The Greeks at first employed the letters of the entire alphabet to
express the first twenty-four numbers; but the system was cumbrous, and
they adopted the happy expedient of dividing their alphabet into three
portions, using the first to symbolize the 9 digits, the second the 9
tens, and the third the 9 hundreds; and, as their alphabet contained only
twenty-four letters, they invented three additional symbols. Their list
of symbols then stood as follows:—
+-----------------+----------------------+---------------------+
| Units. | Tens. | Hundreds. |
+-----------------+----------------------+---------------------+
|α represents 1|ι represents 10|ρ represents 100|
|β 2|κ 20|σ 200|
|γ 3|λ 30|τ 300|
|δ 4|μ 40|υ 400|
|ε 5|ν 50|φ 500|
|ϝ (introduced) 6|ξ 60|χ 600|
|ζ 7|ο 70|ψ 700|
|η 8|π 80|ω 800|
|θ or ϑ 9|Ϟ or ϟ (introduced) 90|ϡ, [symb], [symb] |
| | | (introd’d) 900|
+-----------------+----------------------+---------------------+
By these symbols, only numbers under 1000 could be expressed; but, by
putting a mark called iota under any symbol, its value was increased
a thousand-fold: thus, ᾳ = 1000, κͅ = 20,000; or, by subscribing the
letter Μ, the value of a symbol was raised ten thousand-fold. For these
two marks, single and double dots were afterward substituted. This
improvement enabled them to express with facility all numbers as high as
9,990,000,—a range sufficient for all ordinary purposes.
It has been supposed that the Romans used M to denote 1000 because it
is the first letter of Mille, which is Latin for 1000; and C to denote
100, it being the first letter of Centum, the Latin term for 100. Some
also suppose that D, being formed by dividing the old M in the middle,
was therefore appointed to stand for 500,—that is, half as much as the M
stood for when it was whole; and that L being half a C, was, for the same
reason, used to denominate 50. But the most natural account of the matter
appears to be this:—
The Romans probably put down a single stroke, Ⅰ, for one, as is still the
practice of those who score on a slate, or with chalk; this stroke they
doubled, trebled, and quadrupled, to express two, three, and four: thus,
ⅠⅠ, ⅠⅠⅠ, ⅠⅠⅠⅠ. So far they could easily number the strokes with a glance
of the eye; but they found that if more were added it would be necessary
to count the strokes one by one: for this reason, when they came to five,
it was expressed by joining two strokes together in an acute angle, thus,
Ⅴ.
After they had made this acute angle, Ⅴ, for five, they then added
single strokes to the number of four, thus, ⅤⅠ, ⅤⅠⅠ, ⅤⅠⅠⅠ, ⅤⅠⅠⅠ, and
then, as the strokes could not be further multiplied without confusion,
they doubled their acute angle by prolonging the two lines beyond their
intersection, thus, Ⅹ, to denote two fives, or ten. After they had
doubled, trebled, and quadrupled this double acute angle, thus, ⅩⅩ, ⅩⅩⅩ,
ⅩⅩⅩⅩ, they then, for the same reason which induced them to make a single
angle first, and then to double it, joined two single strokes in another
form, and, instead of an acute angle, made a right angle, Ⅼ, to denote
fifty. When this was doubled, they then doubled the right angle, thus,
⊏, to denote one hundred, and, having numbered this double right angle
four times, thus, ⊏⊏, ⊏⊏⊏, ⊏⊏⊏⊏, when they came to the fifth number, as
before, they reverted it, and put a single stroke before it, thus, Ⅰ⊐,
to denote five hundred; and, when this five hundred was doubled, then
they also doubled their double right angle, setting two double right
angles opposite to each other, with a single stroke between them, thus,
⊏Ⅰ⊐, to denote one thousand: when this note for one thousand had been
repeated four times, they then put down Ⅰ⊐⊐ for five thousand, ⊏⊏Ⅰ⊐⊐ for
ten thousand, and Ⅰ⊐⊐⊐ for fifty thousand.
The corners of the angles being cut off by transcribers for despatch,
these figures were gradually brought into what are now called numerical
letters. When the corners of ⊏Ⅰ⊐ were made round, it stood thus, ⅭⅠↃ,
which is so near the Gothic ന that it soon deviated into that character;
so that Ⅰ⊐ having the corners made round stood thus, ⅠↃ, and then easily
deviated into D. ⊏ also became a plain C by the same means: the single
rectangle, which denoted fifty, was, without any alteration, a capital
L; the double acute angle was an X; the single acute angle, a V; and a
plain single stroke, the letter I. And thus these seven letters, M, D,
C, L, X, V, I, became numerals. As a further proof of this assertion,
let it be considered that ⅭⅠↃ is still used for one thousand, and ⅠↃ for
five hundred, instead of M and D; and this mark, ന, is sometimes used to
denote one thousand, which may easily be derived from this figure, ⊏Ⅰ⊐,
but cannot be deviations from, or corruptions of, the Roman letter M.
The Romans also expressed any number of thousands by a line drawn over
any numeral less than one thousand: thus, V̅ denotes five thousand, L̅X̅
sixty thousand; so, likewise, M̅ is one million, M̅M̅ two millions, &c.
Upon the discovery of printing, and before capitals were invented, small
letters served for numerals; not only when Gothic characters were in
vogue, but when Roman had become the prevailing character. Thus, in early
times, ~i~ ~b~ ~x~ ~l~ ~c~ ~d~ ~m~ were, and in Roman type are still,
of the same signification as capitals when used as numerals. Though the
capital J is not a numeral letter, yet the lower-case ~j~ is as often and
as significantly used as the vowel ~i~, especially where the former is
employed as a closing letter, in ~ij~ ~iij~ ~bj~ ~bij~ ~biij~ ~dcij~, &c.
In Roman lower-case numerals, the j is not regarded, but the i stands for
figure 1 wherever it is used numerically.
During the existence of the French Republic, books were dated in France
from the first year of the Republic: thus An. XII. (1803,) or twelve
years from 1792.