Giuseppe Antonio Borgnis, an Italian "engineer and member of many academies" and professor of mechanics at the University of Pavia in Italy, in his monumental, nine-volume _Traité complet de méchanique appliquée aux arts_, caused a bifurcation of the structure built upon Hachette's foundation of classification when he introduced six orders of machine elements and subdivided these into classes and species. His six orders were _récepteurs_ (receivers of motion from the prime mover), _communicateurs_, _modificateurs_ (modifiers of velocity), _supports_ (e.g., bearings), _regulateurs_ (e.g., governors), and _operateurs_, which produced the final effect.[65] [Footnote 65: Giuseppe Antonio Borgnis, _Théorie de la mécanique usuelle_ in _Traité complet de mécanique appliquée aux arts_, Paris, 1818, vol. 1, pp. xiv-xvi.] The brilliant Gaspard-Gustave de Coriolis (1792-1843)--remembered mainly for a paper of a dozen pages explaining the nature of the acceleration that bears his name[66]--was another graduate of the Ecole Polytechnique who wrote on the subject of machines. His book,[67] published in 1829, was provoked by his recognition that the designer of machines needed more knowledge than his undergraduate work at the Ecole Polytechnique was likely to give him. Although he embraced a part of Borgnis' approach, adopting _récepteurs_, _communicateurs_, and _operateurs_, Coriolis indicated by the title of his book that he was more concerned with forces than with relative displacements. However, the attractively simple three-element scheme of Coriolis became well fixed in French thinking.[68] [Footnote 66: Gaspard-Gustave de Coriolis, "Memoire sur les equations du mouvement relatif des systèmes de corps," _Journal de l'Ecole Polytechnique_, 1835, vol. 15, pp. 142-154.] [Footnote 67: Gaspard-Gustave de Coriolis, _De Calcul de l'effet des machines_, Paris, 1829. In this book Coriolis proposed the now generally accepted equation, work = force × distance (pp. iii, 2).] [Footnote 68: The renowned Jean Victor Poncelet lent weight to this scheme. (See Franz Reuleaux, _Theoretische Kinematik: Grundzüge einer Theorie des Maschinenwesens_, Braunschweig, 1875, translated by Alexander B. W. Kennedy as _The Kinematics of Machinery: Outlines of a Theory of Machines_, London, 1876, pp. 11, 487. I have used the Kennedy translation in the Reuleaux references throughout the present work.)] Michel Chasles (1793-1880), another graduate of the Ecole Polytechnique, contributed some incisive ideas in his papers on instant centers[69] published during the 1830's, but their tremendous importance in kinematic analysis was not recognized until much later. [Footnote 69: The instant center was probably first recognized by Jean Bernoulli (1667-1748) in his "De Centro Spontaneo Rotationis" (_Johannis Bernoulli ... Opera Omnia ..._, Lausanne, 1742, vol. 4, p. 265ff.).]