Diophantos' solutions to the problems of Arithmetica have been the object of extensive reading and interpretation in modern times, especially from the point of view of identifying ``hidden steps'' or ``general methods''. In this paper, after examining the relevance of various interpretations given for the famous problem II 8 in the context of modern algebra or geometry, we focus on a close reading of the ancient text of some problems of Arithmetica in order to investigate Diophantos' solving practices. This inquiry (...) reveals certain pointers, which enable us to create a framework for defining the generality of Diophantos' methods. (shrink)

Grammar as a discipline devoted to the study of language was greatly advanced by the Alexandrian philologists, and especially by Aristarchus, as demonstrated by Stephanos Matthaios. In order to edit Homer and other literary authors, whose texts were often written in archaic Greek and presented many linguistic problems, the Alexandrians had to recognize linguistic grammatical categories and declensional patterns. In particular, to determine the correct orthography or accentuation of debated morphological forms they often employed analogy, which is generally defined as (...) the doctrine that grammatical forms must follow strict rules of declension. Modern scholars have often opposed the Alexandrian doctrine of analogy to the Pergamene doctrine of ‘anomaly’, which favoured spoken usage to determine debated forms. Detlev Fehling and David Blank, however, have shown that this strong opposition never really existed and it is mostly due to Varro. More correctly, ancient grammarians identified inflectional rules as well as forms derived from spoken usage or otherwise aberrant forms—however, respect for spoken usage in the latter case was not labelled ‘anomaly’, which was never a technical term of ancient grammar. Rather, and especially in the Roman period, grammarians used the term ‘pathology’ to account for and explain irregular forms. (shrink)

In his paper ‘The wrong text of Euclid: on Heiberg's text and its alternatives', published in 1996, W.R. Knorr resuscitated the debate which had taken place in the 1880s between the orientalist M. Klamroth and the editor of Euclid's Elements, J.L. Heiberg. In nuce the debate concerned the fundamental question of which manuscript tradition of the Elements should be assigned textual anteriority: the Greek tradition or the Arabic tradition. Whereas Klamroth argued for the latter position, Heiberg, whose view became the (...) prevailing one, endorsed the anteriority of the Greek tradition. (shrink)

The paper shows that, contrary to what has been held since the sixteenth-century mathematician Christoph Clavius, there is no application of consequentia mirabilis (CM) in Greek mathematical works. This is shown by means of a detailed discussion of the logical structure of the proofs where CM is allegedly employed. The point is further enlarged to a critical assessment of the unsound methodology applied by many interpreters in seeking for specific logical rules at work in ancient mathematical texts.