"The law of mutual interaction"

[Richardbryant]

Recently i am reading Classical Mechanics from Gregory
In section 3.3 , he provide a statement which he named " The law of mutual interaction." as follow

"The law of mutual interaction"
Suppose that two particles P1 and P2 interact with each other and that P2 induces an instantaneous acceleration in a12in P1 while P1 induces an instantaneous acceleration a21 in P2. Then
i) these accelerations are opposite in direction and parallel to the straight line joining P1 and P2
ii) The ration of the magnitude of these accelerations, |a21|/|a12| is a constant independent of the nature of the mutual interaction between P1 and P2, and independent of the positions and velocities of P1 and P2( where relativistic effects are negligible)

Moreover, suppose that when P2 interact with a third particle P3 the induced accelerations are a23 and a32, and when P1 interacts with P3 the induced accelerations are a13 and a31 then the magnitude of these accelerations satisfy the consistency relation

|a21|/|a12|x|a13|/|a31|x|a23|/|a32| =1

I have no idea of the the content from the last paragraph how can it be

 

[Orodruin]

This is a direct consequence of Newton's second and third laws.