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δεκάς (ἡ)

ΔΕΚΑΣ

LEXARITHMOS 230

The Decad (δεκάς), beyond its simple arithmetical value as ten, held for the Pythagoreans a sacred and cosmogonic significance, the Tetractys, the sum of the first four numbers (1+2+3+4=10) symbolizing the completeness and order of the cosmos. Its lexarithmos (230) suggests a connection to abundance and culmination.

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Definition

According to the Liddell-Scott-Jones Lexicon, δεκάς primarily means "the number ten" or "a group of ten things." The word is used to denote a collection of ten units, whether people, objects, or periods of time. In classical Athens, for instance, there were "ten generals" or "ten tribes," where the decad signified an organizational structure.

The significance of the decad extends beyond mere quantity, acquiring profound philosophical and symbolic content, particularly within the Pythagorean school. For the Pythagoreans, the decad was the sacred number, the "Tetractys," derived from the sum of the first four natural numbers (1+2+3+4=10). This decad was considered the source of eternal nature, the key to understanding the harmony of the world and the music of the spheres.

Furthermore, the decad was employed to denote temporal periods, such as a decade or a ten-day interval. In administrative and military organization, a "decad" could refer to a unit of ten men or a committee of ten individuals, highlighting its functional use in ancient Greek society.

Etymology

δεκάς ← δέκα (Ancient Greek root of the number ten)
The word «δέκα» and by extension «δεκάς» originates from an Ancient Greek root belonging to the oldest stratum of the language. Its precise origin is unknown, but it constitutes a fundamental numerical concept found throughout all periods of the Greek language. The form «δεκάς» is a nominalized use of the numeral, denoting the aggregate or group.

From the root of the number ten, a rich family of words is derived, signifying multiples, subdivisions, temporal periods, or organizational structures based on the number ten. Examples include the adverb «δεκάκις» (ten times), compound adjectives such as «δεκαετής» (of ten years) and «δεκαήμερος» (lasting ten days), as well as nouns describing groups or administrations, like «δεκαρχία» (rule of ten men) or «δεκάτη» (the tenth part).

Main Meanings

  1. The number ten — The basic arithmetical concept, the sum of ten units.
  2. Group of ten — A set or collection of ten persons or things, e.g., a military decury.
  3. Period of ten — A period of ten days or ten years (a decade).
  4. Pythagorean Tetractys — For the Pythagoreans, the sacred decad, the sum of the first four numbers (1+2+3+4), symbolizing cosmic harmony.
  5. Symbol of completeness/perfection — Due to its Pythagorean significance, the decad was often regarded as a number denoting completion and perfection.
  6. Administrative/Military unit — A group of ten men or a committee of ten individuals in a political or military context.
  7. A tenth part (tithe) — The tenth share or the tenth part of a whole, often as a tax or offering.

Word Family

deka- (root of the number ten)

The root deka- forms the basis for a series of words related to the number ten, its multiples, subdivisions, as well as temporal and organizational structures based on it. From its simple arithmetical use, this root extends to philosophical concepts, such as the Pythagorean decad, and to practical applications in politics, administration, and religion. This family highlights the central importance of the number ten in ancient Greek thought and society.

δέκα numeral · lex. 30
The basic number "ten." Used as an adjective or a noun to denote quantity. In Pythagorean philosophy, the basis for the sacred decad.
δεκάκις adverb · lex. 260
Meaning "ten times." Used to denote multiplication or repetition, e.g., «δεκάκις χίλιοι» (ten thousand).
δεκαετής adjective · lex. 543
Lasting ten years or being ten years old. Often refers to periods of time or age, e.g., «δεκαετὴς πόλεμος» (a ten-year war).
δεκαήμερος adjective · lex. 453
Lasting ten days. Used to describe events or periods, e.g., «δεκαήμερος νηστεία» (a ten-day fast).
δεκαρχία ἡ · noun · lex. 741
The government or rule of ten men. Particularly known is the "Decarchy" established by the Spartans in various cities after the Peloponnesian War.
δεκάλογος ὁ · noun · lex. 403
The collection of ten words or commandments. Primarily refers to the Ten Commandments of Moses, as transmitted in the Old Testament.
δεκάτη ἡ · noun · lex. 338
The tenth part, the tenth share. Often refers to the tax or offering of a tenth, i.e., the "tithe" given to gods or rulers.

Philosophical Journey

The decad, as a number and a philosophical concept, traverses Greek thought from its simple arithmetical use to its cosmological significance.

8th-7th C. BCE (Archaic Period)
Early References
In Homeric epics and Hesiod, the word «δέκα» is used simply as a quantitative determinant, without particular symbolic depth, e.g., «δέκα βόες» (ten oxen).
6th C. BCE (Pythagorean School)
The Sacred Tetractys
Pythagoras and his disciples elevated the decad to a central philosophical concept, the "Tetractys," as the source of nature and the harmony of the cosmos. The decad became a symbol of perfection.
5th-4th C. BCE (Classical Period)
Administrative & Philosophical Use
Among Athenians, the decad was used in administrative structures (e.g., «δέκα στρατηγοί» — ten generals, «δέκα φύλαρχοι» — ten tribal leaders) and for temporal periods. Plato, influenced by the Pythagoreans, refers to numerical harmony.
3rd C. BCE - 2nd C. CE (Hellenistic & Roman Period)
Mathematical & Practical Application
The decad continued to be used in mathematical texts (Euclid), astronomy (Ptolemy), and everyday measurements. The concept of a decade as a temporal period became established.
3rd-6th C. CE (Late Antiquity)
Neoplatonic Interpretation
Neoplatonic philosophers, such as Proclus, continued to explore the symbolic significance of numbers, including the decad, in cosmology and theology.
Byzantine Period
Religious & Administrative Continuity
The use of the decad persisted both in arithmetic and in religious texts (e.g., «Δεκάλογος» for the Ten Commandments), as well as in administrative and chronological references.

In Ancient Texts

The philosophical and practical significance of the decad is highlighted in various ancient texts.

«Ἔστι δὲ ἡ δεκὰς τετρακτὺς καὶ πηγή τις ἀενάου φύσεως.»
“The decad is the Tetractys and a source of eternal nature.”
Iamblichus, De Vita Pythagorica 137 (attributed to the Pythagoreans)
«Δέκα γὰρ ἀριθμὸς τέλειος.»
“For the number ten is perfect.”
Philo of Alexandria, De Opificio Mundi 102
«Δέκα δὲ στρατηγοὺς ᾑροῦντο, ἕνα ἐκ φυλῆς ἑκάστης.»
“They elected ten generals, one from each tribe.”
Aristotle, Athenaion Politeia 61.1

Lexarithmic Analysis

The lexarithmos of the word ΔΕΚΑΣ is 230, from the sum of its letter values:

Δ = 4
Delta
Ε = 5
Epsilon
Κ = 20
Kappa
Α = 1
Alpha
Σ = 200
Sigma
= 230
Total
4 + 5 + 20 + 1 + 200 = 230

230 decomposes into 200 (hundreds) + 30 (tens) + 0 (units).

The 18 Methods

Applying the 18 traditional lexarithmic methods to the word ΔΕΚΑΣ:

MethodResultMeaning
Isopsephy230Base lexarithmos
Decade Numerology52+3+0=5 — The Pentad, the number of life, harmony, and man, symbolizing the union of masculine (3) and feminine (2) or the perfection of a cycle.
Letter Count55 letters — The Pentad, the number of life and balance, associated with the human form (five extremities) and the senses.
Cumulative0/30/200Units 0 · Tens 30 · Hundreds 200
Odd/EvenEvenFeminine force
Left/Right HandRightDivine (≥100)
QuotientComparative method
NotarikonΔ-Ε-Κ-Α-ΣDikaiosyne Eirene Kosmos Aletheia Sophia (Righteousness, Peace, Order, Truth, Wisdom) (interpretive)
Grammatical Groups2V · 3C2 vowels (E, A) and 3 consonants (D, K, S), indicating a balanced structure.
PalindromesNo
OnomancyComparative
Sphere of DemocritusDivination with lunar day
Zodiacal IsopsephySaturn ♄ / Gemini ♊230 mod 7 = 6 · 230 mod 12 = 2

Isopsephic Words (230)

Words from the Liddell-Scott-Jones lexicon with the same lexarithmos (230) as the decad, but from different roots, offering an interesting numerical coincidence.

ἱρόν
τὸ ἱρόν, a sacred thing or place. The numerical coincidence with the decad is notable, given the sacred significance of the decad for the Pythagoreans.
οἰκίον
τὸ οἰκίον, a small house or room. Represents the private, domestic sphere, in contrast to the cosmic order symbolized by the decad.
ὀλεθρεία
ἡ ὀλεθρεία, destruction, ruin. A word with a negative connotation, contrasting with the concept of completeness and harmony attributed to the decad.
δεισία
ἡ δεισία, fear, cowardice. Associated with human weakness, in contrast to the strength and perfection implied by the decad.
ἀνακοπή
ἡ ἀνακοπή, an interruption, a cutting short. Suggests a pause or an end, whereas the decad often symbolizes the completion of a cycle.
ἔνδορα
τὰ ἔνδορα, entrails, internal organs. A word referring to the internal parts of the body, contrasting with the abstract and cosmic significance of the decad.

The LSJ lexicon contains a total of 29 words with lexarithmos 230. For the full catalog and AI semantic filtering, see the interactive tool.

Sources & Bibliography

  • Liddell, H. G., Scott, R., Jones, H. S.A Greek-English Lexicon, 9th ed. with revised supplement. Oxford: Clarendon Press, 1996.
  • Kirk, G. S., Raven, J. E., Schofield, M.The Presocratic Philosophers: A Critical History with a Selection of Texts. 2nd ed. Cambridge: Cambridge University Press, 1983.
  • IamblichusDe Vita Pythagorica (On the Pythagorean Way of Life). Edited and translated by John Dillon and Jackson Hershbell. Atlanta: Society of Biblical Literature, 1991.
  • Philo of AlexandriaOn the Creation of the World (De Opificio Mundi). Translated by F. H. Colson and G. H. Whitaker. Loeb Classical Library. Cambridge, MA: Harvard University Press, 1929.
  • AristotleConstitution of the Athenians. Edited and translated by P. J. Rhodes. Penguin Classics. London: Penguin Books, 1984.
  • Heath, T. L.A History of Greek Mathematics. Vol. 1: From Thales to Euclid. Oxford: Clarendon Press, 1921.
  • PlatoRepublic. Translated by G. M. A. Grube, revised by C. D. C. Reeve. Indianapolis: Hackett Publishing Company, 1992.
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