The Rule of Four Quantities: $\frac{\sin \overparen{B D}}{\sin \overparen{C E}}=\frac{\sin \overparen{A D}}{\sin \overparen{A E}}$
证明: 因为$\sin\overparen{BF}=\sin\overparen{CF}=1$ 对$\triangle DEF$的截线$ABC$用Menelaus定理$\frac{1}{\sin \overparen{C E}}=\frac{1}{\sin \overparen{B D}} \cdot \frac{\sin \overparen{A D}}{\sin \overparen{A E}}\hskip1em$
$_\square$Spherical Trigonometry Through the Ages - Lauren Roberts - 4.1 The Rule of Four Quantities
Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry - Princeton (2012) - Glen Van Brummelen - Chapter 4 page 60
