Crossing at critical temperature of a gas This is written in the book 'Treatise on Thermodynamics' by Max Plank-

the crossing of the critical temperature at any pressure other than the critical pressure differs in no way from the crossing of any other temperature.

But from the phase diagram of the states, it seems that if we change the temperature at a pressure greater than the critical pressure, then on crossing the critical temperature the gas will liquify where as crossing at other temperatures the gaseous state won't change.
So is the statement in the book wrong?
At the critical temperature/pressure, all properties of liquid and gaseous phase  mutually converge to the same values. There is just one phase at these temperatures, neither liquid, neither gas. Or, both at the same time.
Changing  pressure at temperature above the critical temperature causes continuous changes of the supercritical phase properties without the edge of the gas/liquid phase transition.
Changing  temperature at pressure above the critical pressure causes continuous changes of the supercritical phase properties without the edge of the gas/liquid phase transition.