A history of Greek mathematics - Wilbourhall.org

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 Catoptrica, 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 ') mentioned
by Eutocius (on Archimedes, Sphere and Cylinder), the
Zygicc (balancings) associated by Pappus with the Automata, 1
or of a work on the use of the astrolabe mentioned in the
Fihrist.
We are in this work concerned with the treatises of mathematical
content, and therefore can leave out of account such
works as the Pneumatica, the Automata, and the Belopoe'ica.
The Pneumatica 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 Pneumatica 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.
(a)
Geometry.
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 Commentary
on Euclid's Elements, of which we possess a number
of extracts in an-Nairlzi 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 caves of Euclid's
propositions according as the figure is drawn in one way
or another.
1
Pappus, viii, p. 1024. 28.