Analysis of information sources in references of the Wikipedia article "Εξηνταδικό σύστημα αρίθμησης" in Greek language version.
In other words: it is only in strictly mathematical or astronomical contexts that the sexagesimal system is consistently applied. In all other matters (dates, measures of weight, areas, etc.), use was made of mixed systems which have their exact parallel in the chaos of 60-division, 24-division, 12-division, 10-division, 2-division which characterizes the units of our own civilization.
Combined with this, another process was taking place. In economic texts units of weight, measuring silver, were of primary importance. These units seem to have been arranged from early times in a ratio 60 to 1 for the main units “mana” (the Greek μνα ̃ “mina”) and shekel. Though the details of this process cannot be described accurately, it is not surprising to see this same ratio applied to other units and then to numbers in general. In other words, any sixtieth could have been called a shekel because of the familiar meaning of this concept in all financial transactions. Thus the “sexagesimal” order eventually became the main numerical system and with it the place value writing derived from the use of bigger and smaller signs. The decimal substratum, however, always remained visible for all numbers up to 60.
Beside these basic elements, many modifications of number symbols were in use for different classes of objects, such as capacity measures, weights, areas, etc. Among these a clear decimal system has been recognized with signs for 1, 10, and 100. The numbers 1 and 10 we have already described. The 100 was written as a circular impression which looks like 10, but is made much bigger. Thus 100 is simply “big 10”. Another system proceeds sexagesimally, at least partially. Distinct units are 1 and 10 as before. A big 1 represents 60. Two big units written in opposing directions are combined into one sign to form 120. A 10-sign added in the middle gives 1200. A very big 10 sign stands for 3600. Variations of these systems, both decimal and more or less sexagesimal, can be established at different localities. The main facts, however, are common to all of them, namely, the existence of a decimal substratum and the use of bigger symbols to represent higher units.
The other inconsistency of the modern astronomical notation, namely, to continue beyond the seconds with decimal fractions, is a recent innovation. It is interesting to see that it took about 2000 years of migration of astronomical knowledge from Mesopotamia via Greeks, Hindus, and Arabs to arrive at a truly absurd numerical system.
