I was reading through the proof of the Cauchy Integral Formula here. I do not understand how the transition is made from equation (8) to equation (9). While taking the limit as $r\to 0$, doesn't the closed curve $\gamma_r$ also vanish? So, by then the closed curve $\gamma_r$ around $z_0$ is degenerate(a point), I think.
Can you please explain what is going on? Thank you.