Jean Christianidis

Trends in the historiography of science

I Methodological Issues in the Historiography of Science.- Charting the Scientific Community.- Theory and Practice in Early Modern Physics.- Styles of Scientific Thinking or Reasoning: A New Analytical Tool for Historians and Philosophers of the Sciences.- Kinds and (In)commensurability.- Types of Discourse and the Reading of the History of the Physical Sciences.- On Demarcations between Science in Context and the Context of Science.- On the Harmful Effects of Excessive Anti-Whiggism.- Issues in the Historiography of Post-Byzantine Science.- Social Environment, Foundations of Science, and the Possible Histories of Science.- Scientific Discoveries as Historical Artifacts.- Selection, System and Historiography.- Can the History of Instrumentation Tell Us Anything about Scientific Practice?.- The One in the Philosophy of Proclus: Logic versus Metaphysics.- Rational versus Sociological Reductionism: Imre Lakatos and the Edinburgh School.- Sociocultural Factors and the Historiography of Science.- II Historiography of Mathematics.- Is Mathematics Ahistorical? An Attempt to an Answer Motivated by Greek Mathematics.- The Story of the Discovery of Incommensurability, Revisited.- On the History of Indeterminate Problems of the First Degree in Greek Mathematics.- On the Justification of the Method of Historical Interpretation.- The Infinite in Leibnizs Mathematics - The Historiographical Method of Comprehension in Context.- John Landen: First Attempt for the Algebrization of the Infinitesimal Calculus.- Historiographical Trends in the Social History of Mathematics and Science.- The Conception of the Scientific Research Programs and the Real History of Mathematics.- III Historiography of the Sciences.- Scientists and the State: The Legacy of World War II.- Unification, Geometry and Ambivalence: Hilbert, Weyl and the Gottingen Community.- The Two-Dimensional View of the History of Chemistry.- The Problem of Method in the Study of the Influence a Philosophy Has on Scientific Practice. The Case of Thermoelectricity.- Reopening the Texts of Romantic Science: The Language of Experience in J. W. Ritters Beweis.- Problems and Methodology of Exploring the Scientific Thought during the Greek Enlightenment (1750-1821).- History of Science and History of Mathematization: The Example the Science of Motion at the Turn of the 17th and 18th Centuries.- The Artistic Culture of the Renaissance and the Genesis of Modern European Science.- Archaeoastronomy in Greece: Data, Problems and Perspectives.- Index of Names.

'Aρίμητικη Στoιχειωσις: Un traité perdu de Diophante d'Alexandrie?

In this essay, the author suggests a conjecture about the existence of a lost theoretical treatise of Diophantus, entitledTeaching of the Elements of Arithmetic. His claims are based on a scholium of an anonymous Byzantine commentator.

The Meaning of Hypostasis in Diophantus’ Arithmetica

Historians of ancient philosophy and theological writers often come up against the puzzling issue of understanding the meaning of the term hypostasis used by different ancient authors. One could hardly expect that the same issue would be of interest for historians of ancient mathematics. Indeed, altogether absent from the works of Euclid, Archimedes, and Apollonius, and scarcely appearing in a nonmathematical context in the works of Heron and Nicomachus, the term hypostasis and its cognates appear 127 times in the six books of Diophantus’ Arithmetica preserved in Greek. This chapter examines Diophantus’ use of the term hypostasis and argues in favour of interpreting it as a term for numbers qua specific, individual entities. It is composed of three parts. The first part discusses the different statuses of numbers in a worked-out problem according to Diophantus’ general method, and the relevant issue of the Diophantine conception of an arithmetical problem; the second part investigates all instances of the term within Diophantus’ text; and the third part surveys briefly the testimonies of the Byzantine commentators of the Arithmetica, which provide further evidence supporting the interpretation proposed in this paper.

On Archimedes’ Pursuit Concerning Geometrical Analysis

Archimedes practices the heuristic method of analysis and synthesis only in Book II of his On the Sphere and Cylinder. This paper has a twofold objective. Firstly, the discussion of his analytical practice through the first problem of Book II, in relation to Pappus’ study of the method of analysis and synthesis in Book VII of his Mathematical Collection. The conclusion of this discussion is that Archimedes applies the analytical method in a way, which does not substantially differ from Pappus’ way. Secondly, the discussion about the missing part from the analysis of problem 4 of On the Sphere and Cylinder, II, combined with the above conclusion, lead us to advance a conjecture vis-a-vis a lost analytical treatise of Archimedes under the title Book of Data.