A history of Greek mathematics - Wilbourhall.org

306 HERON OF ALEXANDRIA
the surface. He then inquires what is the reason why the
diver is not oppressed though he has an unlimited weight of
water on his back. He accepts, therefore, the view of Ptolemy
as to the fact, however strange this may seem. But he is not
satisfied with the explanation given :
'
Some say ', he goes on,
'
it is because water in itself is uniformly heavy (/o-o/Sape? avro
Kad' avro) '—this seems to be equivalent to Ptolemy's dictum
that water in water has no weight—' but they give no explanation
whatever why divers
.'
. . He himself attempts an
explanation based on Archimedes. It is suggested, therefore,
that Heron's criticism is directed specifically against Ptolemy
and no one else. (4) It is suggested that the Dionysius to whom
Heron dedicated his Definitions is a certain Dionysius who
was praefectus r urbi at Rome in a.d. 301. The grounds are
these
(a) Heron addresses Dionysius as Aiovvcrie XafX7rp6raTe,
where Xau-rrpoTaTo? obviously corresponds to the Latin clarissirnus,
a title which in the third century and under Diocletian
was not yet in common use. Further, this Dionysius was
curator aquarv/m and curator operum publicorum, so that he
was the sort of person who would have to do with the
engineers, architects and craftsmen for whom Heron wrote.
mentioned in an inscription commemorating an
Lastly, he is
improvement of water supply and dedicated to Tiberinus,
'
father of all waters, and to the ancient inventors of marvellous
constructions ' (repertoribus admirabilium fabricarum
pritcis viris), an expression which is not found in any other
inscription, but which recalls the sort of tribute that Heron
frequently pays to his predecessors. This identification of the
an ingenious conjecture, but
two persons named Dionysius is
the evidence is not such as to make it anything more. 1
The result of the whole investigation just summarized is to
place Heron in the third century A.D., and perhaps little, if
anything, earlier than Pappus. Heiberg accepts this conclusion,
2 which may therefore, I suppose, be said to hold the field
for the present.
1
Dionysius was of course a very common name. Diophantus dedicated
kiovixxu), whom he
his Arithmetica to a person of this name {rifuarare /uoi
praised for his ambition to learn the solutions of arithmetical problems.
This Dionysius must have lived in the second half of the third century
A. D., and if Heron also belonged to this time, is it not possible that
Heron's Dionysius was the same person?
2
Heron, vol. v, p. ix,