Both spellings ("plane" and "plain") have been in use for several centuries,

Plane sailing is based on the assumption that the meridian through the point of departure, the parallel through the destination, and the course line form a right triangle in a plane, called the "plane sailing triangle".

This is the usual method used to navigate using paper charts and maps.

The expression "plane sailing" has, by analogy, taken on a more general meaning of any activity that is relatively straightforward.

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