Geometria et Geometriae : e mathematica ad philosopiam

Abstract

Resumen: Luego de exponer las posibilidades filosóficas que las geometrías abren a las orientaciones de nuevos espacios, el artículo considera los procedimientos euclidianos y la conexión con las geometrías no-euclidianas. Hay muchas posiciones acerca de las bases filosóficas de las distintas geometrías. Hay además formulaciones muy importantes, desde la gnoseología a la ontología, respecto de las extensiones métricas de la alta geometría.

Abstract: This article was written to demonstrate the meaning of Euclidean and non-Euclidean geometries as well as their ap-plications and their philosophical foundations. Nevertheless, not only do I refer to the mathematical conditions according to new geometries, but also to the philosophical aims. There are many different positions on the philosophical foundations of the different metrics. There are also very important formulations, from gnoseology to ontology, on the extensions of the higher geometry.

Synopsis: Geometria, quae metricum spatium mathematicos docit, apud abstractam quantitatem sicut eius philosophicum de corporum extensione fundamentum esse, ab Euclideo comparata fuit. Novae geometriae mathematicam extensionem ex Euclideis Geometria, secundum metricam formulationem, patefecit. In hoc articulo philosophicum fundamentum, de Gnoseologia ad Ontologiam, scribere in superiorem geometriam invicem volumus.