I haven't gotten very far in Mach, but I like something that he said on page 13: "In fact, we regard a phenomenon as explained when we find in it known simpler phenomena." That's an important statement of what physicists value in our theories and derivations. We want to start from as few assumptions as possible, and then show that that small set of assumptions is sufficient to derive the phenomenon of interest. Mach applies this to the derivations of the law of levers throughout history, from Archimedes to Galileo and others. He takes them to task by unpacking their derivations and showing that in each one there was a hidden assumption that went farther than the assumptions enumerated at the start. I admire this effort of Mach's. Personally, I think I can come up with a derivation of the law of the lever that starts from a few explicitly stated assumptions, but still a list that is (in keeping with Mach's argument) longer than the one assumption stated by Galileo and others. However, it requires a lot drawing, so I will probably do it by hand, scan it, and post it at some point.
Also, before I post this I need to do an experiment at home with a hanger, string, and ruler.