## Accounting History - Greek Roots of Numeration

History of Accounting > **The Greek Roots of Numeration**

With regard to the earliest Greek notation for numbers our information is scanty, for the oldest inscriptions contain no numerals. There is reason to believe that a set of symbols where 1, 2, 3, 4 were denoted by upright strokes, 5 by f, the initial letter of Wi/re, 10 by A (&*<*), 100 by H (

Among the letters of the alphabet the Greeks inserted three strange letters, ? (sigma), 9 or ^ (koppa), ^ (sampi), in order to obtain the twenty-seven symbols2 necessary to express all the numbers from 1 to 999.

The following table gives their scheme for representing numbers:—

a’ £’ 7? 3? e’ ?’ {‘ r,’ ff

123456789

t’ K’ ’ M’ “‘ £’ o’ Tt’ <•

10 20 30 40 50 60 70 80 90

pr a* T’ v’ d>’ v’ 1/ a/ A’

100 200 300 400 500 600 700 800 900

1 See illustration opposite page 26.

1 Nine for units, nine for tens, and nine for hundreds.

To denote thousands they began the alphabet again and put a short stroke at the left of the letter. Thus

,a = 1000 £ = 2000 /y = 3000, &c.

To denote 10,000 they generally employed Mi> or M, and

if there were several tens of thousands they wrote the number

• of them above the M ; thus M = 20,000.

Their notation for whole numbers will be understood from the following examples :— Ky’ = 23, rfif = 340, pvy’ = 153, /X°7? = 4673, M/y^a’ = 8,473,921.

Fractions whose numerator was unity were expressed by writing the denominator and affixing two accents ; thus & = 7?, Tt = tS”. If the numerator was not unity, it was written to the left of the denominator; thus ^ =»/ iy”. The symbol for £ in Archimedes resembles L, in Heron a capital S.

The numerical notation of the Romans is much inferior to that of the Greeks, though far fewer symbols are employed in it. The symbols are:

I V X L C D M

1 5 10 50 100 500 1000

The character for 500, namely D, is a modified form of D, CI3 is 1000, 133 is 5000, CCI33 is 10,000, and so on. Sometimes a stroke was placed over a number to indicate that its value was increased a thousand fold; thus 1=1000, Y = 5000, X = 10,000.

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