Across means from one side to the other side of something, such as a road, river, or area. As an adverb, it can also mean 'in every part of' or 'on the other side'.
From Middle English phrase 'a-crois', literally 'in cross', from Old French 'en croix' (in a cross). It originally suggested a crossing movement in the shape of a cross.
Across carries the ghost of a cross in it—movement that cuts from one side to another. That’s why we say 'across the world' when we imagine a line stretching over the whole globe.
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