1571 Ortelius

This 1571 edition of the “Theater of the World” by Ortelius contains maps with oval-shaped projections in Figure 2 and 3.   

For a discussion of the Ortelius projections, see pp. 178-79 in An Album of Map Projections, which catalogs the vast array of map projections now available.

Figure 3 is a hemispheric map of the Americas. It appears to depict New Guinea as part of Antarctica, plus Terra Del Fuego looks as if it part of Antarctica (or just about!).  

ADDITIONAL RESOURCE:

Smith, Cynthia. Ortelius: A Legendary Mapmaker. World Revealed: Geography & Maps at the Library of Congress.