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

CONTROVERSIES AS TO HERON'S DATE 301
Philon's date cannot be later than the end of the second
century B.C. (If Ctesibius flourished before 247 B.C. the argument
would apparently suggest rather the beginning than the
end of the second century.) Next, Heron is supposed to have
been a younger contemporary of Philon, the grounds being
the following. (1) Heron mentions a ' stationary-automaton'
representation by Philon of the Nauplius-story, 1 and this is
identified by Tittel with a representation of the same story by
some contemporary of Heron's (ol kocO' f)/xd$ 2 ). But a careful
perusal of the whole passage
seems to me rather to suggest
that the latter representation was not Philon's, and that
Philon was included by Heron among the { ancient ' automaton-makers,
and not among his contemporaries." (2) Another
argument adduced to show that Philon was contemporary
lb., p. 412. 13.
1
Heron, Autom., pp. 404. 11-408. 9.
2
3
The relevant remarks of Heron are as follows. (1) He says that he
has found no arrangements of 'stationary automata' better or more
instructive than those described by Philon of Byzantium (p. 404. 11).
As an instance he mentions Philon's setting of the Nauplius-story, in
which he found everything good except two things (a) the mechanism
for the appearance of Athene, which was too difficult (epycodeo-Tepov), and
(b) the absence of an incident promised by Philon in his description,
namely the falling of a thunderbolt on Ajax with a sound of thunder
accompanying it (pp. 404. 15-408. 9). This latter incident Heron could
not find anywhere in Philon, though he had consulted a great number
of copies of his work. He continues (p. 408. 9-13) that we are not to
suppose that he is running down Philon or charging him with not being
capable of carrying out what he promised. On the contrary, the omission
was probably due to a slip of memory, for it is easy enough to make
stage-thunder (he proceeds to show how to do it). But the rest of
Philon's arrangements seemed to him satisfactory, and this, he says, is
'
why he has not ignored Philon's work : for I think that my readers will
get the most benefit if they are shown, first what has been well said b}^
the ancients and then, separately from this, what the ancients overlooked
or what in their work needed improvement '
(pp. 408. 22-410. 6). (2) The
next chapter (pp. 410. 7-412. 2) explains generally the sort of thing the
automaton-picture has to show, and Heron says he will give one example
which»he regards as the best. Then (3), after drawing a contrast between
the simpler pictures made by the ancients ' ', which involved three different
movements only, and the contemporary (ol *a0' fjpas) representations of
interesting stories by means of more numerous and varied movements
(p. 412. 3-15), he proceeds to describe a setting of the Nauplius-story.
This is the representation which Tittel identifies with Philon's. But it
is to be observed that the description includes that of the episode of the
thunderbolt striking Ajax (c.30, pp. 448. 1-452. 7) which Heron expressly
says that Philon omitted. Further, the mechanism for the appearance
of Athene described in c. 29 is clearly not Philon's 'more difficult'
arrangement, but the simpler device described (pp. 404. 18-408. 5) as
possible and preferable to Philon's (cf. Heron, vol. i, ed. Schmidt, pp.
Ixviii-lxix).
302 HERON OF ALEXANDRIA
with Heron is the fact that Philon has some criticisms of
details of construction of projectile-throwers which are found
in Heron, whence it is inferred that Philon had Heron's work
specifically in view. But if Heron's BeXoirouKd was based on
the work of Ctesibius, it is equally possible that Philon may
be referring to Ctesibius.
A difficulty in the way of the earlier date is the relation in
which Heron stands to Posidonius. In Heron's Mechanics,
i. 24, there is a definition of ' centre of gravity ' which
is
attributed by Heron to ' Posidonius a Stoic '. But this can
hardly be Posidonius of Apamea, Cicero's teacher, because the
next sentence in Heron, stating a distinction drawn by Archimedes
in connexion with this definition, seems to imply that
the Posidonius referred to lived before Archimedes. But the
Definitions of Heron do contain definitions of geometrical
notions which are put down by Proclus to Posidonius of
Apamea or Rhodes, and, in particular, definitions of figure
'
and of 'parallels'.
Now Posidonius lived from 135 to 51 B.C.,
and the supporters of the earlier date for Heron can only
suggest that either Posidonius was not the first to give these
definitions, or alternatively, if he was, and if they were
included in Heron's Definitions by Heron himself and not by
some later editor, all that this obliges us to admit is that
Heron cannot have lived before the first century B. c.
Again, if Heron lived at the beginning of the first century
B.C., it is remarkable that he is nowhere mentioned by
Vitruvius. The De architectural was apparently brought out
in 14 B.C. and in the preface to Book VII Vitruvius gives
a list of authorities on machinationes from whom he made
extracts. The list contains twelve names and has every
appearance of being scrupulously complete ;
but, while it
includes Archytas (second), Archimedes (third), Ctesibius
(fourth), and Philon of Byzantium (sixth), it does not mention
Heron. Nor is it possible to establish interdependence
between Heron and Vitruvius ; the differences seem, on the
whole, to be more numerous than the resemblances. A few of
the differences may be mentioned. Vitruvius uses 3 as the
value of 7r, whereas Heron always uses the Archimedean value
3f.
Both writers make extracts from the Aristotelian
Mrj^avLKa 7rpofi\rj/Accra, but their selections are different. The