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# Greek numerals

The Greek numerals, like the Roman numerals, use letters of the alphabet (in this case, the Greek alphabet) to represent numbers. There were various attempts with very primitive systems. The earliest system to gain anywhere near widespread acceptance was the Attic or Herodianic system, used a small subset of letters which were mostly abbreviations for number words: Π (5) for ΠΕΝΤΕ, Δ (10) for ΔΕΚΑ, and so on and so forth. But instead of having different letters for 50 and 500 (like the Romans), in this system a variant of Π is combined with the symbol for the relevant power of 10.[1]

The Attic system later fell into disuse, replaced by the Ionian system, in which all the letters of the Greek alphabet and then some are used.[2] Neither system has a symbol for zero.

• α' 1
• β' 2
• γ' 3
• δ' 4
• ε' 5
• (vau) 6
• ζ' 7 (or 6)
• η' 8 (or 7)
• θ' 9 (or 8)
• ι' 10 (or 9)
• κ' 20 (or 10)
• λ' 30 (or 11)
• μ' 40 (or 12)
• ν' 50 (or 13)
• ξ' 60 (or 14)
• ο' 70 (or 15)
• π' 80 (or 16)
• (koppa) 90
• ρ' 100 (or 17)
• σ' 200 (or 18)
• τ' 300 (or 19)
• υ' 400 (or 20)
• φ' 500 (or 21)
• χ' 600 (or 22)
• ψ' 700 (or 23)
• ω' 800 (or 24)
• (sampi) 900[3]

For ceremonial numbering purposes, when there are 24 items or less (such as chapters in Homer's Odyssey), the 24 letters of the modern alphabet are used in sequence to represent the integers from 1 to 24.

For other values from 11 to 999, symbols may simply be combined without regard to order, but are generally placed in descending order. 561, for example, is φξα', but it could just as easily be ξφα' or perhaps even αξφ'.

And then, from 1001 to 999999, a comma before a symbol multiplies it by 1000.[4] Thus ,αψκθ' is 1729.

For numbers greater than the myriad, either ruby numerals were placed over the Μ, or dots over the letters.[5]

In our modern times it is easy to assume that computation with Greek numerals must have been rather cumbersome and inconvenient, as "many scholars have exaggerated the difficulties of performing calculations using Ionian numerals."[6] To do a multiplication like σ times ξ, "the Greeks had first to go back from σ = 200 and ξ = 60 to the 'root numbers' β = 2 and (vau) = 6. They were then able to calculate as we do ${\displaystyle 2\times 6=12}$, i.e. β times (vau) = ιβ. Before the result could be written down, it had be multiplied by ${\displaystyle 100\times 10=1000}$ giving the partial result Μ(with ruby α),β. Adding all the partial results obtained in this way gave the final answer. ... This method of multiplying was known as Greek multiplication to distinguish it from the Egyptian method of repeated doubling which was known to the Greeks."[7]

## Notes

1. Flegg, p. 88
2. Flegg, p. 88