As long as we're advising on possessives, it's a lot more acceptable to pluralize proper names with apostrophe + S (in particular, even when the name ends with an S). So it would be "Archimedes's" imho. Exceptions are only a few traditional phrases like Achilles' heel and Jesus' sake ..., but alas! not including poor old Archimedes. —Dan ----- No worries. Your latest statement sounds equivalent to the one from "Mathematics Magazine". So we've got it all straightened out except that the spelling "Archimede's" is really not an acceptable approximation to "Archimedes' ". Ouch! I guess I need to watch those apostrophes more closely -----