# Milesian system

 If characters are not displayed correctly in the following, this is due to the character set , see Unicode block Ancient Greek numerals and help with display problems .
 ͵βκʹ 2020 represented as a milesic number

The Milesian system is a numbering system that was used in ancient Greece as well as in Byzantium . It is also known as the "alphabetical number system". It divides the alphabet into three groups of nine characters each to represent the ones, tens and hundreds. It was not until the 14th century that it was replaced by the Indo-Arabic number system in the Byzantine Empire . The latter  finally prevailed - especially through the work of Adam Ries - against the Roman number system .

## Greece

Middle of the 4th century BC Chr. Were the first three of each consisting of nine digits hieratic demotic series of numbers replaced by letters of the alphabet. In order to have the required total number of 3 × 9 = 27 characters available, three additional characters have been added for the purpose of number representation:

•    6 =  Digamma
It corresponds to the Latin F. The word ending variant of the sigma (ς) is used as a minuscule together with a tau (τ) as a ligature (ϛ), which is also interpreted as a stigma . In today's printing works the letters sigma is usually tau (στ) used.
•  90 =  Koppa
This is the old Qoph, i.e. the Latin Q. Originally written in the form ϙ, later also in the form: ϟ.
• 900 =  Sampi
Sampi or Tsampi corresponds to the Phoenician Sade (San), as well as the Hebrew Tzade ; graphically in Greek: ϡ.

With these 27 characters and the numerical values ​​assigned to them, the numbers 1 to 999 could be written by adding together units, tens and hundreds, i.e. 8 = η (Eta), 88 = πη (Pi + Eta = 80 + 8), 318 = τιη (Tau + Iota + Eta = 300 + 10 + 8). There was no sign for the zero and was also not required for the purposes of the number spelling, by adding about 200 = σ (Sigma), 202 = σβ (Sigma + Beta = 200 +2), 220 = σκ (Sigma + Kappa = 200 + 20) wrote.

α β γ δ ε ϛ ζ η θ
1 2 3 4th 5 6th 7th 8th 9
ι κ λ μ ν ξ ο π ϟ
10 20th 30th 40 50 60 70 80 90
ρ σ τ υ φ χ ψ ω ϡ
100 200 300 400 500 600 700 800 900

In order to distinguish the numbers in the typeface from words, the former were usually overwritten with a line in the manuscripts, for example = 310. However, if the identity as a number is clear, this is sometimes omitted. ${\ displaystyle {\ overline {\ tau \ iota}}}$

Numbers from 1000 can also be represented with alphabetic numeric characters. To do this, the first number letter was multiplied by a thousand by adding a diacritical mark. In handwriting, one usually uses a sign that is in the form of a small hook open to the left, in front of the number at the top left.

Numerical values
Hebrew value Greek
Aleph א 1 alpha α
Beth ב 2 beta β
Gimel ג 3 gamma γ
Daleth ד 4th delta δ
Hey ה 5 epsilon ε
Waw ו 6th Digamma ϝ
Zajin ז 7th Zeta ζ
Chet ח 8th Eta η
Tet ט 9 Theta θ
iodine י 10 Iota ι
Cap כ 20th Kappa κ
Lamed ל 30th Lambda λ
Mem מ 40 My μ
Now נ 50 Ny ν
Samech ס 60 Xi ξ
Ajin ע 70 Omicron ο
Pe פ 80 pi π
Koph ק 100 Rho ρ
Resch ר 200 Sigma σ
Shin ש 300 dew τ
Taw ת 400 Ypsilon υ
Cape (final) ך 500 Phi φ
Meme (final) ם 600 Chi χ
Well (final) ן 700 Psi ψ
Pe (final) ף 800 omega ω
Tzade (final) ץ 900 Sampi ϡ

## Hebrew numerals

The Hebrew numerals also use this system. The similarities in the designation of the letters and the extensive correspondence in the numerical values ​​are partly explained by the common origin of the Greek and Hebrew alphabets in the Phoenician script .

## Other use

Up to the present day the Milesian system is used in number symbolism , especially in gematria . Research suggests that this use goes back mainly to Greek influences, as Pythagorean number mysticism was widespread. There are different currents of development in Kabbalistic up to the Hermetic Kabbalah and other esoteric currents. An oft-cited example are the songs of King Solomon :

• 1 Kings 5.12  EU reports that the wise King Solomon composed 1,005 songs. This corresponds to the sum of the numerical value of the Hebrew lettersשיר למלך שלמהwhich mean "songs of King Solomon".

## literature

• Hans Wußing : 6000 years of mathematics: a cultural-historical journey through time . 1. From the beginning to Leibniz and Newton. Springer-Verlag, 2008.

## Individual evidence

1. std.dkuug.dk (PDF)
2. O. Böcher: Gematrie , Col. 777.
3. כ = ך; see. Carlsteueragel: The number of proverbs and songs of Solomon (1. Reg 5,12) . In: ZAW 30, 1910, p. 70 f. With regard to the “3,000 sayings” of Solomon in verse 12, Steueragel points out that the sum of the natural phenomena mentioned in the following verse (when a word is written in plenum) results in the numerical value 3,000.