To behave in a Keplerian (and thus in a Goethean) fashion regarding a mathematical formula which expresses an observed fact of nature, does not mean that to submit such a formula to algebraic transformation is altogether impermissible. All we have to make sure of is that the transformation is required by the observed facts themselves: for instance, by the need for an even clearer manifestation of their ideal content. Such is indeed the case with the equation which embodies Kepler’s third law. We said that in its original form this equation contains a concrete statement because it expresses comparisons between spatial extensions, on the one hand, and between temporal extensions, on the other. Now, in the form in which the spatial magnitudes occur, they express something which is directly conceivable. The third power of a spatial distance (r³) represents the measure of a volume in three-dimensional space. The same cannot be said of the temporal magnitudes on the other side of the equation (t²). For our conception of time forbids us to connect any concrete idea with ‘squared time’. We are therefore called upon to find out what form we can give this side of the equation so as to express the time-factor in a manner which is in accord with our conception of time, that is, in linear form.¹³ This form readily suggests itself if we consider that we have here to do with a ratio of squares. For such a ratio may be resolved into a ratio of two simple ratios.