ESPINOSA, MELANCOLIA E O ABSOLUTAMENTE INFINITO NA GEOMETRIA DOS INDIVISÍVEIS DO SÉCULO XVII

The article aims to reconstruct the seventeenth-century debate of the scientific nature of mathematics and the possibility of conceiving an idea of a positive infinite to address the philosophical implications of mathematics in Spinoza’s work, emphasizing the geometric ordering in his Ethics. We will approach the mathematical thinking of that philosopher from three perspectives: the pedagogical, the epistemological and the ontological. In the pedagogical sense, his synthetic geometry aims to inhabit the evidence as rhetorical and pedagogical expression of a perfect and self-evident concatenation that leads the progress of the reader through philosophical propositions. In the epistemological sense, we have the aim of inhabiting the thing defined by a genetic definition that provides the very acting (atuosa) essence of a thing. That epistemological sense provides us the difference between a definition of a thing by its predicates (or effects) or through its inner essence (or efficient cause). And finally, in the ontological sense of inhabiting the infinite itself, because geometry can bring us the proper way to conceive the positive idea of the absolutely infinite in which we necessarily are and take part.