A history of Greek mathematics - Wilbourhall.org

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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