Now there's an interesting question... none of the books I've looked at appear to have much of the maths in them. The bulk of the books are either "Build a CNC like I did" and then are essentially a set of plans (or not in one case) but with little explanation why... or are more focussed on the programming and usage but relatively little on the design aspects... something we have great debates on the forum about, between those that prefer the suck it and see based on experience of doing it several times before (and there's nothing like experience I agree) and prefer empirical evidence of what works or doesn't work and others (and I include myself in this category) who want to understand what constitutes a good design from good engineering principles and want evidence to demonstrate that, and indeed want to understand how to make it an optimal design.

Of course, those that build big commercial CNC machines must, we assume, have done the full blown structural design, but most of the low-end 'Chinese' machines are almost certainly 'empirical' in nature (and it shows in many of them). There is very little on the web about the calculations, though plenty of generic 'bending of beams' etc stuff which is 1st year undergrad (or when when I did it 30y ago). As always its in knowing how to apply the knowledge that counts. There are nuggets out there, like this thread on CNCZone and this one here, but again they don't explain too much of the 'why'.

That is one of the reasons we say that no question is stupid... and reading through build threads past and present will give a good cross-section of both the 'calculated' and 'empirical' approaches. If you have specific questions about calculations abd/or principles then ask away...