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Nicolas-Auguste Tissot (1824--1897) published a series of papers oncartography in which he introduced a tool which became known later on, amonggeographers, under the name of the "Tissot indicatrix." This tool was broadlyused during the twentieth century in the theory and in the practical aspects ofthe drawing of geographical maps. The Tissot indicatrix is a graphicalrepresentation of a field of ellipses on a map that describes its distortion.Tissot studied extensively, from a mathematical viewpoint, the distortion ofmappings from the sphere onto the Euclidean plane that are used in drawinggeographical maps, and more generally he developed a theory for the distorsionof mappings between general surfaces. His ideas are at the heart of the work onquasiconformal mappings that was developed several decades after him byGr{\"o}tzsch, Lavrentieff, Ahlfors and Teichm{\"u}ller. Gr{\"o}tzsch mentionsthe work of Tissot and he uses the terminology related to his name (inparticular, Gr{\"o}tzsch uses the Tissot indicatrix). Teichm{\"u}ller mentionsthe name of Tissot in a historical section in one of his fundamental paperswhere he claims that quasiconformal mappings were used by geographers, butwithout giving any hint about the nature of Tissot's work. The name of Tissotis also missing from all the historical surveys on quasiconformal mappings. Inthe present paper, we report on this work of Tissot. We shall also mention somerelated works on cartography, on the differential geometry of surfaces, and onthe theory of quasiconformal mappings. This will place Tissot's work in itsproper context. The final version of this paper will appear in the journalArch. Hist. Exact Sciences.

Nicolas-Auguste Tissot: A link between cartography and quasiconformal theory