One of the most important German contributions to geography of the Renaissance as one of the first works to base geography on mathematics and measurement.

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 included Gemma 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.

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 for 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.

The large world map, a reduced version of Apianus's celebrated cordiform world map 'Charta Cosmographica' after Waldseemüller's map of 1507, is important for being one of the earliest to show the entire east coast of north America. The map displays the eastern side of north America as a narrow landmass, named "Baccalearum," after the cod fisheries off the coasts of new england and Canada. It employs a truncated cordiform projection, much used by Renaissance cartographers to represent the relationship between the Americas and the old World, and maintains the tantalizing possibility of a northwest passage to Asia over the top of north America. The map is also notable for being the first printed map to depict the Yucatán as a peninsula rather than an island, anticipating Ruscelli's 1561 map of new Spain. Cuba and hispaniola are shown as huge islands. Also prominent are the Mountains of the Moon, considered the source of the River nile. Signs of the zodiac and the Ptolemaic climatic zones border the map. Zeus and Mars, wearing the coats-of-arms of Charles V, holy Roman emperor, are shown atop the map while wind-heads at the south represent the traditionally believed plague-bearing nature of those winds.