How Eratosthenes measured the size of Earth - GIF

[Ralphxyz]

How was the timing done? Both shadows had to be measured at the same time.

[Frank S]

How was the timing done? Both shadows had to be measured at the same time.

For all we know he may have done both measurements himself but a year apart

[mklotz]

How was the timing done? Both shadows had to be measured at the same time.

They probably made their measurements at high noon - when the sun was on their meridian*. High noon occurs when the obelisk shadow is shortest - easy to determine if you mark the shadow end point for an hour or so around noon.

*Alexandria and Fayum are not on the same meridian but Eratosthenes assumed they were. They're close to the same meridian and the slight error probably accounts for part of the error in his calculation.