During the summer of 1689, Sauveur was chosen to be the science and mathematics teacher for the Duke of Chartres, Louis XIV's nephew. For the prince, he drew up a manuscript outlining the "elements" of geometry and, in collaboration with Marshal Vauban, a manuscript on the "elements of military fortification." (In 1691 Sauveur and Chartres were present at the siege of Mons by the French.) Another of the prince's teachers was Étienne Loulié, a musician engaged to teach him the "elements" of musical theory and notation. Loulié and Sauveur joined forces to show the prince how mathematics and musical theory were inter-related. Remnants of this joint course have survived in Sauveur's manuscript treatise on the theory of music, and in Loulié's "Éléments". In the years that followed, Sauveur taught mathematics to various princes of the royal family. In 1686 he obtained the mathematics chair at the Collège de France, which granted him a rare exemption: since he was incapable of reciting a speech from memory, he was permitted to read his inaugural lecture.