Funny thing. So for years I've been meaning to look up what certain math terms mean etymologically - and recently I've been doing this on occasion. It's just for fun and I'm not being systematic about it.

Anyway, I was looking up the word "set" and it pointed to this Latin word "secta" and I thought, "Hey, that sounds like section," so I looked up section.

http://www.etymonline.com/index.php?search=Soap-rock

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.

Makes sense to me. The PIE root means 'to cut' and the English seax became the thing doing the cutting and the Latin saxum the thing being cut (or, in this case, carved).

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): 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., sigðe '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.

No mantle taken, Nuncle.