I don't understand why English and Latin (see the two quotations below) uses the notion of "(be)fall" to signify "happening". How are they related semantically?
Word Origins (2005 2e) by John Ayto. p 3 Left column.accident
Etymologically, an accident is simply ‘something which happens’ – ‘an event’. That was what the word originally meant in English, and it was only subsequently that the senses ‘something which happens by chance’ and ‘mishap’ developed. It comes from the Latin verb cadere ‘fall’ (also the source of such diverse English words as case, decadent, and deciduous). The addition of the prefix ad- ‘to’ produced *accidere*, literally ‘fall to’, hence ‘happen to’. Its present participle was used as an adjective in the Latin phrase rēs accidēns ‘thing happening’, and accidēns soon took on the role
of a noun on its own, passing (in its stem form accident-) into Old French and thence into English.
I omit the rest of the entry, as it appertains the second unrelated definition of case meaning "container". Op cit. p 96.case
There are two distinct words case in English, both acquired via Old French from Latin and both members of very large families. Case ‘circumstance’ was borrowed from Old French cas*, which in turn came from Latin *cāsus ‘fall, chance’. This was formed from the base of the verb cadere ‘fall’. The progression of senses is from the concrete ‘that which falls’ to the metaphorical ‘that which befalls, that which happens (by chance)’ (and English chance is also derived ultimately from Latin cadere). Other related words in English include accident, cadence, cadaver, cheat, chute, coincide, decadent, decay, deciduous, and occasion.
Op cit, p 355.occasion
Like English befall, occasion depends on a metaphorical connection between ‘falling’ and ‘happening’. Its ultimate source is the Latin verb occidere ‘go down’, a compound formed from the prefix ob- ‘down’ and cadere ‘fall’ (source of English cadence, case, circumstance, decadent, etc). The figurative notion of a ‘falling together of favourable circumstances’ led to the coining of a derived noun *occasiō*, meaning ‘appropriate time, opportunity’, and hence ‘reason’ and ‘cause’. English acquired it via Old French occasion.
Also from Latin occidere comes English occident , a reference to the ‘west’ as the quarter in which the sun ‘goes down’ or sets.