I remember reading somewhere that the aim of Aristotle's Prior and Posterior analytics was to show which kinds of syllogisms produce understanding. I do not remember where I read this but I think it was in a translation of one of al Farabi's works. in any case, this notion is very interesting to me because it means that Aristotle was not merely trying to investigate syllogisms in general, but was instead trying to discover which ones lead to understanding. I feel that knowing this would help me a lot practically in my studies because whenever I study a subject, I often have difficulties identifying whether or not I really understand something. Too often, I feel like I understand something, and then some years down the line a counter example comes up which shows that I didn't really understand the thing at a fundamental level.
More recently, I am starting to come to the conclusion that the kinds of syllogisms which produce understanding are ones which show how I think originates from first principles. In other words, it is no good learning how to use something practically (for example), or the relations it bears to other things within the same subject, as this will not lead to fundamental understanding. The only kind of explanation that will lead to fundamental understanding is one that shows how the thing originates from the first principles of the subject, just like Euclid's Elements.
So my question is this: Was this really the aim of Aristotle's two books on analytics, and if so, is there a short modern explanation of Aristotle's conclusions on "syllogisms which produce understanding"?
Note: I am not a philosopher and have never taken philosophy, so I apologize in advance for any errors in my post.