THE TEXT OF THE ELEMENTS 
361 
manuscripts bequeathed by Savile to the University in 
places where the Basel text differed from the Latin version 
of Commandinus which he followed in the main. It was 
a pity that even Peyrard in his edition (1814-18) only 
corrected the Basel text by means of P, instead of rejecting 
it altogether and starting afresh; but he adopted many of the 
readings of P and gave a conspectus of them in an appendix. 
E. F. August’s edition (1826-9) followed P more closely, and 
he consulted the Viennese MS. gr. 103 also; but it was 
left for Heiberg to bring out a new and definitive Greek text 
(1883-8) based on P and the best of the Theonine manuscripts, 
and taking account of external sources such as Heron and 
Proclus. Except in a few passages, Proclus’s manuscript does 
not seem to have been of the best, but authors earlier than 
Theon, e. g. Heron, generally agree with our best manuscripts. 
Heiberg concludes that the Elements were most spoiled by 
interpolations about the third century, since Sextus Empiricus 
had a correct text, while lamblicus had an interpolated one. 
The differences between the inferior Theonine manuscripts 
and the best sources are perhaps best illustrated by the arrange 
ment of postulates and axioms in Book I. Our ordinary 
editions based on Simson have three postulates and twelve 
axioms. Of these twelve axioms the eleventh (stating that 
all right angles are equal) is, in the genuine text, the fourth 
Postulate, and the twelfth Axiom (the Parallel-Postulate) is 
the fifth Postulate; the Postulates were thus originally five 
in number. Of the ten remaining Axioms or Common 
Notions Heron only recognized the first three, and Proclus 
only these and two others (that things which coincide are 
equal, and that the whole is greater than the part); it is fairly 
certain, therefore, that the rest are interpolated, including the 
assumption that two straight lines cannot enclose a space 
(Euclid himself regarded this last fact as involved in Postu 
late 1, which implies that a straight line joining one point 
to another is unique). 
Latin and Arabic translations. 
The first Latin translations which we possess in a complete 
form were made not from the Greek but from the Arabic. 
It was as early as the eighth century that the Elements found