Dividing an hour into 60 parts was pretty common in the ancient world, because 60 is a number that divides evenly into many fractions – 1/3, 1/4, 1/2, 1/6. In fact this sexagesimal type of math was pretty common in the ancient world for this reason. Further dividing the minute into 60 seconds is just a logical progression of that. However, people in the pre-modern world would have used relative hours – that is, they counted twelve hours between sunrise and sunset and evenly divided them. This meant that hours were shorter in the winter and longer in the summer, so minutes and seconds would be longer and shorter as well.
It wasn’t until mechanical clocks that the period of the second became standardized as 1/60 of 1/60 of an hour (or 1/24 of the solar day).
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