Mathematics at the International Congress of Philosophy, Paris, 1900

S. GÜNTHER, " On the history of the origins of the newtonian law of gravitation."M. CANTOR, " On the origins of the infinitesimal calculus."H. POINCARÉ, " The principles of mechanics."B. RUSSELL, " The idea of order and absolute position in space and time."H. MACCOLL, l l Symbolic logic.' ' G. PEANO, " Mathematical definitions."C. BURALI-FORTJ, "The different logical methods for the definition of the real number."A. PADOA, " Essay at an algebraic theory of integral numbers, with a logical introduction to any deductive theory whatever.7 ?M. PIERI, " On geometry considered as a pure by logical •system.' ' P. PORETSKY, " The theory of logical equalities with three terms."E. SCHRODER, " An extension of the idea of order."W. E. JOHNSON, " The theory of logical equations."A. MACFARLANE, " The ideas and principles of the geometric calculus.' 'A. CALINON, "The rôle of number in geometry."G. LECHALAS, " The comparability of various spaces."J. HADAMARD, U On induction in mathematics."R. BLONDLOT, "Exposition of the principles of mechanics.' ' M. LE VERRIER, "On the genesis and import of the principles of thermodynamics."A. VASSILIEF, "Principles of the calculus of probabilities."In his paper on the origins of the infinitesimal calculus, M. G. MILHAUD commenced by seeking these origins in antiquity ; in the discovery of the incommensurable magnitudes, which destroyed the atomism of the pythagoreans ; in the theory of ratios of Euclid, applied by Hippocrates to the quadrature of his lunes ; finall} 7 , in the method of exhaustion of Eudoxus employed by Archimedes for the quadrature of the parabola.Passing to modern times, he discussed the method of indivisibles Cavalieri, as compared with the method of exhaustion of the ancients ; then the problem of tangents and the methods proposed by Descartes and Roberval for solving it ; finally, the problem of maxima and minima solved by Fermât.The paper concludes with an account of the contributions of Huygens and Barrow, and their respective relations with Leibniz and Newton.