First mathematical model of cosmology: the concentric spheres of eudoxus

Abstract The cosmological model of Eudoxus of Cnidus (408 - 355 BC), the concentric spheres model, represents the first mathematical model of cosmology, which attempts to explain the motion of celestial bodies. Through the comments of Aristotle (384-322 BC), the writings of Simplicius (490-560 AD) and the approaches made by 19th century historians and mathematicians, the classical mathematical reconstruction of this model will be presented. We also use a modern mathematical method, the rotation matrix method, to illustrate the planetary motions that result from the Eudoxus model, and to determine the parametric equation of the hippopede. Due to the inexistence of the original historical records of the model, it is necessary to consider the main criticisms of this classic reconstruction of the nineteenth century, among them, the uniqueness of the reconstruction of the model. However, even with all the uncertainties in the reconstruction, over the centuries, the Eudoxus model presents itself as the first attempt to understand, with the observations and tools of mathematics of the time, the movements of the Sun, the Moon and the movements retrograde of the planets, and this work is dedicated to discuss these characteristics broadly, exhausting the main works presented in the literature.