The Method of Analysis: Its Geometrical Origin and Its General Significance, Volume 25
As official sponsors of the First International Conference in the History and Philosophy of Science, the two Divisions of the International Union of the History and Philosophy of Science owe a great deal to the University of Jyvliskyla and the 1973 Jyvliskylli Summer Festival for the extra ordinarily generous hospitality they provided. But there is an additional debt owed, not simply for the locale but for the very substance of the Conference, to the two Finnish scholars who have jointly authored the present volume. For this volume represents not only the first part of the published proceedings of this First International Conference in the History and Philosophy of Science, but also, most fittingly, the paper that opened the Conference itself. Yet the appropriateness of the paper from which this book has resulted opening the Conference lies far less in the fact that it was a contribution by two Finnish authors to a meeting hosted in Finland than it does to the fact that this paper, and now the present book, comes to grips in an extreme ly direct way with the very problem the whole Conference was from the outset designed to treat. Generally put, this problem was to bring to gether a number of historians and philosophers of science whose contrib uted papers would bear witness to the ways in which the two disciplines can be, and are, of value to each other.
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The Historical Significance of the Idea of Geometrical Analysis
Pappus on the Direction of Anlalysis and Synthesis
What Pappus Says and What He Does A Comparison and an Example
Analysis as Analysis of Figures The Logic of the Analytical Method
The Problem of Auxiliary Constructions
The Problem of the Resolution
Analysis as Analysis of Figures Pappus Terminology and His Practices
Pappus and the Tradition of Geometrical Analysis
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already analysis and synthesis analysis of figures analysis proper analytical method analytical proof system angles apodeixis Aristotelian Aristotle Aristotle's arkhe auxiliary constructions axioms Chapter configuration conjecture connection Data dedomena deductive steps Descartes description of analysis desired conclusion diorismos direction of analysis Elements enunciation Euclid's Euclid's Elements fact first-order logic Friedlein geometrical analysis geometrical objects given Greek geometers Greek Mathematics Hankel Heath Heiberg Hence Heron heuristic Hintikka Hultsch 634 hypotheses idea of analysis impossible inferred instance instantiated J. L. Heiberg Jaakko Hintikka logical consequence Marinus mathematicians means method of analysis methodological modern Newton passage Philoponus philosophical philosophy of science Plato possible practice premisses problem problematical analysis procedure Proclus proof of impossibility Prop proposition prove resolution role seems sense speaking Speusippus steps of analysis Stoic Szab6 T. L. Heath terminology theoretical analysis thing sought tion translation true word zetoumenon