( Hope springs eternal ) !!!
This saying seems fantabulous ..... but I don`t really perceive its structure, I mean (eternal) is an adj. Could there be an ellipsis of a noun like for example ( eternal life ) or may be (eternal) here is a noun ... mmmm......... I am not sure !!! u tell me !!!!!!!!

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For the grammatical answer...
The structure would be the same as "Hope is eternal."  The verb "springs" here is acting as a linking verb, so the adjective "eternal" is correct.  Other examples of similar usage:

"Something smells funny."
"Sometimes, love grows cold."
"Humility feels unnatural to me."
"George waxed poetic."

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I think they meant "Hope Springs Eternally"? Eternally as an adverb; Hope springs forever.

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I think "eternal" here is a 'adj".It is like the structure of "hope you happy".