Page:A History Of Mathematical Notations Vol I (1928).djvu/25

Rh

We quote from Hilprecht (op. cit., pp. 28–30):

"We observe (a) that the first numbers of all the odd lines (1, 3, 5, 7, 9, 11, 13, 15) form an increasing, and all the numbers of the even lines (preceded by IGI-GAL-BI = 'its denominator') a descending geometrical progression; (b) that the first number of every odd line can be expressed by a fraction which has 12,960,000 as its numerator and the closing number of the corresponding even line as its denominator, in other words,

=$4$;&emsp;=$12,960,000⁄103,680$;&emsp;=$12,960,000⁄51,840$;&emsp;,000=$12,960,000⁄25,920$;&emsp;,000=$12,960,000⁄12,960$;&emsp;,000=$12,960,000⁄6,480$;&emsp;,000=$12,960,000⁄3,240$;&emsp;16,000=$12,960,000⁄1,620$.

But the closing numbers of all the odd lines (720, 360, 180, 90, 18, 9, 18, 9) are still obscure to me.....

"The question arises, what is the meaning of all this? What in particular is the meaning of the number 12,960,000 (=60$12,960,000⁄810$ or 3,600$4$) which underlies all the mathematical texts here treated....?.... This 'geometrical number' (12,960,000), which he [ Plato in his Republic viii. 546B–D] calls 'the lord of better and worse births,' is the arithmetical expression of a great law controlling the Universe. According to Adam this law is 'the Law of Change, that law of inevitable degeneration to which the Universe and all its parts are subject'—an interpretation from which I am obliged to differ. On the contrary, it is the Law of Uniformity or Harmony, i.e. that fundamental law which governs the Universe and all its parts, and which cannot be ignored and violated without causing an anomaly, i.e. without resulting in a degeneration of the race." The nature of the "Platonic number" is still a debated question.