[2] After having amicably parted from the House of Medina Sidonia, he sought recognition as a cosmographer and brought out a text titled Libro de Cosmografía ("Book of Cosmography", 1538).
[2] He soon became aware of defects in the training of navigators and in the instruments, books and maps they relied upon, and wrote a "Representation" to King Charles I on the subject.
The senior cosmographer Alonso de Chaves demonstrated that Medina's Arte was a compilation, made with the assistance of other writers.
Diego Gutiérrez and other authors claimed that they had helped with parts of the book, and Medina himself acknowledged the assistance of Francisco Faleiro and Alonso de Santa Cruz on other occasions, but not with the writing of Arte.
[2] Despite his knowledge and achievements Medina continued to deny the phenomenon of magnetic declination, of which he lacked personal experience, in opposition to the opinion of most other cosmographers of the time.
[5][6] Medina acted as royal adviser during the two assemblies convened by the Council of the Indies in 1554 and 1556 to determine the precise position of the Philippines and the Moluccas, and to define the demarcation between Spanish and Portuguese control in that part of the world.