I am trying to understand the proof of gauss' divergence theorem from my book. Now, there is a statement in the proof which i tried to understand, but I am failing to fully understand its whole meaning. Here is the statement:
$For\; points\; on\; S_2.\\\quad dy\;dx=dS_2\;cos\gamma_2$
Let me mention that $cos\;\gamma_2$ is the direction cosine of normal $\bar n_2$ to $S_2$. I have attached a picture for more clarity:
Now I do understand that $dS_2$ means small area on $S_2$, but why $cos\;\gamma_2$ after $S_2$? it would have made some sense if $\bar n_2$ would have been beside $dS_2$ making it treat like a vector, but $cos\; \gamma_2$ changes the whole scenario? Can anyone please explain me the presence of $cos\;\gamma_2$?