The First Calculus: Formalising Leibniz’s Unfinished Qualitative Calculus develops a constructive qualitative calculus complementary to the quantitative calculus of modern science. Beginning from the Generic Entity and the principle of First-Classness (FC), the work derives the first admissible qualitative distinction as the complementary opposition of toHave and toBe (F/M ontological type). From this basis the paper develops the Indeterminate Dyad, the field of complete perspectives (the sea of monads), the qualitative quadratic, four primitive dispositional dyads, and the H-diagram formalism as a concrete arrow-theoretic calculus of qualitative organisation. The work reconstructs Leibniz’s unfinished Analysis Situs project in operational form, while situating the resulting framework in relation to Category Theory, Geometric Algebra, Heaviside’s operational calculus, and the first-class tradition in computer science. The paper proposes that quantitative process formalisms and qualitative organisational formalisms constitute complementary modes of scientific reasoning rather than reducible alternatives.