It has become generally accepted that the earliest geoheliocentric representation of the planets' motions in which the majority of the planets orbited about the Sun appeared in 1588. For in this year the Danish astronomer Tycho Brahe announced his discovery of a new system of the world, in which Sun and Moon moved about the Earth, and the five planets Mercury, Venus, Mars, Jupiter and Saturn performed their motions about the Sun. Yet the accompanying figure, which depicts a planetary arrangement in general identical with that of Tycho, occurs in a manuscript prepared at least a year before Tycho's publication of his system. Moreover, the author of the manuscript derived this representation of the planets' motions not from Tycho, but rather from Copernicus. The aim of this paper is to show that as a result of the work of Copernicus, a number of sixteenth-century mathematicians produced treatments of the planetary motions similar to the system proposed by Tycho in 1588.