The noted and highly respected pluralist, Dr. Richard Mckeon, in his introductory comments to the International Institute of Philosophy's 'Entretiens in Jerusalem, in 1977, quotes from Descartes response to the second objections in the Meditations. McKeon;'Descartes contends that he distinguishes two things in the writing of the geometers, the order (ordo) and the reasoning (ratio) of demonstrating. There are two ways... by analysis or resolution or by synthesis or composition. Descartes; "Analysis shows the true way by which a thing is discovered (inventa) methodically and as it were a priori, [French version translates a priori by 'shows how effects depend on causes'], so that, Des.; "if the reader wishes to follow it and pay attention to all that it contains, he will understand the thing demonstrated no less perfectly and will make it no less his own than if he had discovered it himself." McKeon; 'This way of demonstration will not convince obstinate or inattentive readers.' It would be an understatement to say that this left my mind boonswaggled. There is more to this presentation but perhaps this enough to ask; How does this square with and does it in any way affect the current usage of a priori?
Richard McKeon (/məˈkiːən/; April 26, 1900 – March 31, 1985) was an American philosopher and longtime professor at the University of Chicago. His ideas formed the basis for the UN's Universal Declaration of Human Rights. If there is not enough info here I can complete Descartes response with his response concerning a posteriori. Charles M. Saunders