Abstract
The aim of this article is to present and discuss the language of the «givens», a typical stylistic resource of Greek mathematics and one of the major features of the proof format of analysis and synthesis. I shall analyze its expressive function and its peculiarities, as well as its general role as a deductive tool, explaining at the same time its particular applications in subgenres of a geometrical proposition like the locus theorems and the so-called «porisms». The main interpretative theses of this study are the following: the language of the «givens» (1) is the standard idiom in which “existence and uniqueness” of a mathematical object was proved, (2) was conceived as an unified framework reducing to a strictly deductive format disparate argumentative steps such as deductions, constructions, and calculations.
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Communicated by Bernard Vitrac.
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Acerbi, F. The language of the “Givens”: its forms and its use as a deductive tool in Greek mathematics. Arch. Hist. Exact Sci. 65, 119–153 (2011). https://doi.org/10.1007/s00407-010-0072-z
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DOI: https://doi.org/10.1007/s00407-010-0072-z