310 
HERON OF ALEXANDRIA 
Besthorn and Heiberg (Codex Leidensis 399. 1, five parts of 
which had appeared up to 1910). The commentary extended 
as far as Elem. VIII. 27 at least. 
The Gatoptrica, as above remarked under Ptolemy, exists in 
a Latin translation from the Greek, presumed to be by William 
of Moerbeke, and is included in vol. ii of Heronis Opera, 
edited, with introduction, by W. Schmidt. 
Nothing is known of the Camarica (‘ on vaultings ’) men 
tioned by Eutocius (on Archimedes, Sphere and Cylinder), the 
Zygia (balancings) associated by Pappus with the Automata, x 
or of a work on the use of the astrolabe mentioned in the 
Fihrist. 
We are in this work concerned with the treatises of mathe 
matical content, and therefore can leave out of account such 
works as the Pneumática, the Automata, and the Belopoéica. 
The Pneumático, and Automata have, however, an interest to 
the historian of physics in so far as they employ the force of 
compressed air, water, or steam. In the Pneumática the 
reader will find such things as siphons, ‘ Heron’s fountain ’, 
£ penny-in-the-slot ’ machines, a fire-engine, a water-organ, and 
many arrangements employing the force of steam. 
Geometry. 
(a) Commentary on Euclid’s Elements. 
In giving an account of the geometry and mensuration 
(or geodesy) of Heron it will be well, I think, to begin 
with what relates to the elements, and first the Commen 
tary on Euclid’s Elements, of which we possess a number 
of extracts in an-Nairizi and Proclus, enabling us to form 
a general idea of the character of the work. Speaking 
generally, Heron’s comments do not appear to have contained 
much that can be called important. They may be classified 
as follows : 
(1) A few general notes, e.g. that Heron would not admit 
more than three axioms. 
(2) Distinctions of a number of particular cases of Euclid’s 
propositions according as the figure is drawn in one way 
or another. 
1 Pappus, viii, p. 1024. 28.