and while I never quite understand what these entries are telling me, section is somehow related to an OE word seax which means a short sword, but it looks like it derives from the Latin saxum which means stone.

Etymologies, especially the ones in dictionary entries, are greatly compressed histories of related words (and languages). The entry you were referring to (not to mantle Faldo's toes):
Quote:
1550s, from M.Fr. section, from L. sectionem (nom. sectio) "a cutting, cutting off, division," from sectus, pp. of secare "to cut," from PIE base *sek- "cut" (cf. O.C.S. seko, sesti "to cut," secivo "ax, hatchet;" Lith. isekti "to engrave, carve;" Alb. sate "mattock;" O.S. segasna, O.E. sigše "scythe;" O.E. secg "sword," seax "knife, short sword;" O.Ir. doescim "I cut;" L. saxum "rock, stone").
Posits a PIE root (base) *sek- 'to cut' from which are descended many cognate words in various daughter languages. Latin has two words: (1) seco, secare, sectus, 'to cut' (which has an abstract noun sectio from the past passive participle sectus and (2) a noun saxum meaning 'stone'. The noun saxum is not a descendant of seco, they are more like siblings or cousins, both of which descend from the PIE base. Same thing in Old English, except in that case, there are three nouns, i.e., sigše 'scythe' secg 'sword' and seax 'knife, short sword'. The great thing about language is that you can take words or roots (bases) and by using affixes and other morphological processes derive whole families of semantically related words to use.


Ceci n'est pas un seing.