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

CONTROVERSIES AS TO HERONS DATE 305
the distance between Rome and Alexandria. 1 Unfortunately
the text is in places corrupt and deficient, so that the method
cannot be reconstructed in detail. But it involved the observation
of the same lunar eclipse at Rome and Alexandria
respectively and the drawing of the analemma for Rome.
That is to say, the mathematical method w T hich Ptolemy
claims to have invented is spoken of by Heron as a thing
generally known to experts and not more remarkable than
other technical matters dealt with in the same book. Consequently
Heron must have been later than Ptolemy. (It is
right to add that some hold that the chapter of the Dioptra
in question is not germane to the subject of the treatise, and
was probably not written by Heron but interpolated by some
later editor ; if this is so, the argument based upon it falls to
the ground.) (2) The dioptra described in Heron's work is a
fine and accurate instrument, very much better than anything
Ptolemy had at his disposal. If Ptolemy had been aware of
its existence, it is highly unlikely that he would have taken
the trouble to make his separate and imperfect ' parallactic '
instrument, since it could easily have been grafted on to
Heron's dioptra. Not only, therefore, must Heron have been
later than Ptolemy but, seeing that the technique of instrument-making
had made such strides in the interval, he must
have been considerably later. (3) In his work irepl po-rrcov 2
Ptolemy, as we have seen, disputed the view of Aristotle that
air has weight even when surrounded by air. Aristotle
satisfied himself experimentally that a vessel full of air is
heavier than the same vessel empty ; Ptolemy, also by experiment,
convinced himself that the former is actually the
lighter. Ptolemy then extended his argument to water, and
held that water with water round it
has no weight, and that
the diver, however deep he dives, does not feel the weight of
the water above him. Heron 3 asserts that water has no
appreciable weight and has no appreciable power of compressing
the air in a vessel inverted and forced down into
the water. In confirmation of this he cites the case of the
diver, who is not prevented from breathing when far below
1
Heron, Dioptra, c. 35 (vol. iii, pp. 302-6).
2
Simplicius on De caelo, p. 710. 14, Heib. (Ptolemy, vol. ii, p. 263).
3
Heron, Pneum«tica, i. Pref. (vol. i, p. 22. 14 sq.).
1523.2 X.
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.
Lastly, he is mentioned in an inscription commemorating an
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
two persons named Dionysius is an ingenious conjecture, but
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,