.

Betacode
*mo/non kai\ e(\n diafe/rei: mona\s h( e)n toi=s nohtoi=s ou)=sa, e(\n de\ to\ e)n toi=s ai)sqhtoi=s a)riqmoi=s. kai\ h( me\n mona\s kata\ th\n i)so/thta kai\ me/tron lamba/netai, h( de\ dua\s kaq' u(perbolh\n kai\ e)/lleiyin.

Notes (2)

  1. The headword phrase summarises the following quoted text (on which see below), with slight variation in the first of the two terms being contrasted: mo/non is the neuter nominative, vocative, and accusative (and masculine accusative) singular form of the adjective mo/nos, -h, -on ("alone, solitary"; see LSJ s.v. The other term, e(/n ("one"), is the neuter form of the numeral adjective ei(=s and mi/a, masculine and feminine gender, respectively (see LSJ s.v. and Smyth §347).
  2. 1The importance of the difference between noetic (pure, ideal, intelligible, abstract) and aesthetic (sensible, tangible, concrete) numbers to Greek philosophy and mathematics is explained by Klein (p. 10 and pp. 46-51). ↩
  3. 2Together with the headword phrase, this quotation approximates the Life of Pythagoras in Photius, Bibliotheca 249.438b33-8. The Suda omits that part of Photius' entry attributing the distinction between noetic and aesthetic numbers to the followers of Pythagoras (C6 BCE); cf. pi 3120, pi 3121, pi 3123, pi 3124, and OCD(4) s.v. But Aristotle, Metaphysics 987a19-20 (web address 1), asserts that the Pythagoreans had no such distinction; they maintained that number was the being (ta\ ou)si/a, "essence") of all things. Indeed he claims that the distinction is Platonic in origin. At Metaphysics 987b7-11 (web address 2) he points to Plato's separation of numbers as Forms or Ideas from sensible things and further to his mentor's having posited a realm of "mathematical entities" intermediate between noetic and aesthetic being; cf. Metaphysics 987b14-18 (web address 2) and Burkert, pp. 30-1. ↩

References


H.W. Smyth, Greek Grammar, Cambridge, MA: Harvard University Press, 1956
J. Klein, Greek Mathematical Thought and the Origin of Algebra, trans. E. Brann, Cambridge, MA: M.I.T. Press, 1968
W. Burkert, Lore and Science in Ancient Pythagoreanism, trans. E.L. Minar, Jr., Cambridge, MA: Harvard University Press, 1972

External resources

Neighbouring entries

μ1230Μονόλοπαsingle-coated [ones]μ1231Μονομαχοτροφεῖονgladiator-houseμ1232Μόνον καὶ ἓν διαφέρειmonad and one differμ1233Μονονοῦall but, nearlyμ1234Μονονουχίall but
Revision history6 revisions · last 18 May 2016
  1. coding — David Whitehead
  2. cosmeticule — Catharine Roth
  3. Revised — David Whitehead
  4. Revised — David Whitehead
  5. tweaks and cosmetics — David Whitehead
  6. tweaks and cosmetics — Catharine Roth
  7. Translated — Ronald Allen

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