In a fair, reasonable, or morally correct manner; deservedly or rightfully.
From Middle English justly, from Old French juste meaning 'righteous' plus the suffix -ly. The root traces to Latin justus meaning 'lawful, righteous' from jus meaning 'law, right'.
The word 'justly' carries the weight of centuries of human struggle for fairness - it's one of those deceptively simple words that encapsulates humanity's highest aspirations for moral behavior. Interestingly, its Latin root 'jus' gave us not only 'justice' but also 'jury' and 'jurisdiction', showing how deeply embedded legal and moral concepts are in our language.
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