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Rough Draft for an essay on the meeting of a man from Lyon and his language

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Preprint

French

ID: <10670/1.73ffuv>

Abstract

when talking about Desagues in history or epistemology texts, it is often emphasised that it uses a very specific vocabulary, sometimes referred to as flower, and most commonly as obscure. This starts with Jean de Beaugrand, who in 1640 in his charitable Advis attacked Desargues frontally on this subject, and was reflected in contemporary texts. Beyond vocabulary, Gille-Gaston Granger looked at what he referred to as the “style” argued in a very interesting text, but which did not extend to the end of the consequences that could be drawn from such an analysis, which calls for a great deal of detail in the study of the deepest work of the surveyor, the Brouillon Project on the conics. One of the aims of this text is to deepen Granger’s reflection, focusing our work in two main directions. The first concerns the role and use of the definition in Desargues, and we will see in particular how the Brouillon Project finds two broad types of definitions, both of which show that Lyon has a radically new approach in this field compared to the euclidian tradition. The second concerns the role and use of the sentence, in particular in demonstration practice. We will see that language offers Desargues a powerful tool for analysing concepts and methods, with a view to unifying them, but also a tool generating a new conception of the practice of geometry, through its confidence in the reasoning of speech. This will allow us to illustrate precisely what Granger means by its concept of style. We will conclude this study by proposing the epistemological and didactic avenues offered by reading and analysing the Brouillon Project, reconsidering the roles of definition but also formalism, in a sensitive and literary approach.

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