ケイシーの定理
t 12 t 34 + t 14 t 23 = 1 R 2 ⋅ R − R 1 R − R 2 R − R 3 R − R 4 ( K 1 K 2 ̄ ⋅ K 3 K 4 ̄ + K 1 K 4 ̄ ⋅ K 2 K 3 ̄ ) = 1 R 2 ⋅ R − R 1 R − R 2 R − R 3 R − R 4 ( K 1 K 3 ̄ ⋅ K 2 K 4 ̄ ) = t 13 t 24 {\displaystyle {\begin{aligned}&t_{12}t_{34}+t_{14}t_{23}\\[4pt]={}&{\frac {1}{R^{2}}}\cdot {\sqrt {R-R_{1}}}{\sqrt {R-R_{2}}}{\sqrt {R-R_{3}}}{\sqrt {R-R_{4}}}\left({\overline {K_{1}K_{2}}}\cdot {\overline {K_{3}K_{4}}}+{\overline {K_{1}K_{4}}}\cdot {\overline {K_{2}K_{3}}}\right)\\[4pt]={}&{\frac {1}{R^{2}}}\cdot {\sqrt {R-R_{1}}}{\sqrt {R-R_{2}}}{\sqrt {R-R_{3}}}{\sqrt {R-R_{4}}}\left({\overline {K_{1}K_{3}}}\cdot {\overline {K_{2}K_{4}}}\right)\\[4pt]={}&t_{13}t_{24}\end{aligned}}}