Final answer:
Nicolaus Copernicus is the one who discovered non-geocentric cosmology by introducing the heliocentric model, where the Sun is at the center of the universe, not Earth. His work set the stage for other astronomers like Johannes Kepler and Galileo Galilei to further support and expand upon this model.
Step-by-step explanation:
The individual who discovered non-geocentric cosmology was Nicolaus Copernicus (1473–1543). He challenged the long-accepted geocentric model of the universe that placed the Earth at its center. In his seminal work, De Revolutionibus, Copernicus proposed a revolutionary heliocentric model, in which the Sun, not the Earth, was at the center of the universe.
This idea was further supported and mathematically substantiated by subsequent astronomers such as Johannes Kepler, who established the laws of planetary motion, and Galileo Galilei, whose telescopic observations strongly supported the Copernican theory.