A method is a set of procedures the human mind follows in order to arrive at truth. These procedures differ depending on the object of study, so each type of science has its own method.
Let's begin by examining the different procedures the mind follows in order to arrive at truth.
There are two general procedures – analysis and synthesis. We'll have to define these words clearly, for they're often given different meanings.
For Condillac, analysis is the method followed by the mind when it breaks down a whole into its parts. Synthesis, by contrast, is the procedure of recomposition. When I dismantle something, I can be said to be analyzing it, and when I restore it to what it was previously, I'm synthesizing.
The Port-Royal logicians, however, gave these words a completely different meaning. For them, analysis is a regressive procedure that examines the conditions of a proposition until it arrives at something true. Synthesis is the inverse, as it begins with the proposition at which analysis arrived and ends at the proposition from which analysis began.
This definition was taken from geometry, which defines the two words in this way. For the Port-Royal school, analysis finds new truths, while synthesis proves to others what we already know to be true.
In the search for truth, the inventor follows the analytic method, while the synthetic method is – according to an expression of Port-Royal – one “of doctrine.”
Kant gave these words yet another meaning.