The key to predicting eclipses

Noticing that they occur in cycles, or at more or less regular intervals. The Sun goes round the sky once a year; the Moon once a month. This means that, every month, the Moon ‘overtakes’ the sun. This happens at the New Moon, and this is when solar eclipses occur. But, of course, we don’t get an eclipse every New Moon. This is because the Moon has an elliptical orbit: sometimes it passes above the Sun when it overtakes it, sometimes below. But the Moon’s elliptical orbit has its own cycle: it returns to the same place it started from every 18 years or so. Thus – if seen from the same place on Earth – an eclipse will be followed by another one just over 18 years later.