What he did was simple geometry, and in a way he was the right man in the right place. He heard that the sun was in zenith during the summer solstice ina certain town. He had a good runner measure the distance between Alexandria and that town and then measured the angle of the sun during the solistice in Alexandria (for simplicity, say it was 6 degrees). To get the full circle, just multiple by 60.

6th graders maths.