This article is published in a Class A scientific journal - 11/C5 - History of Philosophy. This article was subject to a rigorous double blind peer review process. The purpose of this article is to present Galileo Galilei's first reflection on chapter 1 of the first book of Aristotle's Posterior Analytics. Specifically, Galilei discusses the problem of the praecognitiones i.e. the knowledge on which is based the demonstrative structure . The treatment of the prerequisites of the subject and of his passiones, that is, of his property, acquires, in the sphere of aristotelianism of the fifteenth and sixteenth centuries, a particular importance because, in the university field, there is a clear tendency to consider the subject of demonstration in relationship with the subject of science.