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

CONTROVERSIES AS TO HERON'S DATE 307
Heron was known as 6 'AXegavSpevs (e.g. by Pappus) or
6 nrf^aviKos (mechanicus), to distinguish him from other
persons of the same name
;
Proclus and Damianus use the
latter title, while Pappus also speaks of ol nepl rbv "Hpoova
/j.r}\a^LK0L.
Character of works.
Heron was an almost encyclopaedic writer on mathematical
and physical subjects. Practical utility rather than theoretical
completeness was the object aimed at; his environment in
Egypt no doubt accounts largely for this. His Metrica begins
with the old legend of the traditional origin of geometry in
Egypt, and in the Dioptra we find one of the very problems
which geometry was intended to solve, namely that of reestablishing
boundaries of lands when the flooding of the
Nile '
had destroyed the land -marks : When the boundaries
of an area have become obliterated to such an extent that
only two or three marks remain, in addition to a plan of the
area, to supply afresh the remaining marks.' 1 Heron makes
little or no claim to originality; he often quotes authorities,
but, in accordance with Greek practice, he more frequently
omits to do so, evidently without any idea of misleading any
one ; only when he has made what is in his opinion any
slight improvement on the methods of his
predecessors does
he trouble to mention the fact, a habit which clearly indicates
that, except in these cases, he is simply giving the best
traditional methods in the form which seemed to him easiest
of comprehension and application. The Metrica seems to be
richest in definite references to the discoveries of predecessors
;
the names mentioned are Archimedes, Dionysodorus,
Eudoxus, Plato ; in the Dioptra Eratosthenes is quoted, and
in the introduction to the Gatoptrica Plato and Aristotle are
mentioned.
The practical utility of Heron's manuals being so great, it
was natural that they should have great vogue, and equally
natural that the most popular of them at any rate should be
re-edited, altered and added to by later writers ; this was
inevitable with books which, like the Elements of Euclid,
were in regular use in Greek, Byzantine, Roman, and Arabian
1
Heron, Dioptra, c. 25, p. 268. 17-19.
x 2
308 HERON OF ALEXANDRIA
education for centuries. The geometrical or mensurational
books in particular gave scope for expansion by multiplication
of examples, so that it is difficult to disentangle the genuine
Heron from the rest of the collections which have come down
to us under his name. Hultsch's considered criterion is as
follows : The Heron texts which have come down to our
'
time are authentic in so far as they bear the author's name
and have kept the original design and form of Heron's works,
but are unauthentic in so far as, being constantly in use for
practical
purposes, they were repeatedly re-edited and, in the
course of re-editing, were rewritten with a view to the
particular needs of the
List
time.'
of Treatises.
Such of the works of Heron as have survived have reached
us in very different ways. Those which have come down in
the Greek are
I. The Metrica, first discovered in 1896 in a manuscript
of the eleventh (or twelfth) century at Constantinople by
R. Schone and edited by his son, H. Scheme (Heronis Opera, iii,
Teubner, 1903).
II. On the Dioptra, edited in an Italian version by Venturi
in 1814 ;
the Greek text was first brought out by A. J. H.
Vincent 1 in 1858, and the critical edition of it byH. Schone is
included in the Teubner vol. iii just mentioned.
III. The Pneumatica, in two Books, which appeared first in
a Latin translation by Commandinus, published after his
death in 1575; the Greek text was first edited by TheVenot
in Vetevum mathematicovum opera Graece et Latine edita
(Paris, 1693), and is now available in Heronis Opera, i (Teubner,
1899), by W. Schmidt.
IV. On the art of constructing automata (irepl avTo/jiaToiroLrjTLKrjs),
or The automaton-theatre, first edited in an Italian
translation by B. Baldi in 1589 ; the Greek text was included
in TheVenot's Vet, math., and now forms part of Heronis
Opera, vol. i, by W. Schmidt.
V. Belopoe'ica (on the construction of engines of war), edited
1
Notices et extraits des manuscrits de la Biblioiheque impe'riale, xix, pt. 2,
pp. 157-337.