How did rebellions in the Americas and Europe reflect Enlightenment ideals?

Rebellions and revolutions in the Americas and Europe often occurred due to the rise of new ideals of government based upon Enlightenment philosophies. In France, dissatisfaction with the existing monarchy led to the formation of a Republic. The monarchy previously in power was overthrown and the monarchs were executed. This new system of a Republic employed represented the interests of all of the citizens. Focuses of Enlightenment included personal freedoms, natural rights, and the elimination of the abuses of a Monarchy, all of which were attempted to achieve in the formation of a Republic. Napoleon Bonaparte, a student of Enlightenment though and a military leader, also used Enlightenment ideals while ruling countries in Europe. In North America, colonists became increasingly connected with other countries and in turn new ideas brought forth by the Enlightenment. With exposure to these new ideals in government, rebellions began to occur in the colonies. Colonists protested taxation without representation, and later emerged as an independent country. The Declaration of Independence of the colonies also emphasized an Enlightened Doctrine of Rights, that included the rights of, "life, liberty, and the pursuit of happiness." In South America, revolutions also were led by leaders educated with Enlightenment ideals. New ideaologies of government inspired by the Enlightenment included conservatism, romanticism, and nationalism (which coordinated with liberalism). These government forms evolved after rebellions in the Americas in Europe in response to protests of the current government.
Below: the First French Republic

Source: http://en.wikipedia.org/wiki/French_First_Republic
Smith, Bonnie G., Richard Von Glahn, and Kris E. Lane. Crossroads and Cultures: A History of the World's Peoples. Boston: Bedford/St. Martin's, 2012. Print.