Meaning:

This proverb teaches us that it is best to act in a way between two opposite (especially extreme) ones to solve a problem or to deal with something.

If you say "Safety lies in the middle course," you mean it is safe to act or do something in a moderate way.

Example:

I think those two parties need to take more time to negotiate. We cannot accept either of their proposals. One is extremely conservative, and the other is extremely radical. Safety lies in the middle course.

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