In notes at the end of the book, Davis says "The loculus Archimedius
is described by W.W.R. Ball in this 'Mathematical Recreations,' 10th
edition, 1931, p. 54. The construction is ascribed to H. Suter in
'Zeitschrift fur Math. und Physik,' Vol. 44, 1899, pp. 491-499." I
don't have access to either of those references, but I did look in
both the 6th (1914) and 11th (1939) editions of Ball's book and did
not find any mention of the loculus. Maybe I missed it.
Davis's book is an engagingly readable history of Alexandria, and it
lavishes a lot of attention on mathematicians associated with the
city. This surprised me until I did some digging and found that Davis
himself was a mathematician. I heartily recommend the book. Some
enterprising publisher should reprint it.
Barry Cipra
cipra@microassist.com