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It's a common misconception that when Columbus suggested that the world was round, that it was a new and radical idea.  Actually the Greeks thought of it first.  They did it by picking up two powerful clues.

1)    During a Partial Lunar Eclipse the Earth's shadow was always circular in shape.  The only geometric form that is circular from any viewing angle is a sphere.  Thus, they concluded, the Earth is spherical!

2)    It was also noted that the Sun cast shadows of different lengths at noon in different cities.  This could not happen if the Earth were flat, so its surface was assumed to be curved.

A Greek scientist named Eratosthenes devised a way to combine both observations into a way of determining the diameter of the Earth.

Eratosthenes had heard that, on noon during the Summer solstice in the city of Syene, the Sun was at zenith and cast no shadow (so what's it's latitude?), while in his home city of Alexandria, he observed a 7° shadow.  He concluded that, if the Earth where a sphere, that the Distance between Alexandria and Syene must be 7/360 ~ 2% of the Earth's circumference.

To figure out the Earth's diameter, Eratosthenes walked from Alexandria to Syene to measure the distance.  This he could convert to a circumference, and ultimately a diameter for the Earth.

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