The term 'axiom' was used by Proclus , but not by Euclid. He speaks, instead, of 'common notions' common either to all men or to all sciences.
Euclid , says Proclus, was younger than Plato and older than Eratosthenes and Archimedes , the latter of whom mentions him. He was of the Platonic sect, and well read in its doctrines. He collected the Elements , put in order much that Eudoxus had prepared, completed many things of Theætetus, and was the first who reduced to unobjectionable demonstration the imperfect attempts of his predecessors.
There has been much controversy among ancient and modern critics on the postulates and axioms. An immense preponderance of manuscripts and the testimony of Proclus place the 'axioms' about right angles and parallels (Axioms 11 and 12) among the postulates . This is indeed their proper place, for they are really assumptions , and not common notions or axioms.
The regular solids were studied so extensively by the Platonists that they received the name of "Platonic figures." The statement of Proclus that the whole aim of Euclid in writing the Elements was to arrive at the construction of the regular solids, is obviously wrong. The fourteenth and fifteenth books, treating of solid geometry, are apocryphal .
About the time of Anaxagoras, but isolated from the Ionic school, flourished Œnopides of Chios. Proclus ascribes to him the solution of the following problems: From a point without, to draw a perpendicular to a given line, and to draw an angle on a line equal to a given angle. That a man could gain a reputation by solving problems so elementary as these, indicates that geometry was still in its infancy, and that the Greeks had not yet gotten far beyond the Egyptian constructions.