The main uptake is that I'm really surprised how little has changed, how similar the work and presentation is to what we do today. That gives me a lot of confidence, actually; I'm glad to be in a discipline with "deep roots" that is stable and consistent. The presentation my be a bit more concise -- but that's kind of funny because everyone I know that's engaged in writing an in-house custom algebra text says that their goal is too write something "short, just what they need, with the extraneous parts cut out". Well, you don't get much more concise than a real math text. (Most of the theorems and presentations are all of 4 lines long at most.) One novelty I really like here is that instead of separate worked-out examples within the text, the protocol is to simply begin a block of exercises with the first few including fully worked-out solutions (which I think would clarify to the student what work we're expecting them to do; and as always you've got answers to the odd-numbered questions at the back for them to check).
Sure, a couple pieces of terminology are just a bit different. Graphs of functions are are generally called "loci". What I've always seen as a "greatest common factor (GCF)" is herein called a "highest common factor "HCF)". And probably the single biggest difference is the claim that a statement like "x = x+1" or "0 = 1" does not count as an equation whatsoever (whereas I'd call it an equation with no solutions, i.e., an equation of the inconsistent variety).
But here's my point. Granted how relatively little has changed in this near century-old math textbook as compared to the class I teach each night right now; and granted the tremendous struggle we have these days to make good textbooks accessible and affordable to our students -- might we consider actually using out-of-copyright math textbooks as a resource? We could totally scan a brief, high-quality, public-domain text such as this and distribute it for free to anyone who wanted it. Do you think that would ever be workable?
