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08423_Field_TCGG T188.txt
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1996-04-10
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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