Since the application of Postulate I.2 in the Elements is not uniform, one could wonder in what way should it be applied in Euclid’s plane geometry. Besides legitimizing the question itself from the perspective of a philosophy of mathematical practice, we sketch a general perspective of conceptual a...
In this note we shall consider different ways to apply Postulate 2 in Euclid’s Elements, each of which corresponds to a different interpretation of this. We conclude that Euclid’s text displays a non-uniform practice, and suggest a way to explain differences and give a coherent account of these diff...