In a principal, chief, or fundamental way; relating to the most important aspects of something.
From cardinal (from Latin cardinalis, 'serving as a hinge or pivot') plus the adverbial suffix -ally. The word emphasizes importance because a hinge is the pivotal point on which a door turns.
The word 'cardinal' literally comes from a hinge—because just as a door's entire function depends on its hinge, cardinal directions, cardinal numbers, and cardinal virtues are the 'hinges' on which whole systems turn.
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