2022-05-052022-05-052022-03-24RIBEIRO, André Luiz. Geometria e aritmética: um encaixe imperfeito. 2022. 45f. Trabalho de Conclusão de Curso (Graduação) – Unidade Acadêmica Especial de Ciências Humanas, Universidade Federal de Goiás, Cidade de Goiás, 2022.http://repositorio.bc.ufg.br/handle/ri/20705In the present work we clarify how the discovery of incommensurable magnitudes impacted Greek mathematics and how, even today, we experience the consequences of this fact. Furthermore, contrasting Eudoxus' doctrine on ratio and proportion and Descartes' formulations that enabled an arithmetical treatment of geometric quantities, we show how, at the beginning of modernity, the effort to overcome the abyss between Geometry and Arithmetic took shape. Finally, exploring the divergences between modern mathematicians and contemporary constructivists regarding the notion of existence, we show how, by adopting a more rigorous conception of existence as meaning “hand possession” of a method for identifying mathematical objects, the imperfect fit between Geometry and Arithmetic then returns to the fore, thus rehabilitating the distinction between numbers and magnitudes and the logical independence between geometric proofs and arithmetic proofs.porAcesso AbertoGeometriaAritméticaIncomensurabilidadeExistênciaGeometryArithmeticIncommensurabilityExistenceTCC