Trying to follow i "beginer's" proof/derivation from relativity demistified. I'm trying to follow this proof/derivation in Relativity demystified basically the book is showing transformations and how they work according to the invariance of the speed of light. (im working on chapter 1 pg 9-13 in case any one has the book). The first question i have is, at one point in the book they say that a flash of light moving out from some origin is described by the function of C^2*t^2=x^2+y^2+z^2 (i assume a circle). then they set that equal to zero as well as another coordinate system (F`), and since its in standard form (or something similar) aka only the x direction is moving the y and z and y` and z` cancel out so it leaves us with the equation c^2*t^2-x^2=c^2*t`^2-x`^2 then the author goes on to say "now we use the fact that the transformation is linear while leaving y an z unchanged. the linearity of the transformation means it must have the form x`=Ax+Bc*t c*t`=Cx+Dc*t im confused how is it linear aren't there squared terms and how did he rearrange these equations into these two linear equations? I have more questions but this i all i will ask for now.