# Translations:The principle of least time/9/en

Let us take an isotropic medium in which the velocity varies continuously so that there is no interface at which reflection and/or refraction could occur. We now show that in such a case, Fermat’s principle holds in its original formulation (i.e., traveltime is a minimum). Let an arbitrary path between two wavefronts be given (Figure 9b). This arbitrary path is called the *test path*. Let us first figure out what happens between two closely spaced wavefronts. Because the wavefronts are so close together, we might consider the parts of them within a small region to be two parallel straight lines. The test path *AC* would be a straight line between the two wavefronts, and the flow line *AB* would be a straight line orthogonal to both wavefronts. If is the angle between the test path and the flow line, if *ds* is equal to the length of the flow line, and if is the length of the test path, then .