http://individual.utoronto.ca/acephalous/Saito_Sidoli_2010.pdf

The function of diorism in ancient Greek analysis

This survey deals with research in ancient Greek mathematics and, to a lesser extent, mathematical sciences in the long first decade of the 21st century. It is modeled on the two foregoing surveys by J.L. Berggren and K. Saito and gives my personal appraisal of the most important work and trends of the last years, with no attempt to be exhaustive.

Research on Ancient Greek Mathematical Sciences, 1998-2012

http://www.individual.utoronto.ca/acephalous/Sidoli_Saito_2012.pdf

Comparative analysis in Greek geometry

This paper is a contribution to our understanding of the technical concept of given in Greek mathematical texts. By working through mathematical arguments by Menaechmus, Euclid, Apollonius, Heron and Ptolemy, I elucidate the meaning of given in various mathematical practices. I next show how the concept of given is related to the terms discussed by Marinus in his philosophical discussion of Euclid’s Data. I will argue that what is given does not simply exist, but can be unproblematically assumed or produced through some effective procedure. Arguments by givens are shown to be general claims about constructibility and computability. The claim that an object is given is related to our concept of an assignment—what is given is available in some uniquely determined, or determinable, way for future mathematical work.

The concept of given in Greek mathematics

The Latin edition of the Mathematicae Collectiones was published in print in 1588, thirteen years after Federico Commandino’s demise. For his Latin version of Pappus’s work, Comandino used two Greek codices, formerly identified by Treweek. In this article, another Greek manuscript, revised and annotated by Commandino, is revealed. Two letters from Commandino to Ettore Ausonio shed new light on the edition of Pappus’s Collectio and show the partnership between the two mathematicians in elaborating supplementary proofs to include in the comments. Using these letters, we can date the first draft of the Latin version in the late 1560s. The posthumous edition of the Mathematicae Collectiones involved Commandino’s disciples and, in particular, Guidobaldo del Monte. The comparison between the manuscripts and the printed edition reveals an important role played by the disciple in revising the Latin translation of his master.

Federico Commandino and the Latin edition of Pappus’ Collection

Greek geometrical analysis : A new interpretation through the givens -terminology

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.

Philippos Fournarakis

Papers

Greek geometrical analysis : A new interpretation through the givens -terminology

On Archimedes’ Pursuit Concerning Geometrical Analysis