It is assumed that the linear perspective in painting and drawing has its origin in the 13th century Florence. The architect Filippo Brunelleschi is generally credited with having perfected it in about 1415. Author Toby Lester makes in his book "The Fourth Part of the World" a possible connection between the projection systems used in maps and the linear perspective. It was also in 1415 that the book Geography of Ptolemy began to circulate in Florence in its new form.
Source: Toby Lester, 2009, The Fourth Part of the World.