The processes employed were justified largely on the ground that they worked, and it was in until the eighteenth century had almost elapsed, after a number of absurdities and contradictions had crept into mathematics, that mathematicians flit it was essential that the basis of their work be logically examined and rigorously established. The painstaking effort to place analysis on a logically rigor roust foundation was a natural reaction to the Pell, mell employment of intuition and formalism of the previous century.