um, hello...
Erasthones wasn't proving the earth is a globe, he was calculating an estimate of the circumference of the globe.
so, whatever you were quoting there, is pretty ignorant.
it was already well proven the earth is spherical from many ways, for hundreds of years before Erasthones, from ships disappearing over the horizon, from the motion of stars, from the sunrise and sunset, from the shadow of the earth during an eclipse of the moon, etc.