ΤΜΗΜΑ
Tmēma, a word fundamental to both geometry and philosophy, denotes a 'cut piece' or 'division' of a whole. Derived from the ancient Greek verb temnō (to cut), tmēma emerges as the essence of analysis and categorization. Its lexarithmos, 389, mathematically reflects the complexity of division and composition, as division is often the initial step towards understanding the entirety.
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According to the Liddell-Scott-Jones Lexicon, tmēma (τοῦ τμήματος) is a noun derived from the verb temnō ('to cut') and originally means 'a piece cut off, a section, a division'. Its primary usage in classical Greek largely concerns physical divisions, such as a plot of land, a part of the body, or a severed portion of an object.
The word acquired particular technical significance in geometry, where it refers to a 'segment of a line' (segmentum lineae) or a 'segment of a circle' (segmentum circuli), as found in Euclid's Elements. In this context, a tmēma is not merely a piece, but a precisely defined subdivision with specific properties and relationships to the larger whole.
Beyond geometry, tmēma is also employed in abstract concepts, signifying a 'part' or 'chapter' of a work, a 'category' or 'class' within a division, or even a 'share' or 'portion'. Its meaning extends to organization and structure, both in literary texts and in social or administrative frameworks, underscoring the Greek language's capacity to express complex ideas of division and analysis.
Etymology
From the same root tem-/tmē- derive numerous words that retain the core meaning of 'cutting' or 'dividing'. Cognate words include the verb temnō, the noun tomē (the act of cutting or the point of incision), the adjective tmētikos (that which has the property of cutting), as well as compounds such as anatomē (the dissection of a body into parts), diatomē (a cross-section), and ektomē (excision by cutting). This word family highlights the central importance of division and analysis in Greek thought.
Main Meanings
- Cut piece, section — The basic meaning: a part that has been cut off from a larger whole. E.g., «τμῆμα γῆς» (a piece of land).
- Geometric segment — In Euclidean geometry, a segment of a line or a segment of a circle. E.g., «τμῆμα κύκλου» (a circular segment).
- Division, subdivision — A distinct unit or subgroup within a larger whole. E.g., «τμῆμα στρατοῦ» (a division of an army).
- Part of a work, chapter — A distinct section of a literary, philosophical, or scientific work. E.g., «τμῆμα βιβλίου» (a chapter of a book).
- Category, class — A division or classification in an abstract context. E.g., «τμῆμα φιλοσόφων» (a class of philosophers).
- Portion, share — A part belonging to someone or allocated to them. E.g., «τμῆμα κληρονομίας» (a portion of an inheritance).
- Anatomical section — A distinct part of the body or an organism, especially in medicine and biology.
Word Family
tem- / tmē- (root of the verb temnō, meaning 'to cut, to divide')
The root tem-/tmē- is one of the most productive roots in Ancient Greek, expressing the fundamental concept of breaking apart, separating, and severing. From this root arise words that describe both the act of cutting and its result — the piece, the part, the division. The vowel alternation (ablaut) between the e-grade (temnō) and zero-grade (tmē-) is characteristic of Greek morphology, allowing for the creation of a rich family of words that maintain the core meaning of division in various contexts, from the physical to the abstract and scientific.
Philosophical Journey
The word tmēma, though simple in concept, has a rich history of usage that reflects the evolution of Greek thought from physical divisions to abstract and scientific notions.
In Ancient Texts
Three characteristic passages that highlight the diverse use of tmēma in ancient Greek literature:
Lexarithmic Analysis
The lexarithmos of the word ΤΜΗΜΑ is 389, from the sum of its letter values:
389 is a prime number — indivisible, a quality the Pythagoreans considered the mark of pure essence.
The 18 Methods
Applying the 18 traditional lexarithmic methods to the word ΤΜΗΜΑ:
| Method | Result | Meaning |
|---|---|---|
| Isopsephy | 389 | Prime number |
| Decade Numerology | 2 | 3+8+9 = 20 → 2+0 = 2 — Dyad, the principle of division and duality, the distinction between parts. |
| Letter Count | 5 | 5 letters — Pentad, the number of harmony and balance, achieved through proper division. |
| Cumulative | 9/80/300 | Units 9 · Tens 80 · Hundreds 300 |
| Odd/Even | Odd | Masculine force |
| Left/Right Hand | Right | Divine (≥100) |
| Quotient | — | Comparative method |
| Notarikon | T-M-H-M-A | Taxis Metron Ethikon Mesos Archon (interpretive, suggesting the organization and distinction of moral principles) |
| Grammatical Groups | 2V · 3C · 0S | 2 vowels (A, H), 3 consonants (T, M, M). The ratio of vowels to consonants indicates a balance in pronunciation. |
| Palindromes | No | |
| Onomancy | — | Comparative |
| Sphere of Democritus | — | Divination with lunar day |
| Zodiacal Isopsephy | Mars ♂ / Virgo ♍ | 389 mod 7 = 4 · 389 mod 12 = 5 |
Isopsephic Words (389)
Words from the Liddell-Scott-Jones Lexicon with the same lexarithmos (389) as tmēma, but of different roots, offering a glimpse into the numerical coexistence of concepts:
The LSJ lexicon contains a total of 61 words with lexarithmos 389. 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, with a revised supplement. Clarendon Press, Oxford, 1996.
- Euclid — Elements. Edited by J.L. Heiberg, Teubner, Leipzig, 1883-1888.
- Plato — Republic. Edited by John Burnet, Oxford University Press, 1903.
- Aristotle — Nicomachean Ethics. Edited by I. Bywater, Oxford University Press, 1894.
- Chantraine, P. — Dictionnaire étymologique de la langue grecque: histoire des mots. Klincksieck, Paris, 1968-1980.
- Montanari, F. — Vocabolario della lingua greca. Loescher, Torino, 2013.