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[U Texas :] Pokorny Etymon: 3. mē-, m-e-t- 'to measure'
Semantic Field: to Measure[...] Italic: Latin: mēnsa
[ Wiktionary : ]
- a table
- a table of food; meal, course, feast
- an altar (sacrificial table)
- vocative singular of mēnsa
2 reminds me of the semantic shift of the English 'meal', from this same PIE root to >repast or time for eating<. But what explains the semantic shift to 1 or 3?
Is it as direct and simple as the fact that tables were used by the Romans to eat?
The entry for this word in the Etymological Dictionary of Latin and the other Italic languages (2008), by Michiel de Vaan, may provide some illumination.
De Vaan says that mensa has an Umbrian cognate mefa that is supposed to have the meaning "a certain sacrificial object, maybe cake".
As Rafael said in a comment, the derivation from the verb meaning 'measure', met(ior), is supposed to have occurred via a participle form. A sacrifice of food could be described fairly literally as "a thing measured out". De Vaan suggests that
In Latin, the meaning then shifted from the offering itself to the object on which the offerings were placed.
