The second [Babylonian] tablet records the magnitude of the illuminated portion of the moon's disc for every day from new to full moon, the whole disc being assumed to consist of 240 parts. ...This table not only exhibits the use of the sexagesimal system but also indicates the acquaintance of the Babylonians with [ geometric and arithmetic ] progressions.
Many clever men like you have trusted to civilization . Many clever Babylonians, many clever Egyptians, many clever men at the end of Rome. Can you tell me, in a world that is flagrant with the failures of civilisation, what there is particularly immortal about yours?gilbert keith chesterton
Newton was not the first of the age of reason . He was the last of the magicians , the last of the Babylonians and Sumerians, the last great mind that looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10 000 years ago.john maynard keynes
The sexagesimal system was used also in fractions. Thus, in the Babylonian inscriptions, 1/2 and 1/3 are designated by 30 and 20, the reader being expected, in his mind, to supply the word "sixtieths." The Greek geometer Hypsicles and the Alexandrian astronomer Ptolemæus borrowed the sexagesimal notation of fractions from the Babylonians and introduced it into Greece. From that time sexagesimal fractions held almost full sway in astronomical and mathematical calculations until the sixteenth century, when they finally yielded their place to the decimal fractions.
Many clever men like you have trusted to civilization. Many clever Babylonians, many clever Egyptians, many clever men at the end of Rome. Can you tell me, in a world that is flagrant with the failures of civilisation, what there is particularly immortal about yours?
Let us suppose that we have set the problem of finding a solution to the equation This is a problem for which the Babylonians around 1700 BC found the excellent approximation ...This is the identical problem which Pythagoras asserted had no fractional solution and in whose honor he was supposed to have sacrificed a hecatomb of oxen the problem which caused the existentialist crisis in ancient Greek mathematics. The exists (as the diagonal of the unit square); yet it does not exist (as a fraction)!
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