Compose a dialogue between an old Euclids epigone, named Simplicius, and two young mathematicians supporters of a rigourous foundation of Euclids geometry, named Mugochi and Wilkens. Through the fiction of their words, it must emerge your knowledge and, above all, understanding of the concepts studied during the course, their meaning, the ideas behind them and their purpose, and presenting the modern approach of which Mugochi and Wilkens are champions.