Greek numerals
In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world.
[5] The present system uses the 24 letters adopted under Eucleides, as well as three Phoenician and Ionic ones that had not been dropped from the Athenian alphabet (although kept for numbers): digamma, koppa, and sampi.
[citation needed]) This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total.
(It was not always the case that the numbers ran from highest to lowest: a 4th-century BC inscription at Athens placed the units to the left of the tens.
[9]) In ancient and medieval manuscripts, these numerals were eventually distinguished from letters using overbars: α, β, γ, etc.
During antiquity, the original letter form of digamma (Ϝ) came to be avoided in favour of a special numerical one ().
Alexander the Great's father Philip II of Macedon is thus known as Φίλιππος Βʹ in modern Greek.
The declining use of ligatures in the 20th century also means that stigma is frequently written as the separate letters ΣΤʹ, although a single keraia is used for the group.
This would defy the then-held notion that it is impossible to name a number greater than that of the sand on a beach or on the entire world.
Pappus of Alexandria reports that Apollonius of Perga developed a simpler system based on powers of the myriad; αΜ was 10,000, βΜ was 10,0002 = 100,000,000, γΜ was 10,0003 = 1012 and so on.
Each number in the second column, labeled εὐθειῶν, ["straight lines" or "segments"] is the length of the corresponding chord of the circle, when the diameter is 120.
The next column, labeled ἐξηκοστῶν, for "sixtieths", is the number to be added to the chord length for each 1' increase in the arc, over the span of the next 1°.
This gradual change from an invented symbol to ο does not support the hypothesis that the latter was the initial of οὐδέν meaning "nothing".
[12][13] Note that the letter ο was still used with its original numerical value of 70; however, there was no ambiguity, as 70 could not appear in the fractional part of a sexagesimal number, and zero was usually omitted when it was the integer.
