Minimum Along the Entire Length

Consider an actual path of a particle through the hemolymph and say the true path traverses point A and point B. If the action is minimal along the entire path, then the path between a smaller section of the line, between points A and B for example, is also minimal. So every subsection of the path our particle follows must also be a minimum no matter how short we make our subsection. So now the statement about what happens over the entire longer path also describes what happens over any shorter piece of the path.

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