number of state

Here we are finding number of state less than energy E for particle trapped in 3D harmonic potential .For large value of E as compare to hw , we assumed energy levels as continuous.And we introduces coordinate system in terms of which surface of constant energy is plane E = E_1 + E_2 + E_3 .Number of state with energy less than E in these conditions is given below in image. I am not understanding how the terms in denominator came and why we chosed first octant in plane ?


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