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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