A history of Greek mathematics - Wilbourhall.org

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CONTROVERSIES AS TO HERON'S DATE 299
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 Ktyio-l^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 h.3LS f 'Hpcovos 'A\e£ai>-
Specos BtXoTrouKd, 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 yapiov aTTOTop,r\ of Apollonius, and
two to the (books) about straight ' lines (chords) in a circle
(SeStLKTcu 8e kv rots rrepl tcou kv kvkXco zvOeicov). 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 1 50 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 naXaiol yeco/jLtTpcu) 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
1
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 ordinary geometrical methods, since
the problem is by nature