THE PHAENOMENA AND OPTICS 
441 
while the best manuscript of the older and better version (a) 
is the Viennese MS.Vind. gr. XXXI. 13 of the twelfth century. 
A new text edited by Menge and taking account of both 
recensions is now available in the last volume of the Heiberg- 
Mengc edition of Euclid. 1 
(/3) Optics and Catoptrica. 
The Optics, a treatise included by Pappus in the collection of 
works known as the Little Astronomy, survives in two forms. 
One is the recension of Theon translated by Zambertus in 
1505; the Greek text was first edited by Johannes Pena 
(de la Pene) in 1557, and this form of the treatise was alone 
included in the editions up to Gregory’s. But Heiberg dis 
covered the earlier form in two manuscripts, one at Vienna 
(Vind. gr. XXXI. 13) and one at Florence (Laurent. XXVIII. 3), 
and both recensions are contained in vol. vii of the Heiberg- 
Menge text of Euclid (Teubner, 1895). There is no reason to 
doubt that the earlier recension is Euclid’s own work; the 
style is much more like that of the Elements, and the proofs of 
the propositions are more complete and clear. The later recen 
sion is further differentiated by a preface of some length, which 
is said by a scholiast to be taken from the commentary or 
elucidation by Theon. It would appear that the text of this 
recension is Theon’s, and that the preface was a reproduction 
by a pupil of what was explained by Theon in lectures. It 
cannot have been written much, if anything, later than Theon’s 
time, for it is quoted by Nemesius about A.D. 400. Only the 
earlier and genuine version need concern us here. It is 
a kind of elementary treatise on perspective, and it may have 
been intended to forearm students of astronomy against 
paradoxical theories such as those of the Epicureans, who 
maintained that the heavenly bodies are of the size that they 
look. It begins in the orthodox fashion with Definitions, the 
first of which embodies the same idea of the process of vision 
as we find in Plato, namely that it is due to rays proceeding 
from our eyes and impinging upon the object, instead of 
the other way about: ‘ the straight lines (rays) which issue 
from the eye traverse the distances (or dimensions) of great 
1 Eudidis Phaenomena et scripta Musica edidit Henricus Menge, 
Fragmenta collegit et disposuit J. L. Heiberg, Teubner, 1910.