In his second set of replies to objections, Descartes makes the following point regarding his method of demonstration:
As for the method of demonstration, this divides into two varieties: the first proceeds by analysis and the second by synthesis.
Analysis shows the true way by means of which the thing in question was discovered methodically and as it were a priori, so that if the reader is willing to follow it and give sufficient attention to all points, he will make the thing his own and understand it just as perfectly as if he had discovered it for himself. But this method contains nothing to compel belief in an argumentative or inattentive reader; for if he fails to attend even to the smallest point, he will not see the necessity of the conclusion. Moreover there are many truths which—although it is vital to be aware of them—this method often scarcely mentions, since they are transparently clear to anyone who gives them his attention.
Synthesis, by contrast, employs a directly opposite method where the search is, as it were, a posteriori (though the proof itself is often more a priori than it is in the analytic method). It demonstrates the conclusion clearly and employs a long series of definitions, postulates, axioms, theorems and problems, so that if anyone denies one of the conclusions it can be shown at once that it is contained in what has gone before, and hence the reader, however argumentative or stubborn he may be, is compelled to give his assent. However this method is not as satisfying as the method of analysis, nor does it engage the minds of those who are eager to learn, since it does not show how the thing in question was discovered.
It was synthesis alone that the ancient geometers usually employed in their writings. But in my view this was not because they were utterly ignorant of analysis, but because they had such a high regard for it that they kept it to themselves like a sacred mystery.
Now it is analysis which is the best and the truest method of instruction, and it was this method alone that I employed in the Meditations. As for synthesis, which is what you are undoubtedly asking me to use here, it is a method which may well be very suitable to employ in geometry as a follow up to analysis, but it cannot be so conveniently applied to these metaphysical subjects.
(From The Philosophical Writings of Descartes. Volume II. 110-111)
Notice that Descartes is claiming a pedagogic and instructional value to the process of analysis, as opposed to what he sees as the ancient tendency to keep esoteric knowledge esoteric. In a note that will become a key for the Enlightenment that follows historically, everyone is capable of their own wisdom and the instructor has a kind of obligation to make the knowledge process accessible for all. His Meditations was one of the very earliest philosophical texts to be translated from the traditional Latin into French.