Selfin, those are the FAA definitions based on such items as the NACA reports they are most certainly correct
FAR part 1 is defining EAS as CAS after having been corrected for adiabatic compressibility
The Bernoulli equation for dynamic pressure, q = ½ ρ V², is an incompressible solution to Euler's equation. This is still true even if ρ V² is swapped for γ p M².
I know what you're talking about...true! but I'm not getting into Fluid Mechanics, continuity and such right now...not enough sleep... and no patience for copying and pasting integrals