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In the book "Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein, Volume 2: The Now Mighty Theoretical Physics, 1870 to 1925" you can find, on pages 131-134 some parts are translated.

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So what I understand from reading the other answers is this: Here on earth: 1 Kilogram of lettuce: Mass-> 1 Kg, Weight-> 1 Kgf In another hypotetical planet where gravity is half of earth: 1 Kilogram of lettuce: Mass-> 1 Kg, Weight-> 0.5 Kgf Since there is no practical easy way to measure mass, in everyday life we use the kilogram as a unit of weight ...

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Check out Feynman's thesis: Feynman, Richard P., Laurie M. Brown, and P. A. M. Dirac. Feynman’s Thesis a New Approach to Quantum Theory, 2005. Feynman invented the path integral formulation of Quantum Mechanics (QM), in which he grounds QM in a least-action principle similar to that of Fermat. In "§7 Discussion of the Wave Equation: The Classical Limit," ...

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Do we have a deeper understanding of Fermat's Principle? I thought we did. See the derivation section of the Wikipedia article: "Fermat's principle is the main principle of quantum electrodynamics which states that any particle (e.g. a photon or an electron) propagates over all available, unobstructed paths and that the interference, or superposition, ...

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