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Pardon me commenting so late. I'm not sure if this has any point (pardon the pun), but I noted that Steve H mentioned he'd never seen this method used before...
I have! (This fact astonishes me, as I'm shockingly inept at all kinds of mathematics!)
It's in the first set of Euclid's books (I can't remember which book, but I'm pretty sure it's books 1-3 (out of 13)). It's actually described in the proof of making an equilateral triangle using only some string and a pencil/goosequill/whatever (instead of a compass), but this extrapolation (finding the centre of any circle using only string/setsquare/pencil) appears in the next few lemmas and proofs.
The reason I know about this at all is because I bought the set of Euclid's books as a way of teaching myself the basics of maths again. Unfortunately the greek used is, well, greek (i.e. not English) - so I bought an English translation.
The problem there is that English translations of Euclid fall into 2 categories - a) 18th century with archaic lingo but no mathematical assumptions (with the focus on the original greek language used, not the mathematics involved), or b) 21st century with clear language but assuming the reader is not actually learning mathematic proofs from the books, but instead using them as "recreation" while sitting in the Advanced Mathematics chair in King's College!
If anyone can recommend a _readable_ version of Euclid that's still available, it'd be much appreciated - almost as much as I appreciated Steve's article! (Yes, there *was* a point to this meandering!)
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