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I am reading Whittaker and Watson's A Course of Modern Analysis. In the third chapter where they discuss different ways to visualize functions that map the complex plane to the complex plane, they remark:

One suggestion (made by Lie and Weierstrass) is to use a doubly-manifold system of lines in the quadruply-manifold totality of lines in three-dimensional space.

This is their entire description of Lie and Weierstrass' approach, and it is too vague for me to figure out what is being suggested.

Does anyone know what this refers to? Does anyone have references for Lie and Weierstrass' work on complex function visualization?

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    What's the page number in W&W of that quotation?2012-05-11
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    @deoxygerbe The quote is on page 41 in either the third (1920) or fourth (1927) edition — the first section of the third chapter.2012-05-12

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