By the early sixteenth century, Ptolemy’s projection had become widely accepted in educated circles, even as the limitations of the data included in the Geographia were becoming increasingly clear. Translated roughly, the inscription along the lower right reads “Here there is not land, but sea; in which there are such islands not conceived by Ptolemy.” The surrounding area further suggests the need for a new frame of reference. Left blank, it underscores the need to resolve the fundamental problem of systematically rendering curved space in two dimensions if geographic features are to be located accurately.
Along with the known problems, the Ptolemaic view of the world contained a more significant, and still unknown error of scale. Though Eratosthenes (276–194 BCE) had measured the globe with an error of less than 1 percent, his results had been substantially distorted by the time Greek geography was reconstituted in Europe. Columbus, in gathering support for his famous expedition, suggested that Cathay was roughly twenty-four hundred nautical miles from Lisbon; less than a quarter of the actual distance. The discrepancy accounts for his assertion that the Caribbean islands were in the vicinity of India, a belief he maintained to his death.