A picture to hold: you are walking, and on one side the ground simply ends. Not a slope you could scramble down, but an edge with a long fall under it. Both uses of precipice can be seen as growing out of that one feeling, one more step and there is nothing there.

可以想成這樣一個畫面:你走著走著,旁邊的地就沒有了。不是可以慢慢爬下去的斜坡,而是一道邊,邊的下面是很長的一段空。precipice 的兩個用法,都可以看成從「再一步就沒有地了」這個感覺長出來的。

From the word’s history

Latin praecipitium, a steep place, from praeceps, steep or headlong, which is prae (forward) plus caput (head). The old word pictures going down head first, which is exactly the kind of drop the modern word names.

拉丁文 praecipitium(陡峭之處)來自 praeceps(陡、頭朝前的),拆開是 prae(向前)加 caput(頭)。字面上就是「頭朝前栽下去」,正好對上這個字今天講的那道落差。

Wiktionary etymology supplied in this packet (kaikki:3f6f69a190036ae4:468998380:22131)

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