A history of Greek mathematics - Wilbourhall.org

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 manuscript
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-
3bh\y 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 commentary
on Book X actually survive in the Arabic (see above,
vol. i, pp. 154-5, 209), and again Eutocius in his note on Archimedes,
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