What is Potential and voltage?

Example 6.20 (Three ways to the same answer)

In the figure, $E_1 = 10\,\mathrm{V}$, $R_1 = 1.0\,\mathrm{k}\Omega$, $E_2 = 5.0\,\mathrm{V}$, $R_2 = 2.0\,\mathrm{k}\Omega$, $R_3 = 2.0\,\mathrm{k}\Omega$. Millman: $V_N = (10/1 + 5/2 + 0/2)/(1 + 0.5 + 0.5) = 12.5/2 = 6.25\,\mathrm{V}$. Superposition: $E_1$ alone sees $R_2 \parallel R_3 = 1\,\mathrm{k}\Omega$, so $u = 10 \times 1/2 = 5\,\mathrm{V}$; $E_2$ alone sees $R_1 \parallel R_3 = 0.667\,\mathrm{k}\Omega$, $u = 5 \times 0.667/2.667 = 1.25\,\mathrm{V}$; total $6.25\,\mathrm{V}$. Thévenin seen from $R_3$: $E_{\mathrm{Th}}$ is the open-circuit voltage of the divider $(E_1, R_1, R_2, E_2)$: $E_2 + (E_1 - E_2)R_2/(R_1 + R_2) = 5 + 5 \times 2/3 = 8.33\,\mathrm{V}$; $R_{\mathrm{Th}} = R_1 \parallel R_2 = 0.667\,\mathrm{k}\Omega$; then $u = 8.33 \times 2/2.667 = 6.25\,\mathrm{V}$.