Translations:The principle of least time/12/en

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The traveltime along the flow line between the two wavefronts is . The traveltime along the test path is . Because cos at any point is always less than or equal to one, it follows that . Thus, the traveltime along the flow line is less than the traveltime along any test path except along the flow line itself. Finally, the flow line - that is, the line whose direction at any point coincides with the direction of the gradient - is the least-time path.