Although several mathematical instruments of the first importance are contained in the collections of the Bibliotheque Nationale de France, few of them are well known. The primary aim of the present work is therefore to make them available, through detailed descriptions and ample photographs, to all who concern themselves with the development of mathematical instrumentation. European armillary spheres are listed because of their close connection with the mathematical art of astronomy/astrology, as are two Arab-Islamic solid celestial spheres because of their intrinsic relation with astrolabes from the same area. Complete balances are included in the catalogue, but the extensive collection of monetary weights has been left to one side together with details of the, often miscellaneous, weights in boxed-sets for money-changing. Within the various sections into which the catalogue is divided, items are arranged in as strict a chronological order as is possible, given the uncertainty of dating for some of them, without respect to their place of origin.