First Italian edition of the work of the French mathematician Clairaut, a leading figure in the eighteenth-century European scientific community and a member of both the Académie des Sciences in Paris and the Royal Society of London. The work introduced a new way of teaching mathematics, based on intuition and the progressive understanding of concepts, which was to have a particularly significant influence in Italy. It became a fundamental reference for the development of the active method in teaching intuitive geometry, which was revived and reworked in the twentieth century by the mathematician Emma Castelnuovo, who in 1946 noted its exceptional clarity of exposition, calling it a true masterpiece.