masterThesis
El Analysis situs y la Geometría proyectiva: Un estudio sobre los parecidos y vínculos entre la geometría de Leibniz y la geometría de Russell
Autor
Bautista Alarcón, David Fernando
Institución
Resumen
This work aims to identify the respective links that exist between Leibniz's geometry (Analysis situs), and the projective geometry that Russell postulated in his Foundations of geometry of 1897. For this, i make a methodological trace on the geometric origin of the method of analysis and its role in Leibniz in formulating the first general features of Analysis situs. On the other hand, it shows the factors that for Leibniz are problematic and hinder the rigorous demonstration of Euclidean geometry, a fact that motivates him to propose a qualitative geometry with characters or symbols. At this point the work shows how Leibniz's geometry builds notions such as point, plane, line, among others. Finally, concepts that are common between projective geometry and Analysis situs are presented, such as the idea of intensive space, as a supposition for metric geometries; This allows opening binding paths between these two qualitative geometries.
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