Page:A History of Mathematics (1893).djvu/83

quently in Athenian inscriptions and are, on that account, now generally called Attic. For some unknown reason these symbols were afterwards replaced by the alphabetic numerals, in which the letters of the Greek alphabet were used, together with three strange and antique letters ϛ, ϙ, and ϡ, and the symbol Ϻ. This change was decidedly for the worse, for the old Attic numerals were less burdensome on the memory, inasmuch as they contained fewer symbols and were better adapted to show forth analogies in numerical operations. The following table shows the Greek alphabetic numerals and their respective values:—

$\scriptstyle {\alpha }$	$\scriptstyle {\beta }$	$\scriptstyle {\gamma }$	$\scriptstyle {\delta }$	$\scriptstyle {\epsilon }$	ϛ	$\scriptstyle {\zeta }$	$\scriptstyle {\eta }$	$\scriptstyle {\theta }$	$\scriptstyle {\iota }$	$\scriptstyle {\kappa }$	$\scriptstyle {\lambda }$	$\scriptstyle {\mu }$	$\scriptstyle {\nu }$	$\scriptstyle {\xi }$	$\scriptstyle {\mathrm {o} }$	$\scriptstyle {\pi }$	ϙ
1	2	3	4	5	6	7	8	9	10	20	30	40	50	60	70	80	90

$\scriptstyle {\rho }$	$\scriptstyle {\sigma }$	$\scriptstyle {\tau }$	$\scriptstyle {\upsilon }$	$\scriptstyle {\phi }$	$\scriptstyle {\chi }$	$\scriptstyle {\psi }$	$\scriptstyle {\omega }$	$\scriptstyle {\mathrm {\sampi} }$	$\scriptstyle {_{_{'}}{\alpha }}$	$\scriptstyle {_{_{'}}{\beta }}$	$\scriptstyle {_{_{'}}{\gamma }}$	etc.
100	200	300	400	500	600	700	800	900	1000	2000	3000

Ϻ	β Ϻ	γ Ϻ	etc.
10.000	20,000	30,000

It will be noticed that at 1000, the alphabet is begun over again, but, to prevent confusion, a stroke is now placed before the letter and generally somewhat below it. A horizontal line drawn over a number served to distinguish it more readily from words. The coefficient for Ϻ was sometimes placed before or behind instead of over the Ϻ. Thus 43,678 was written δϺ_'γχον. It is to be observed that the Greeks had no zero.

Fractions were denoted by first writing the numerator marked with an accent, then the denominator marked with two accents and written twice. Thus, $\scriptstyle {{\iota \gamma '\kappa \theta ''\kappa \theta ''}={13 \over 29}}$. In case of fractions having unity for the numerator, the $\scriptstyle {{\alpha }'}$ was omitted and the denominator was written only once. Thus $\scriptstyle {{\mu \delta ''}={1 \over 44}}$.