${\displaystyle 6\nu _{1}={\begin{vmatrix}1&x_{1}&y_{1}&z_{1}\\1&x_{2}&y_{2}&z_{2}\\1&x_{4}&y_{4}&z_{4}\\1&x_{5}&y_{5}&z_{5}\end{vmatrix}}=\mu \nu {\begin{vmatrix}x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\\alpha _{2}&\beta _{2}&\gamma _{2}\\\alpha _{3}&\beta _{3}&\gamma _{3}\end{vmatrix}}=\mu \nu \mathrm {A} ,}$

${\displaystyle 6\nu _{2}=\nu \lambda {\begin{vmatrix}x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\\alpha _{3}&\beta _{3}&\gamma _{3}\\\alpha _{1}&\beta _{1}&\gamma _{1}\end{vmatrix}}=\nu \lambda \mathrm {B} ,}$

${\displaystyle 6\nu _{3}=\lambda \mu {\begin{vmatrix}x_{2}-x_{1}&y_{2}-y_{1}&z_{2}-z_{1}\\\alpha _{1}&\beta _{1}&\gamma _{1}\\\alpha _{2}&\beta _{2}&\gamma _{2}\end{vmatrix}}=\lambda \mu \mathrm {C} ,}$

${\displaystyle {\frac {1}{6^{\frac {1}{2}}}}{\frac {\nu _{1}+\nu _{2}+\nu _{3}}{\sqrt {\nu _{1}\nu _{2}\nu _{3}}}}={\frac {\mu \nu \mathrm {A} +\nu \lambda \mathrm {B} +\lambda \mu \mathrm {C} }{\lambda \mu \nu {\sqrt {\mathrm {ABC} }}}}.}$

${\displaystyle {\begin{vmatrix}1&x_{2}&y_{2}&z_{2}\\1&x_{3}&y_{3}&z_{3}\\1&x_{4}&y_{4}&z_{4}\\1&x_{5}&y_{5}&z_{5}\end{vmatrix}}=0,}$

μνA + νλB + λμC = λμν ${\displaystyle {\begin{vmatrix}\alpha _{1}&\beta _{1}&\gamma _{1}\\\alpha _{2}&\beta _{2}&\gamma _{2}\\\alpha _{3}&\beta _{3}&\gamma _{3}\end{vmatrix}}}$ = λμνD,

${\displaystyle {\frac {1}{6^{\frac {1}{2}}}}\left({\sqrt {\frac {\nu _{1}}{\nu _{2}\nu _{3}}}}+{\sqrt {\frac {\nu _{2}}{\nu _{3}\nu _{1}}}}+{\sqrt {\frac {\nu _{3}}{\nu _{1}\nu _{2}}}}\right)={\frac {\mathrm {D} }{\sqrt {\mathrm {ABC} }}}}$,