 |
(1)
|
對於 球面三角形，
 |
(2)
|
這可以推廣到 
-邊形 ![P=[V_1,...,V_n]](/images/equations/MenelausTheorem/Inline2.svg)
，其中一條橫截線與邊 
相交於 
，對於 
, ..., 
，透過
![product_(i=1)^n[(V_iW_i)/(W_iV_(i+1))]=(-1)^n.](/images/equations/MenelausTheorem/NumberedEquation3.svg) |
(3)
|
這裡，
並且
![[(AB)/(CD)]](/images/equations/MenelausTheorem/NumberedEquation4.svg) |
(4)
|
是長度 ![[A,B]](/images/equations/MenelausTheorem/Inline8.svg)
和 ![[C,D]](/images/equations/MenelausTheorem/Inline9.svg)
的比率，帶有 正 或 負號，取決於這些線段是同向還是反向 (Grünbaum and Shepard 1995)。
的情況是 帕施公理。
梅涅勞斯定理
另請參閱
塞瓦定理, 霍恩定理, 帕施公理使用 探索
參考文獻
Beyer, W. H. (編). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 122, 1987.Coxeter, H. S. M. and Greitzer, S. L. "Menelaus's Theorem." §3.4 in Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 66-67, 1967.Durell, C. V. Modern Geometry: The Straight Line and Circle. London: Macmillan, pp. 42-44, 1928.Graustein, W. C. Introduction to Higher Geometry. New York: Macmillan, p. 81, 1930.Grünbaum, B. and Shepard, G. C. "Ceva, Menelaus, and the Area Principle." Math. Mag. 68, 254-268, 1995.Honsberger, R. "The Theorem of Menelaus." 章 13 in Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer., pp. 147-154, 1995.Pedoe, D. Circles: A Mathematical View, rev. ed. Washington, DC: Math. Assoc. Amer., p. xxi, 1995.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, p. 150, 1991.在 中被引用
梅涅勞斯定理引用為
Weisstein, Eric W. “梅涅勞斯定理。” 來自 —— 資源。 https://mathworld.tw/MenelausTheorem.html