nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqky223zcc4q69d8t0me4vg5uw8mw0yxeukjgvz6h92laqnenr0ajsgze5g0 (nprofile…e5g0) Years ago, I encountered a book on Euclidean geometry, written by a pair of Russian (well, Slavic, nowadays) mathematicians. The book set out to show that almost all of Euclidean geometry in The Elements could be proven with only a straight edge. At the end, they proved, using a straight edge, that (A) it is impossible to find the center of a circle, and (B) it is possible to find the center of a circle if there exists another circle somewhere. They posited that (A) was an example of Goedel's Incompleteness.
I found the book in the math library at Weizmann Institute 45 years ago. Might still be there.