Greek numerals

Figure taken from a cryptographic papyrus in uncial Greek of the fourth century. For clarity the special letters digomma (blue, shaped stigma), coppa (green) and sampi (red, shaped as of spices).

The Greek numerals (Greek: Ελληνικό σύστημα αρίθμησης; Latin: Numeri Graeci) was a non-positional decimal alphabetic numbering system invented by the Ionian Greeks and widely spread by the eastern Mediterranean. It was the first alphabetic numbering, that is, it used letters as if they were figures, giving them their ordinal position in the alphabet as their value (Α=1, Β=2...). The origin of this system is attributed to the city of Miletus (in Ionia), which is why it is more specifically known as ionic numbering or milesia and also as Alexandrian numbering. This system was very successful and was widely adapted and modified, giving rise to multiple systems such as Hebrew, Abjadi Arabic, Armenian, Georgian, Cyrillic, etc.

In modern Greece this system is still frequently used for ordinal numbers and more rarely for cardinal numbers, similar to the use of Roman numerals in Western Europe and America. For all other uses, modern Arabic numerals are used.

Background

Mycenaean system

Used by the Minoan civilization and the Mycenaean Greeks, it appears in Linear A, Linear B scripts. In the Cypro-Minoan syllabary only the hundred sign appears on a tablet found at Enkomi.

Attic system

The oldest numbering system that uses the Greek alphabet was the Attic numbering, of acrophonic type, which worked in a similar way to the Roman one, which derives from this system through the Etruscan system. The acrophonic formula was as follows:

HE = 1, ENTE = 5, Δ = 10, Η = 100, LAND = 1000 and MEN = 10 000.

It is called acrophonic because, with the exception of the symbol for 1 (a mere vertical stroke), the others came from the first letter of each number in archaic script: πέντε (pénte, “five”), δεκα (déka, “ten »), ηεκατον (hekaton, «one hundred»), χιλιοι (chílioi, «thousand»), μυριας (myrías « ten thousand").

There were also combinations of Π (πεντε, pénte, 5), for 50, 500, 5000 and 50,000 adding to it tiny versions of the symbols for the various powers of ten:

, = 50,, = 500,, = 5000,, = 50 000

Ionian system

From the IV century B.C. C., the acrophonic system was being replaced by a quasidecimal alphabetic system, sometimes called Ionic. Each unit digit (1 - 9) is assigned a letter, each ten (10 - 90) another letter, and each hundred (100 - 900) another letter. This requires 27 letters, so three more old-fashioned letters were added to the 24-letter Greek system:

• saymma ()) or stigma (),) for the 6 (in modern Greek the sigma-tau combination is frequently used: στ),
• qoppa ()) for 90 (in modern Greek qoppa is used numeric:,, and there is the uncial form),),
• sampi (.) for 900.

An acute accent is placed at the end of the group to distinguish numbers from letters. The alphabetic or Ionian system is based on the addition principle in which the numerical values of the letters are added to form the total. For example, 241 is represented as σμα´ (200 + 40 + 1).

To represent numbers from 1,000 to 999,999, the same unit letters, tens, and hundreds are used again, adding an acute inverted accent or a comma to distinguish them. For example, 2004 is represented as ͵βδ´ (2000 + 4). No symbol is used to represent 0.

In modern Greek they are used in both lowercase and uppercase depending on the context. Thus, when used as cardinals they appear almost exclusively in lowercase (e.g. ͵αωκɣ΄, «1823»), while when used as ordinals they are often used in lowercase in lists or in the pagination of the foreword of a publication and capitalized in dynastic names (e.g. Φίλιππος Β΄, "Philip II") and in book chapter numbering.

The Hellenistic Zero

Hellenistic astronomers extended this number system to a sexagesimal positional one by limiting each position to a maximum value of 50+9 and including a special symbol for 0. This zero was more often used alone than in the representation of numbers. In the latter case, it was usually limited to fractions (called minutes, seconds, thirds, fourths, etc.) – they were not used in the whole part of a number.

The system, probably adapted from Babylonian numbering by Hipparchus around 140 B.C. C., was used by Ptolemy (around the year 140), Theon (around 380) and his daughter Hypatia (died in 415).

The Greek sexagesimal zero changed over time. The symbol used on papyrus in the II century was a small circle with a bar above a length several times the diameter of the circle and finished at both ends in various ways. Later the upper bar was reduced to a length equal to the diameter, similar to the modern "ō", which was still used in late medieval Arabic documents in which alphabetical numbers were used. The slash was removed in Byzantine manuscripts, leaving a "ο" to dry. This gradual evolution from an invented symbol to "ο", contradicts the hypothesis that the letter is the initial of οὐδέν, meaning &# 34;nothing".

Some of the true zeros appeared on the first line of each of his eclipse tables, where they were a measure of the angular separation between the center of the Moon and either the center of the Sun (for solar eclipses) or the center of Earth's shadow (for lunar eclipses). All these zeros took the form "0 | 0 0", where Ptolemy actually uses three of the symbols described above. The vertical bar (|) indicated that the integral part on the left was in a separate column marked in their table headings as digits (of five arcminutes each), while the fractional part was on the left. in the next column marked minutes of immersion, with the meaning of 1/60 (and 1/360) of a digit