Ptolemy's (ca. 100-ca. 175 CE) map represented only a portion of the terrestrial globe: the oikumene, that is, the known, inhabited world. In contrast, Waldseemüller's (ca. 1470-ca. 1520) map shows the entire surface of the Earth except the southern cap below the 44th parallel. The Ptolemaic oikumene is depicted at the center of the map using Ptolemy's second cartographic method, which supplies the geometric elements needed to expand the drawing. From a geometric standpoint, Waldseemüller's map is indeed an extension of Ptolemy's second cartographic method. Beyond the boundaries of the ancient world lie the remotest regions of Asia described by Marco Polo (1254-1324) and the New World described by Amerigo Vespucci (1454-1512). Ptolemy's world and Vespucci's world are illustrated separately in the two small hemispheres drawn at the top of the sheet, next to the portraits of the two cosmographers. The Ptolemaic hemisphere coincides with the central part of the map, whereas Vespucci's hemisphere is depicted in two halves, one on the left, the other on the right. The top piece illustrates the lands to the north of the parallel passing through Thule, up to the Arctic pole. The map's overall aspect closely resembles a solution developed in the same period by Leonardo da Vinci (1452-1519).