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Saluton estas mallonga por mi donas al vi saluton, kiel bonan tagon, ĉu ne? Angle, vi ne povas diri I give you hello, do kio saluton signifas sole? (Mi pardonpetas por la malbona gramatiko, mi ne estas fluenta)
Saluton is short for mi donas al vi saluton like bonan tagon, right? In English you can't say I give you hello, so what does saluton mean by itself?
There seems to be two questions here:
According to PIV, it means:
Ekstera signo de ĝentileco, kiun oni esprimas per vortoj aŭ movoj al renkontata persono
Which roughly translated means:
An external sign of politeness, that you express with words or movements to someone you recognise.
With this meaning, I don’t think there is anything weird about the phrase mi donas al vi saluton, except that if you actually said it it would probably sound very pompous. Just because in English we would say “hello” in the same situation as we would say “saluton” in Esperanto, doesn’t mean they have the same meaning. Perhaps a closer translation of the word in English could be a greeting or a salutation.
I would imagine the word has the same etymology as salutation in English. According to the Wiktionary, that comes from the Latin salutatio.
salutin French is something likehello(more polite though); deriving from the verb to greet, to salute. I thinksalutonis definitely of French origin.