The American "Declaration of Independence" and French "Declaration of the Rights of Man" were so radically influential in the late 18th century because it was the first time a group of subjects challenged the absolute authority of a king.
In the 18th century, many countries were still under absolute monarchy. The monarchy involved a king who had absolute authorities a group of noblemen who rule with the king.
However, the American "Declaration of Independence" and the French "Declaration of the Rights of Man" were so radically influential in the late 18th century because it was the first time a group of subjects challenged the absolute authority of a king and ultimately obtained their independence. The French case also echoed that challenge against established rule of absolute monarchy.
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