ΔABC has P as mid-point of AB on x-axis.

Q as midpoint of BC on y-axis.

R as midpoint of AC on z-axis.

∴  A = (x₁y₁z₁)

∴  B = (x₂y₂z₂)

∴  C = (x₃y₃z₃)

$\Rightarrow \mathrm{P}=(\frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2},\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2},\frac{{\mathrm{z}}_1+{\mathrm{z}}_2}{2})$

$\mathrm{Q}=(\frac{{\mathrm{x}}_2+{\mathrm{x}}_3}{2},\frac{{\mathrm{y}}_2+{\mathrm{y}}_3}{2},\frac{{\mathrm{z}}_2+{\mathrm{z}}_3}{2})$

$\mathrm{R}=(\frac{{\mathrm{x}}_3+{\mathrm{x}}_1}{2},\frac{{\mathrm{y}}_3+{\mathrm{y}}_1}{2},\frac{{\mathrm{z}}_3+{\mathrm{z}}_1}{2})$

P = α,0,0

Q = 0,β,0

R = 0,0,γ

$\therefore \frac{{\mathrm{x}}_1+{\mathrm{x}}_2}{2}=\mathrm{\alpha },\frac{{\mathrm{y}}_1+{\mathrm{y}}_2}{2}=0,\frac{{\mathrm{z}}_1+{\mathrm{z}}_2}{2}=0$

$\frac{{\mathrm{x}}_2+{\mathrm{x}}_3}{2}=0,\frac{{\mathrm{y}}_2+{\mathrm{y}}_3}{2}=\mathrm{\beta },\frac{{\mathrm{z}}_2+{\mathrm{z}}_3}{2}=0$

$\frac{{\mathrm{x}}_3+{\mathrm{x}}_1}{2}=0,\frac{{\mathrm{y}}_3+{\mathrm{y}}_1}{2}=0,\frac{{\mathrm{z}}_3+{\mathrm{z}}_1}{2}=\mathrm{\gamma }$

∴  x₁ + x₂ + x₃ = α, y₁ + y₂ + y₃ = β, z₁ + z₂ + z₃ = γ