intellectual and ideological context in which revolutions swept the atlantic world from 1750 to 1900 answers

The intellectual and ideological context was fundamentally liberal. Inspired by the ideas of philosophers such as John Locke, Montesquieu, Jean-Jacques Rosseau, among others, revolutionaries sought to topple the monarchic regimes, and replace them with democratic institutions.

In Europe, the French Revolution abolished the monarchy, and established a brief period of democracy that ended in the dictatorship of Napoleon.

In the Americas, the English Colonies formed a federal country: the United States, and in the Spanish Americas, several countries were carved out of the former colonial empire, and all of the new countries became liberal democracies.