An early Latin edition of Apianus's important contribution to the geography of the Renaissance was edited by his student, Gemma Frisius (1508-1555); it contains his account of Peru, and describes the discovery of America by Amerigo Vespucci, in 1497. The woodcut illustrations demonstrate the astronomical, cartological, mathematical and geographical concepts discussed in the treatise.

The 'Cosmographia' is one of the most popular books on cosmography ever published. It went through no fewer than 45 editions, was published in four languages, and was manufactured in seven cities, by at least 18 printers. This popularity derived principally from its maps and discussion of the New World, but also from its ingenious use of volvelles. Indeed, Frisius's revisions to the work include a fourth volvelle showing the phases of the moon, not present in the original edition.

Peter Bienevitz (1501-52), better known as Petrus Apianus (1495-1552), was professor of mathematics and astronomy, holding chairs at Ingolstadt and Innsbruck. First published in 1524, the 'Cosmographia' was his first major work. It covers "the division of the earth into climatic zones, the uses of parallels and meridians, the determination of latitude, several methods for determining longitude including that of lunar distance, the use of trigonometry to determine distances, several types of map projections, and many other topics" (Karrow). Editions of the 'Cosmographia' printed after 1533 also include Frisius's treatise on topographical triangulation, in which he was the first person to propose it as a means of locating and mapping places: a landmark in the history of cartography.