EUDOXUS 
323 
the poem of Aratus was drawn, so far as verses 19-732 are 
concerned, may have been a revision of the former work and 
even, perhaps, posthumous. 
But it is the theoretical side of Eudoxus’s astronomy rather 
than the observational that has importance for us; and, 
indeed, no more ingenious and attractive hypothesis than 
that of Eudoxus’s system of concentric spheres has ever been 
put forward to account for the apparent motions of the sun, 
moon and planets. It was the first attempt at a purely 
mathematical theory of astronomy, and, with the great and 
immortal contributions which he made to geometry, puts him 
in the very first rank of mathematicians of all time. He 
was a man of science if there ever was one. No occult or 
superstitious lore appealed to him; Cicero says that Eudoxus, 
‘ in astrologia iudicio doctissimorum hominum facile princeps ’, 
expressed the opinion and left it on record that no sort of 
credence should be given to the Chaldaeans in their predic 
tions and their foretelling of the life of individuals from the 
day of their birth. 1 Nor would he indulge in vain physical 
speculations on things which were inaccessible to observation 
and experience in his time; thus, instead of guessing at 
the nature of the sun, he said that he would gladly be 
burnt up like Phaethon if at that price he could get to the 
sun and so ascertain its form, size, and nature. 1 2 Another 
story (this time presumably apocryphal) is to the effect 
that he grew old at the top of a very high mountain in 
the attempt to discover the movements of the stars and the 
heavens. 3 
In our account of his work we will begin with the sentence 
about him in Proclus’s summary. First, he is said to have 
increased ‘ the number of the so-called general theorems ’. 
‘So-called general theorems’ is an odd phrase; it occurred to 
me whether this could mean theorems which were true of 
everything falling under the conception of magnitude, as are 
the definitions and theorems forming part of Eudoxus’s own 
theory of proportion, which applies to numbers, geometrical 
magnitudes of all sorts, times, &c. A number of propositions 
1 Cic., De div. ii. 42. 
2 Plutarch, Non posse suaviter vivi secundum Epicurum, c. 11, 1094 B. 
3 Petronius Arbiter, Satyricon, 88. 
Y 2