CHAPTER IX. Statement and Criticism of the Old Doctrines.

If such then is the part played by mathematics in an age when even the mathematician has come to the aid of the hangman, and the wretch meets a well-deserved doom in strict accordance with a mathematical formula, a fortiori must empirical discovery have preceded mathematical theory in the second millennium before the Christian era. Just as countless malefactors were successfully executed by empirical Jack Ketches before ever the mathematician turned executioner, so we may be certain that untold sums of gold had been weighed by means of natural seeds and according to a standard empirically obtained before ever the sages of Thebes or Chaldaea had dreamed of applying to metrology the results of their first gropings in Geometry or Astronomy.