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Chrisippian m introducing pure and applied mathematics follows Logique et Algèbre de Structures Mathématiques Modales -Valentes Chrisyppiennes [2](9): going on creating new mathematical objects: m real numbers (m rn), m complex numbers (m cn), their respective intrinsic algebraic structures : two m quasifields (m qf); as well as many other analogue: m extensions of rings, fields, m quasifields: part A, chapter I and II. In part B the book completes [2] (9) since introducing intrinsic mathematical objects and structures of pure and applied mathematics founded on the introductive m diagram commutativity. Intrinsic m applications are presented in chapter III. Chapter IV presents unknown finite fields, chapter V unknown Galois's extensions, chapter VI intuitive m metric, normed spaces. M measures, m integrals, m prehilbert spaces, m quasilinear topological spaces are presented as m spectral components of their respective boolean frames, objects or structures. This way revealing unknown mathematical objects or statements that are not perceptible as long as we stay closed inside an exclusive boolean way of thinking and making an exclusive use of its boolean structures.