Regarding the pressure at a point in a "rested" fluid

[Likith D]

Hey! I just came across this text ;

http://www.feynmanlectures.caltech.edu/img/FLP_II/f40-01/f40-01_tc_big.svgz​

Fig. 40–1. In a static fluid the force per unit area across any surface is normal to the surface and is the same for all orientations of the surface.

"We begin by considering hydrostatics, the theory of liquids at rest. When liquids are at rest, there are no shear forces (even for viscous liquids). The law of hydrostatics, therefore, is that the stresses are always normal to any surface inside the fluid. The normal force per unit area is called the pressure. From the fact that there is no shear in a static fluid it follows that the pressure stress is the same in all directions (Fig. 40-1). We will let you entertain yourself by proving that if there is no shear on any plane in a fluid, the pressure must be the same in any direction."

from http://www.feynmanlectures.caltech.edu/II_40.html

I tried to find "the law of hydrostatics" on the internet, to find no other mention of it. (would appreciate links to more details on it or any ideas regarding the topic)

What is really puzzling is how the absence of shear pressure in all surfaces in a rested fluid (probably or probably not, the one kept on earth) implies the pressure is the same in all directions.
I hope to know how exactly we were able to come to the conclusion.

 

[mfb]

Shear pressure is defined to be the difference between different directions. No shear pressure implies the same pressure in all directions by definition.