What conceptual prerequisite was necessary for the ancient measurement of the Earth's size?
Answer
Accepting the Earth is a sphere
The required conceptual leap for ancient measurement was the acceptance that the Earth was not flat but was instead a sphere. Once this assumption was made, the problem could be reduced to trigonometry.

Related Questions
What conceptual prerequisite was necessary for the ancient measurement of the Earth's size?Who is credited with the most famous and successful early attempt to quantify the Earth's circumference using shadows?What specific solar observation was made in Syene (modern Aswan) at noon on the summer solstice?Eratosthenes' calculation relied on two critical pieces of data. One was the shadow angle; what was the other?What was the approximate angle of the shadow cast by the gnomon in Alexandria that Eratosthenes measured?If the shadow angle measured was $7.2^ ext{o}$, what fraction of the total circle ($360^ ext{o}$) did this angle represent?By multiplying the estimated distance of 5,000 stadia by 50, what total circumference did Eratosthenes calculate?What is the term used to describe the Earth's true geometric shape, which accounts for the equatorial bulge caused by rotation?What is the name of the modern science dedicated to measuring the Earth’s precise geometric shape, orientation in space, and gravity field?Which modern technique involves firing lasers from ground stations at orbiting satellites equipped with retroreflectors to determine precise distances?What term refers to the actual shape the ocean surface would take under the influence of Earth's gravity and rotation alone, excluding winds and tides?