I was surprised to learn from John Stillwell's comment in answer to the question, "Can the unsolvability of quintics be seen in the geometry of the icosahedron?", that
There is not a single picture in the whole ...
of Felix Klein's 1884 book, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree. And now that I have it in my hands, I can verify the lack of figures (but its remarkable clarity nonetheless).
By the time of David Hilbert's and Stephan Cohn-Vossen's 1932
Geometry and the Imagination (citing an earlier MO question),
the use of figures had reached a high art.
This high art is continued today in
Tristan Needham's Visual Complex Analysis, with its stunning figures, e.g.,
(from this MSE answer):
To return to ancient times, it is clear that figures were
valued to illustrate Euclid by 100 AD, and likely earlier:
Finally, my question:
Has the use of figures to illustrate geometry waxed and waned over history in a fashion that could almost be graphed with respect to time, or am I plucking out idiosyncratic examples that do not point to any recognizable trends?
Perhaps this needs to be mapped country by country, different in France (during the Bourbaki period) than in Germany, etc.? Or perhaps any such attempt to capture gross trends is hopelessly historically naive?
