Religious feeling in Classical man focused itself ever more and more intensely upon physically present, _localized_ cults which alone expressed a college of Euclidean deities. Abstractions, _dogmas_ floating homeless in the space of thought, were ever alien to it. A cult of this kind has as much in common with a Roman Catholic dogma as the statue has with the cathedral organ. There is no doubt that something of cult was comprised in the Euclidean mathematic—consider, for instance, the secret doctrines of the Pythagoreans and the Theorems of regular polyhedrons with their esoteric significance in the circle of Plato. Just so, there is a deep relation between Descartes’ analysis of the infinite and contemporary dogmatic theology as it progressed from the final decisions of the Reformation and the Counter-Reformation to entirely desensualized deism. Descartes and Pascal were mathematicians and Jansenists, Leibniz a mathematician and pietist. Voltaire, Lagrange and D’Alembert were contemporaries. Now, the Classical soul felt the principle of the irrational, which overturned the statuesquely-ordered array of whole numbers and the complete and self-sufficing world-order for which these stood, as an impiety against the Divine itself. In Plato’s “Timæus” this feeling is unmistakable. For the transformation of a series of discrete numbers into a continuum challenged not merely the Classical notion of number but the Classical world-idea itself, and so it is understandable that even _negative_ numbers, which to us offer no conceptual difficulty, were impossible in the Classical mathematic, let alone _zero as a number_, that refined creation of a wonderful abstractive power which, for the Indian soul that conceived it as base for a positional numeration, was nothing more nor less than the key to the meaning of existence. _Negative magnitudes_ have no existence. The expression -2×-3=+6 is neither something perceivable nor a representation of magnitude. The series of magnitudes ends with +1, and in graphic representation of negative numbers ( + 3 + 2 + 1 0 - 1 - 2 - 3 ) — ･ — ･ — ･ ･ — ･ — ･ — ･ we have suddenly, from zero onwards, _positive_ symbols of something negative; they _mean_ something, but they no longer _are_. But the fulfilment of this act did not lie within the direction of Classical number-thinking.