These remarks preface two volumes consisting of the proceedings of the Third International Conference on the History and Philosophy of Science of the International Union of History and Philosophy of Science. The conference was held under the auspices of the Union, The Social Sciences and Humanities Research Council of Canada, and the Canadian Society for History and Philosophy of Science. The meetings took place in Montreal, Canada, 25--29 August 1980, with Concordia University as host institution. The program of the conference was arranged by a Joint Commission of the International Union of History and Philosophy of Science consisting of Robert E. Butts (Canada), John Murdoch (U. S. A. ), Vladimir Kirsanov (U. S. S. R. ), and Paul Weingartner (Austria). The Local Arrangements Committee consisted of Stanley G. French, Chair (Concordia), Michel Paradis, treasurer (McGill), Franyois Duchesneau (Universite de Montreal), Robert Nadeau (Universite du Quebec a Montreal), and William Shea (McGill University). Both committees are indebted to Dr. G. R. Paterson, then President of the Canadian Society for History and Philosophy of Science, who shared his expertise in many ways. Dr. French and his staff worked diligently and efficiently on behalf of all participants. The city of Montreal was, as always, the subtle mixture of extravagance, charm, warmth and excitement that retains her status as the jewel of Canadian cities. The funding of major international conferences is always a problem.

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Do Historians and Philosophers of Science Share the Same Heritage?.- I.- Conceptual and Technical Aspects of the Galilean Geometrization of the Motion of Heavy Bodies.- The Galilean Geometrization of Motion: Some Historical Considerations.- Measure, Proportion and Mathematical Structure of Galileo's Mechanics.- II.- Space, Geometrical Objects and Infinity: Newton and Descartes on Extension.- Finite and Otherwise. Aristotle and Some Seven- teenth Century Views.- III.- The Ideal of the Mathematization of All Sciences and of 'More Geometrico' in Descartes and Leibniz.- The "More Geometrico" Pattern in Hypotheses from Descartes to Leibniz.- The Leibnizean Picture of Descartes.- IV.- Force and Inertia: Euler and Kant's Metaphysical Foundations of Natural Science.- Kant on the Foundations of Science.- Non-mechanistic Ideas in Physics and Philosophy: From Newton to Kant.- V.- V. V. Petrov's Hypothetical Experiment and Electrical Experiments of the 18th Century.- The Ideal of Mathematization in B. Bolzano.- "Die schönste Leistung der allgemeinen Relativitäts- theorie": The Genesis of the Tensor-Geometrical Conception of Gravitation.