Here again, I will not source for other reasons, but to point to the distinctive analytic feature of derivation, as Leibnitz was wont to in his reaction to Descartes’ method, re: Pappus, a fellow who distinguished analytic and synthetic derivation of mathematical symbolism.
In particular, and this is referents to my acquisition as purely analytic, as well, so much so that it re-iterates Plato’s Phaedo, that the early classical thinkers separated geometry from algebra, which Rennaissance thinkers confounded.
Again, I found this important difference , early on, but later to offer only confusing and differing methods of derivation , r(x), whereas analytics posit
an ideal model, just as Lebnitz has done, drawing or synthesizing algebra out of geometry, drawing calculus out of trigonometry. The fact, that Papus thought that, the classisists drawing algebra out of geometric principles, proved that they were aware of such distinctions, but held it back due to their misgivings of making such pre-determinations useful, necessary, or, understandable, within future, unwarranted assumptions. To my mind this proves the futility of holding the unpredictable and unmeasurable, infinitesimal measurements irrelevant.