Alphabetic numeral system
[2] Other cultures in contact with Greece adopted this numerical notation, replacing the Greek letters with their own script; these included the Hebrews in the late 2nd century BC.
Unlike the Greek, the Hebrew alphabet's 22 letters allowed for numerical expression up to 400.
Acrophonic numerals do not belong to this group of systems because their letter-numerals do not follow the order of an alphabet.
Higher hundreds – 500, 600, 700, 800, and 900 – can be written only with various cumulative-additive combinations of the lower hundreds (direction of writing is right to left):[7] Armenian numeral signs (minuscule letters): Unlike many alphabetic numeral systems, the Armenian system does not use multiplication by 1,000 or 10,000 in order to express higher values.
[8] As the alphabet ended, various multiplicative methods were used for the expression of higher numbers in the different systems.
In the Greek alphabetic system, for multiples of 1,000, the hasta sign was placed to the left below a numeral-sign to indicate that it should be multiplied by 1,000.
The most common method, used by Aristarchus, involved placing a numeral-phrase above a large M character (M = myriads = 10,000) to indicate multiplication by 10,000.
[11] This method could express 5,462,360,064,000,000 as: Alphabetic numerals were distinguished from the words with special signs, most commonly a horizontal stroke above the numeral-phrase, but occasionally with dots placed to either side of it.
Writing is from left to right in Greek, Coptic, Ethiopic, Gothic, Armenian, Georgian, Glagolitic, and Cyrillic alphabetic numerals along with Shirakatsi's notation.
A mixed number could be written as such: ͵θϡϟϛ δ´ ϛ´ = 9996 + 1⁄4 + 1⁄6 In many astronomical texts, a distinct set of alphabetic numeral systems blend their ordinary alphabetical numerals with a base of 60, such as Babylonian sexagesimal systems.
In the 2nd century BC, a hybrid of Babylonian notation and Greek alphabetic numerals emerged and was used to express fractions.
With this sexagesimal positional system – with a subbase of 10 – for expressing fractions, fourteen of the alphabetic numerals were used (the units from 1 to 9 and the decades from 10 to 50) in order to write any number from 1 through 59.
[14] The first major text in which this blended system appeared was Ptolemy's Almagest, written in the 2nd century AD.
The Greeks adopted this technique using their own sign, whose form and character changed over time from early manuscripts (1st century AD) to an alphabetic notation.
[17] The degree's value is in the ordinary decimal alphabetic numerals, including the use of the multiplicative hasta for 1000, while the latter two positions are written in sexagesimal fractions.
