I was surprised and delighted to find Thomas' and Lonergan's via analytica and via synthetica way back in Plato... We are reading Book VI of the Republic in class these days.
The students found it baffling, and I must confess that I would have too, if not for my reading of Lonergan. But: right now, there is the 'connection' - without much understanding.
One way goes from 'assumptions' to the principles. That is the via analytica, I suppose. The other way begins from assumptions and goes on to draw conclusions. The via synthetica, I suppose.