A hierarchic process of producing taxonomies was formalized by 3rd century AD logician Porphyry in his presentation of Aristotle's classification of categories, and became popular during middle ages in a diagrammatic form of "Porphyrian tree". One starts with the highest category in a field, "summum genus", and proceeds in successive steps by using "differentia" to introduce lower genera and ultimately species. One easily recognizes the taxonomy scheme implemented in biology by Linneaus, and used until today. But Porphyry only summarized an earlier tradition.
One of the earliest examples, even before Plato, was Greek geometer Oenopides (c. 450 BC) distinguishing theorems, which demonstrate a property, from problems, which provide a construction. There is a similar distinction between axioms, asserting what is easy to see, and postulates, asserting what is easy to construct. Plato's dialogues are explicitly structured to create such classifications by making dichotomic distinctions in Socratic arguments. One example is the famous quadrivium: mathematical sciences are first divided into those dealing with quantity, and those dealing with "qualified quantity". The former are subdivided into arithmetic and music, and the latter into geometry and astronomy.
Geminus (c. 50 BC) gives a much more elaborate classification (quoted from Acerbi's paper). "The classification envisages eight primary domains: arithmetic, geometry (namely, those dealing with intelligibles), mechanics, astronomy, optics, geodesy, canonics, logistics (namely, those attending to sensibles). Further divisions are set out for geometry (into plane geometry and stereometry), arithmetic (theory of linear, plane, and solid numbers), optics (optics proper, catoptrics, scene-painting), mechanics (construction of war engines, wonder-working, science of equilibrim and centers of gravity, construction of celestial spheres, and in general everything pertaining to kynetics), astronomy (gnomonics, meteoroscopy, and dioptrics)".
Another example is Geminus's classification of "lines" (geometric curves), which starts with dividing them into incomposite/composite."The second kind includes lines “that are inflected and make an angle”. The first kind is further divided into lines “that are finite and make a figure”/lines “that can be produced indefinitely.” The former class includes the circular line, the contour of the ellipse, the cissoid. The latter class includes parabola, hyperbola, conchoid, straight line etc... Of the latter, some are asymptotic, some are not. Of the former, some are in one single plane, some are not. Of the former, some are equidistant, as parallel straight lines are, some are progressively diminishing the distance between themselves, as an hyperbola does with respect to a straight line and as the conchoid does with respect to a straight line." Some anticipation of modern topological distinctions there.