In a manner that respects or follows bounds and limits; within proper boundaries.
From 'bound' (a boundary or limit) with the suffix '-ly' to form an adverb meaning 'in a way that respects boundaries,' a rare and somewhat archaic formation.
This word is practically extinct in modern English—most people use 'bounded' or 'within bounds' instead—making it a linguistic fossil from when '-ly' was added to nouns more freely.
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