2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67823A geometric realization of the projective completion of the Jordan pair corresponding to a three-graded Lie algebra is given which permits to develop a geometric structure theory of the projective completion. This will be used in Part II of this work to define a manifold structure on the projective completion (in arbitrary dimension and over quite general base fields and -rings).33 pages, plain texRings and Algebras17C30, 17C37text