The analysis of William Ivins strongly supports van 
Groningen when the latter writes: “The conception which they 
have of the future is, of course, only an expected, dreaded or 
desired parallel to the past.” But the visual element in the Greek 
sensibility was still much embedded in the audile-tactile 
complex, giving to their fifth century, as to the Elizabethan 
Age, the character of a relatively balanced sensibility. (15) 
That the same limitation of mere visual parallelism affected 
Greek geometry Ivins points out in his Art and Geometry  (pp. 
57­8):

          When Pappus had finished, the situation was that 
     the late Greek geometers knew two focal ratios, three 
     directrix-focus ratios, and the visual transformation of a 
     circle into an ellipse. They also knew, and these I shall 
     come back to, not only particular cases of the invariance