CONTROVERSIES AS TO HERON’S DATE 399
above quoted; the title, however, in itself* need not imply
more than that Heron’s work was a new edition of a similar
work by Ctesibius, and the Ktt](tl^lov may even have been added
by some well-read editor who knew both works and desired to
indicate that the greater part of the contents of Heron’s work
was due to Ctesibius. One manuscript has" Hpcovos ’AXe£av-
Specos BeXoTrouKoc, which corresponds to the titles of the other
works of Heron and is therefore more likely to be genuine.
The discovery of the Greek text of the Metrica by R. Schone
in 1896 made it possible to fix with certainty an upper limit.
In that work there are a number of allusions to Archimedes,
three references to the yoapiov dvoTopr] of Apollonius, and
two to ‘ the (books) about straight lines (chords) in a circle ’
(SiSeLKTai Se kv tois 7repl tS>v kv kvkXco evdeLcov). Now, although
the first beginnings of trigonometry may go back as far as
Apollonius, we know of no work giving an actual Table of
Chords earlier than that of Hipparchus. We get, therefore,
at once the date 150 B.C. or thereabouts as the terminus 'post
quern. A terminus ante quern is furnished by the date of the
composition of Pappus’s Collection; for Pappus alludes to, and
draws upon, the works of Heron. As Pappus was writing in
the reign of Diocletian (a.d. 284-305), it follows that Heron
could not be much later than, say, a.d. 250. In speaking of
the solutions by ‘ the old geometers ’ (ol TraXouol yeccpirpaL) of
the problem of finding the two mean proportionals, Pappus may
seem at first sight to include Heron along with Eratosthenes,
Nicomedes and Philon in that designation, and it has been
argued, on this basis, that Heron lived long before Pappus.
But a close examination of the passage 1 shows that this is
by no means necessary. The relevant words are as follows :
‘ The ancient geometers were not able to solve the problem
of the two straight lines [the problem of finding two mean
proportionals to them] by ordinal geometrical methods, since
the problem is by nature solid ”... but by attacking it with
mechanical means they managed, in a wonderful way, to
reduce the question to a practical and convenient construction,
as may be seen in the Mesolabon of Eratosthenes and in the
mechanics of Philon and Heron . . . Nicomedes also solved it
by means of the cochloid curve, with which he also trisected
an angle.’
1 Pappus, iii, pp. 54-6.
