I think it is a contraction, in the same way o'clock is.
When I learnt to tell the time, many years ago - Ponitous was still having flying lessons at the time... I was taught:
"One o'clock, Two o'clock to define the hour, when the long hand is on '12'. It was explained that "o'clock" means: The time "of the clock" or as indicated by the clock.
Therefore, one of the clock simply means one hour indicated by, or of the clock's passage in time.
In the same way, "Half past" the hour is an abbreviation of the 18th or 19th century UK English idiom: "half of the hour past", that is you are half way through the last full hour of the clock, [as indicated by the clock]. Its worth remembering that, at this time [no pun intended], clocks and watches in general use were still relatively 'new technology'.
With time and use, "half of the hour past" was gradually shortened to become simply "half past...".
I seem to remember that in German, they refer to, for example, half past three [drei], as:
"halb vier" (half before four)
This may explain why I'm always late for appointments in Germany!
I am not certain of the reason for this fundamental difference, other than:
- German logical thinking
- The German sentence construction is significantly different to that used in English
"Half of the hour past" is used here also:
The Holy Thief