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Updated: June 4, 2025
A system of numeration was thus established which may be looked at from a double point of view; in the first place from its sexagesimal base, which certainly adapts itself to various requirements with greater ease than any other; in the second from the extreme facility with which not only addition, but all kinds of complex calculations may be made by its use.
To Albatani, however, we owe two really valuable heirlooms. The one is the use of the sine, or half-chord of the double arc, instead of the chord of the arc itself, which had been employed by the Greek astronomers; the other, of even more practical benefit, was the introduction of the present decimal arithmetic, instead of the troublesome sexagesimal arithmetic of the Greeks.
I have omitted details not essential; e.g. that in the first period men were born from the earth and only in the second propagated themselves. The period of 36,000 years, known as the Great Platonic Year, was probably a Babylonian astronomical period, and was in any case based on the Babylonian sexagesimal system and connected with the solar year conceived as consisting of 360 days.
Founded upon a sexagesimal numeration, the metrical system of Babylon and Nineveh was "the most scientific of all those known and practised by the ancients: until the elaboration of the French metrical system, it was the only one whose every part was scientifically co-ordinated, and of which the fundamental conception was the natural development of all measures of superficies, of capacity, or of weight, from one single unit of length, a conception which was adopted as a starting point by the French commission of weights and measures."
Ancestral habits and a very early tradition have led us to preserve, as the unit of time, a unit connected with the earth's movement; and the unit to-day adopted is, as we know, the sexagesimal second of mean time.
The system, too, is different, for it is a decimal, and not a sexagesimal, system of numeration.
The cubit of 525 millimetres was the base of the whole system. We shall not here attempt to explain how the other measures itinerary, agrarian, of capacity, of weight were derived from the cubit; to call attention to the traces left in our nomenclature by the duodecimal or sexagesimal system of the Babylonians, even after the complete triumph of the decimal system, is sufficient for our purposes.
The task was no easy one to bring the lunar year into proper conjunction with the solar year, and there are grounds for believing that prior to the division of the year into twelve parts, there was a year of ten months corresponding to a simpler, perhaps a decimal, system, which appears to have preceded the elaborate sexagesimal system.
Ishtar, the daughter of Sin, is number fifteen, the half of thirty. The unit in the sexagesimal the number sixty is assigned to Anu, the chief of the triad, while the other two members, Bel and Ea, follow as fifty and forty respectively.
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