Vaguely comes from vague plus -ly; vague is from French vague, from Latin vagus ('wandering, indefinite, vague'). In current use it is an adverb meaning "in an unclear, imprecise, or slight manner". That sense is explained by the older material without requiring a speculative semantic step: the inherited or borrowed base supplies the field of meaning, while the English formation fixes its modern role. The final -ly makes the underlying adjective or participial form adverbial. The surface form is compositional: its joined elements remain visible in the modern word. A central historical form is Latin vagus. Related English forms include vague and vagueness. The word's history is thus visible in its construction: the components remain interpretable even after the whole expression has settled into a conventional English meaning.