I defend an interpretation of Aristotle’s Posterior Analytics Book I which distinguishes between two projects in different passages of that work: (i) to explain what a given science is and (ii) to explain what properly scientific knowledge is. I present Aristotle’s theory in answer to ii, with special attention to his definition of scientific knowledge in 71b9-12 and showing how this is developed on chapters I.2-9 and I.13 into a solid Theory of Scientific Demonstration. The main point of this theory is that demonstrations need to capture relevant explanations. Some formal requirements of the demonstration (as the syllogistic structure and coextension between terms) are unfoldings ...