Ai! Lá polin saca i quettar!
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This verb appeared in some rough notes from around 1969 in various past forms such tanc “fixed”, tancher/tanker “they fixed” and tanchen “I fix” (PE23/138 note #12). See the discussion of the Sindarin past tense for more detail on these past forms. The verb ✱tag- is clearly based on the root √TAK “fix, fasten”.
Conceptual Development: The verb G. tag- “fix, make firm, construct” appeared in the Gnomish Lexicon of the 1910s (GL/68), likely based on the early root ᴱ√TAKA “fix, fasten” (QL/88).
Neo-Sindarin: For purposes of Neo-Sindarin, I would use tag- only in the later sense of its root: “to fix, ✱fasten”. For “make firm” I would use [N.] tangad(a)- and for “construct” I would use [ᴱN.] adaba- “build”.