On Thursday 03 March 2011 00:10:23 Mike Stay wrote:
Does the OED have anything to say on it? They're a pretty canonical arbiter of such things...
OED regards "geometrical" as more fundamental than "geometric"; it has citations for "geometrical progression" going back to 1557, though their 1557 citation is rather obscure in meaning. (Another, from 1594, is entirely convincing. The same 1594 source is quoted under "arithmetic[al] progression".) All the OED has to say about the origins of the phrase (as opposed to the word "geometric[al]") is: <<< arithmetical progression, †proportion, †ratio, etc. (see arithmetical adj.) relate to differences instead of quotients. The term geometrical points to the fact that problems involving multiplication were originally dealt with by geometry and not by arithmetic.
OED doesn't have much to say about "geometric[al] mean", regrettably. The entry for "mean" has a citation from about 1450 concerning the "meene proporcionalle", which is clearly the same thing as the GM (the OED entry for "mean proportional" quotes the same thing and seems to think it might mean something other than the GM, but I've no idea what else they think it could be). There's nothing for "arithmetic[al] mean" or "geometric[al] mean" until much later. So it's inconclusive, but seems to me like weak evidence against the theory that "geometric mean" came *before* "geometric progression". -- g