The opinion of Aristarchus of Samos, as stated by Archimedes (Arenarius, p. 320, Oxon), was that the sphere of the fixed stars was so large, that it bore to the earth’s orbit the same proportion as a sphere to its centre, or more correctly (as Archimedes explains) the same proportion as the earth’s orbit round the sun to the earth itself.  Compare Cat. xv. 24.