356 
PAPPUS OF ALEXANDRIA 
Date of Pappus. 
Pappus lived at the end of the third century a.d. The 
authority for this date is a marginal note in a Leyden manu 
script of chronological tables by Theon of Alexandria, where, 
opposite to the name of Diocletian, a scholium says, ‘ In his 
time Pappus wrote’. Diocletian reigned from 284 to 305, 
and this must therefore be the period of Pappus’s literary 
activity. It is true that Suidas makes him a contemporary 
of Theon of Alexandria, adding that they both lived under 
Theodosius I (379-395). But Suidas was evidently not well 
acquainted with the works of Pappus; though he mentions 
a description of the earth by him and a commentary on four 
Books of Ptolemy’s Syntaxis, he has no word about his greatest 
work, the Synagoge. As Theon also wrote a commentary on 
Ptolemy and incorporated a great deal of the commentary of 
Pappus, it is probable that Suidas had Theon’s commentary 
before him and from the association of the two names wrongly 
inferred that they were contemporaries. 
• 
Works (commentaries) other than the Collection. 
Besides the Synagoge, which is the main subject of this 
chapter, Pappus wrote several commentaries, now lost except for 
fragments which have survived in Greek or Arabic. One was 
a commentary on the Elements of Euclid. This must presum 
ably have been pretty complete, for, while Proclus (on Eucl. I) 
quotes certain things from Pappus which may be assumed to 
have come in the notes on Book I, fragments of his commen 
tary on Book X actually survive in the Arabic (see above, 
vol. i, pp. 154-5, 209), and again Eutocius in his note on Archi 
medes, On the Sphere and Cylinder, I. 13, says that Pappus 
explained in his commentary on the Elements how to inscribe 
in a circle a polygon similar to a polygon inscribed in another 
circle, which problem would no doubt be solved by Pappus, as 
it is by a scholiast, in a note on XII. 1. Some of the references 
by Proclus deserve passing mention. (1) Pappus said that 
the converse of Post. 4 (equality of all right angles) is not 
true, i.e. it is not true that all angles equal to a right angle are 
themselves right, since the £ angle ’ between the conterminous 
arcs of two semicircles which are equal and have their