1. That Alexandria and Syene lie on the same meridian.
A meridian is an imaginary circle on the Earth’s surface which passes through both the north and south poles [17, p.209 ]. The plane of any meridian bisects the Earth. If Alexandria and Syene both lie on the same meridian, Eratosthenes is guaranteed that two cities and the center of the Earth are all contained in the same plane. Now the geometrical argument takes place in two dimensions (the plane), rather than in three. How does Eratosthenes justify this assumption?
Before his famous calculation of the Earth’s circumference, Eratosthenes attempted the earliest known scientific construction of a map based on mathematical geography. Using the tremendous amount of information available to him at the great library in Alexandria, Eratosthenes sought to correct the traditional Greek map of the world. He examined countless texts, compiling records of measured distances and comparing various accounts of similarities in flora, fauna, climate, astronomical observations, local peoples, etc. [1, p.389]. The map featured a main “parallel”, running east to west through the city of Rhodes, and a main meridian, running north and south through Rhodes [4, p.63]. Using these two perpendicular main lines, Eratosthenes divided the map into rectangular regions he called seals, which could then be used to geometrically calculate any distance in the known world – hence the term “mathematical geography” [2, p.128]. The main meridian in this map runs directly through several cities, including Alexandria and Syene [1, p.389 ]. So Eratosthenes’ first assumption is based on a map which he constructed using the wealth of knowledge available at the library of Alexandria .
A 19th century reproduction of Eratosthenes’ map of the world [19 ].

Eratosthenes’ map of the world appeared in his work entitled
Geography, which was long regarded as the highest authority on geography in the ancient world [
1, p.389 ].