The Musica speculativa of Jean des Murs played a key role in renewing interest in the teaching of Boethius in the fourteenth century. We argue that this treatise is much more than a summary of the Boethian De institutione musica in presenting its core teachings as fully consistent within an Aristotelian theory of knowledge. Two versions of its prologue (1323 and 1325 respectively) are examined together with their relationship to Jean's Notitia artis musicae (1321) and the innovative significance of its mathematical-style presentation of the teaching of Boethius about proportions with its appeal to clear diagrams. We aim to guide the modern reader through the thought patterns and diagrams of Jean des Murs, demonstrating why the Musica speculativa was so widely studied in the later Middle Ages. The two different prologues are presented in English translation for the first time.