Originally Posted by **ling233** 1.) for the Sum of Fx , the author gave P1Δx - P3 (I sin theta) , why the author left off the sin theta at the below there ? |

Because it cancels out. Starting with equation (3-3a) sub in delta_x = l sin(theta) and you get:

P_1 l sin(theta) - P_3 l sin(theta) = 0, so:

P_1 - P_3 = 0.

Originally Posted by **ling233** 2.) Why the author assume Δz = 0 ? What's the purpose of assuming Δz = 0 ? |

I must admit the author doesn't explain this very well, but it seems his purpose is to show that the pressure at a point (i.e. where delta_z = delta_x = delta_y = 0) is the same in all directions. So why doesn't he state that delta_x and delta_y also go to zero? Because those quantities have already cancelled out of the equations, so he ignores them.