✔ 最佳答案
邊長為0的三角形, 根據幾何原本, 不算是三角形.
(當然, 依傢數學界有好多各式各樣的定義什麼是 0 邊長的三角形, 例如 singular complex)
冇錯根據幾何原本, 點是線的一種, 因為點沒有闊度:
Definition 2. A line is breadthless length.
但三角形的定義為三條線""包含""的形狀:
Definition 19. trilateral figures (triangles) being those **contained** by three (straight lines)
Definition 14. A figure is that which is **contained** by any boundary or boundaries.
Definition 13. A boundary is that which is an extremity of anything.
這樣其實仲係好難睇點解要 Rule out 0邊長. 於是, 讓我們看看以下幾點:
Proposition 20. In any triangle the sum of any two sides is greater than the remaining one.
這樣, 如果三角形是 0 邊長, 就錯了.
最後, 每個三角形都有angle (角), Proposition 4, 6, 8, 16, 17, 18, 19 等等都提及了這點. 但, 邊長 0 的"三角形"是沒有角的, 因為:
Definition 8. A plane angle is the inclination to one another of two lines in a plane which meet one another and **do not lie in a straight line**.
但如果得一點 (三點重疊一起), 那這三點就會 lie in a straight line, 於是他們所組成的 "0度角" 就不是 angle 了.
雖然, 我個人認為 Euclid 在寫呢本書時沒有考慮過呢個咁極端的問題:P