The accepted geography of the early sixteenth century was based on that defined by Ptolemy (after 83–161 AD) in his book the Geographia. Ptolemy’s representation of the earth in the second century was much smaller than the expanded world of the early Renaissance, especially after the discovery of the New World. In addition, the methods of cartography and map projection outlined by Ptolemy were insufficient for cartographers in Waldseemüller’s time and many innovations in map construction came out of commentaries on Ptolemy’s book. Waldseemüller in his 1507 map expanded these older classical forms to create a world map that, like Ptolemy’s, gives the impression of a spherical earth but includes the newly discovered lands. The layout of the 1516 Carta Marina on the other hand comes from a different tradition, that of “portolan charts.” Used for sea navigation, these charts were probably invented in the early Middle Ages. Both maps pushed the boundaries of cartography into new areas and depicted a representation of the world that is very modern and reminiscent of maps of today.