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[precipitation (n.) :]  [...]  Latin praecipitationem (nominative praecipitatio)
"act or fact of falling headlong, haste," noun of action
from past participle stem of praecipitare "fall, be hasty," from praeceps "steep" (see precipice).  [...]

[precipice (n.) :] "steep face of rock," 1630s, from Middle French précipice
[3.] from Latin praecipitium "a steep place," literally "a fall or leap,"
[2.] from praeceps (genitive praecipitis) "steep, headlong, headfirst
[1.] from prae "before, forth" (see pre-) + caput "head" (see head (n.)). [...]

Please correct me if my conjecture are incorrect: I conjecture the meaning of 'steep' to originate from the physical properties of the human head: imagine that you are a tick running atop someone's head from the back to the forehead. Then the tick may fly off the human head like a diver running to the end of the diving board before diving.

But "a fall or leap": whence did it originate? How does it connect to 1?
1-3 suggest a conjecture that the Romans liked to fall or leap off precipices? Is this true?
(If so, I hope for diving and fun, and not death.)

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I believe your conjecture is mistaken: the shape of your head has nothing to do with it. As I have always understood it, prae means "forward, first", so praeceps means "head-first". If you enter into a situation head first, such as a fall or a cooking pot or an enemy, you're being hurried or reckless or desperate, because your head is vulnerable: you would normally stick out your hand or foot first, since you're human, not canine like me. If you jump off a cliff head first, you're hasty indeed.

If you stick your head into a cooking pot, you might get burned. I don't know whether praeceps is related to the Tarpeian Rock, but anyone can fall into a precipice. Or from a 2-metre-high ledge: if you jump or fall down head first, you are far more likely to sustain serious injuries. So you would not normally do this, unless you were reckless or somehow desperate (to escape from an attacking lion).

  • +1. Thanks. 1. What situation do you mean with a cooking pot? Was cooking that arduous back then? 2. If you jump off a cliff head first, you're hasty indeed. So do you agree (per user Joel Derfner's answer below) that Romans did fall off precipices? – Greek - Area 51 Proposal Feb 28 '16 at 22:50
  • Would you please respond in your answer, which is easier to read than comments? – Greek - Area 51 Proposal Feb 28 '16 at 22:50
  • Sorry to trouble you again, may I ask whether you have had time to read my comment above? – Greek - Area 51 Proposal Apr 12 '16 at 5:38
  • @LePressentiment: Sorry, done. – Cerberus Apr 13 '16 at 0:45
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I think you're privileging an upright fall or leap. But when the Romans pitched criminals off the Tarpeian Rock, for example, or when Curtius dove into the lake, they were probably pitching themselves head-first, and, therefore, upside-down. Hence "præ" ("first") and "caput" ("head").

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