  Various sorts of demonstration falling short of this ideal model, because they do not give a full explanation of the cause why the fact is true, were allowed in Aristotle's text (PA I 13), and the medieval authors refer to these as demonstration that it is the case (quia) as opposed to demonstration why it is the case (propter quid). Most important here is the sort of demonstration which argues from the cause to the effect rather than effect to cause, for instance, the demonstration that stars, unlike the planets, are far away because they twinkle, and whatever twinkles is far away. Twinkling, of course, does not cause the stars to be far away, but rather, the distance causes the twinkling. This sort of demonstration plays a role in discussions of analysis and synthesis in the fifteenth century. Demonstrations concerning particulars, and demonstrations arguing from theorems in the science which are not traced back to first principles, are also demonstrations that it is the case.