mathematic from Descartes onward is devoted to the theoretical interpretation of this great and wholly religious symbol. The aim of all our physics since Galileo is identical; but in the Classical mathematics and physics the content of this word is simply _not known_. Here, too, Classical names, inherited from the literature of Greece and retained in use, have veiled the realities. Geometry means the art of measuring, arithmetic the art of numbering. The mathematic of the West has long ceased to have anything to do with both these forms of defining, but it has not managed to find new names for its own elements— for the word “analysis” is hopelessly inadequate. The beginning and end of the Classical mathematic is consideration of the properties of individual bodies and their boundary-surfaces; thus indirectly taking in conic sections and higher curves. _We_, on the other hand, at bottom know only the abstract space-element of the point, which can neither be seen, nor measured, nor yet named, but represents simply a centre of reference. The straight line, for the Greeks a measurable edge, is for us an infinite continuum of points. Leibniz illustrates his infinitesimal principle by presenting the straight line as one limiting case and the point as the other limiting case of a circle having infinitely great or infinitely little radius. But for the Greek the circle is a _plane_ and the problem that interested him was that of bringing it into a commensurable condition. Thus the _squaring of the circle became for the Classical intellect the supreme problem of the finite_. The deepest problem of world-form seemed to it to be to alter surfaces bounded by curved lines, without change of magnitude, into rectangles and so to render them measureable. For us, on the other hand, it has become the usual, and not specially significant, practice to represent the number π by algebraic means, regardless of any geometrical image.