A history of Greek mathematics Vol.II from Aristarchus to Diophantus by Heath, Thomas Little, Sir, 1921

356 PAPPUS OF ALEXANDRIA
Date of Pappus.
XIX
PAPPUS OF ALEXANDRIA
We have seen that the Golden Age of Greek geometry
ended with the time of Apollonius of Perga. But the influence
of Euclid, Archimedes and Apollonius continued, and for some
time there was a succession of quite competent mathematicians
who, although not originating anything of capital importance,
kept up the tradition. Besides those who were known for
particular investigations, e.g. of new curves or surfaces, there
were such men as Geminus who, it cannot be doubted, were
thoroughly familiar with the great classics. Geminus, as we
have seen, wrote a comprehensive work of almost encyclopaedic
character on the classification and content of mathematics,
including the history of the development of each subject.
But the beginning of the Christian era sees quite a different
state of things. Except in sphaeric and astronomy (Menelaus
and Ptolemy), production was limited to elementary textbooks
of decidedly feeble quality. In the meantime it would
seem that the study of higher geometry languished or was
completely in abeyance, until Pappus arose to revive interest
in the subject. From the w&y in which he thinks it necessary
to describe the contents of the classical works belonging to
the Treasury of Analysis, for example, one would suppose
that by his time many of them were, if not lost, completely
forgotten, and that the great task which he set himself was
the re-establishment of geometry on its former high plane of
achievement. Presumably such interest as he was able to
arouse soon flickered out, but for us his work has an inestimable
value as constituting, after the works of the great
mathematicians which have actually survived, the most important
of all our sources.
A a 2
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