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At the moment though, I'm not interested in most of the book, only the "Simple Derivation of the Lorentz Transformations" in the appendix. I'm finding it far from simple and I'm hoping someone could help me with it.

First of all, I'll not assume anyone to actually have this book, so here is a link to an online version (of poorer quality) of the derivation: http://www.bartleby.com/173/a1.html

My first problem starts at equation (3) (and (4)). It's not all that obvious to me why we're adding that constant.

The rest of my problems start after equation (7). I (mathematically) understand everything up to (7), but then I get lost. I have no idea, for example, where the equation between (7) and (7a) is coming from. Given that equation, I can understand (7a), but then going on to (7b), I'm lost again. Why are the two snapshots identical?

Then there's (8). I'm willing to believe that by inserting a and b, you get those equations, but how does one acquire the value of b?

The last mystery (I haven't gone on to combining everything yet) is (8a). I'm clueless as to what they did to get this equation. I'm sure they did something with the equations of (8), but what exactly... I don't see it.

I hope I explained things sufficiently clear and I hope someone will be able to help me.