From Tolkien Gateway

IS it for sure that athae is a verb and/or a cognate to asea? First of all, it doesn't look like a verb: its stem is not indicated by a hyphen and I can't recall any verbs whose stem end in -ae-. Secondly, asea is not a verb, therefore the two can't be cognates. If we accept athae as a verb, it could be a cognate to asya-

I believe that athae is a cognate to asea and not a verb, but an adjective. Sage 01:25, 14 May 2011 (UTC)

1. True, it seems like I misread the passage (quoted it below). I missed the semicolon (read it as a comma):
" S athae, ath(a)elas; eitha-, to ease, assist." (PE17, p. 148)
2. Since (what I can see) neither athae nor asëa are given any direct translations (nor put in any lexical categories), any such attempts would have to be "theories" (i.e., original research).
3. The question of cognates is interesting and has relevance for many linguistic articles on TG. In one sense, as I understand it, all the Sindarin and Quenya words listed in the ATH article are cognates, "words that have a common etymological origin", i.e., all those words ultimately derive from ATH (or have an element which derives from ATH). On the other hand, there are words which share a relation to a specific primitive form (itself derived from ATH). The source says:
"athae + lass “leaf”: *aÞayā > Q asëa, S athae, athe: the √ATH = ease, comfort, heal" (PE17, p. 49)
Since asëa and athae are grouped like this, and seemingly derived from aÞayā, I listed them as more closely related in the section "Cognates" in the ATH article.
--Morgan 07:59, 14 May 2011 (UTC)
In fact I think linguists can talk about 'direct' or 'loose' cognates. In this case, I think adjectives asea and athae derive from the PQ adjective athaja. But then, I also think that there was an identical verb *athaja- a verb *athja- whence verbs asya- and eitha- derive Sage 08:51, 14 May 2011 (UTC)