This paper presents a critical analysis of the accepted educational use of the method performed by Eratosthenes to measure the circumference of Earth which is often considered as a relevant means of dealing with issues related to the nature of science and its history. This method relies on a number of assumptions among which the parallelism of sun rays. The assumption of sun rays parallelism (if it is accurate) does not appear spontaneous for students who consider sun rays to be divergent. Here, we propose an educational reconstruction of Eratosthenes’ discovery based on the exploitation of a narrative written by Cleomedes during the first century AD. This implies that the students are involved in an elaboration of parallelism by an approach where the notion of “approximation” remains central.