THE PHAENOMENA AND OPTICS
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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.
