double the volume. This problem cannot be solved just with ruler and compass, and He ̄ro ̄n
uses a special sliding ruler, thus combining geometrical and mechanical methods. The first
book also contains an analysis of the center of gravity related to Archime ̄de ̄s. The second
book covers the five “simple machines”, i.e. mechanical principles for lifting a heavy
weight with a small power: windlass, lever, pulley, wedge, screw, and combinations thereof.
Lastly, Book three considers practical problems of lifting weight and applying power in,
e.g., presses and cranes. Throughout the treatise geometrical, mechanical and practical
solutions and advice are combined.
Artillery Construction (Belopoiika) describes the development from the simple belly-bow to
the torsion catapult. The account is historical, and the newest catapults described were
300 years old when the treatise was written. The function of the account is therefore to
describe how mechanics responds to demands and needs, rather than to provide “recipes”
for artillery. In the introduction, He ̄ro ̄n argues that mechanics rather than philosophy can
offer a tranquil life and thus presents mechanics as a competitor to philosophy. The treatise
ends with a solution to the problem of the doubling of the cube also found in the Mechanics,
but this time introduced as a measure for scaling catapults up or down. It is used in a similar
way by Philo ̄n. A fragment of an additional treatise on hand-operated catapults, Kheiroballista,
is also preserved.
Several of He ̄ro ̄n’s treatises concern measurement. Dioptra describes a surveying
instrument that can measure angular distances and heights. The introduction lists many
uses of the instrument ranging from astronomy and geography, over harbor and aque-
duct construction, to measuring the height of a wall before a siege. The main part of
the treatise primarily concerns problems of water transport, for instance how to con-
struct a tunnel so that the teams digging from either side will meet in the middle. He ̄ro ̄n
also considers instruments and techniques for long distance measurement such as a road
measurer and an astronomical method for measuring the distance from Alexandria to
Rome.
Metrika is a more geometrical treatise on the measurement of two-dimensional figures
(Book I), three-dimensional figures (Book II) and division of areas (Book III). The third book
links division of areas directly to land division and states that geometry secures both equal-
ity and justice. The techniques employed in the treatises combine geometrical proofs with
numerical calculations, and the treatise thus demonstrates a connection between practical
mathematics and geometry. Additionally, the treatise On Measurements compares Egyptian,
Greek and Roman standards.
A group of more purely geometrical treatises, Geometry (Geo ̄metrika) and Stereometry
(Stereometrika), discusses two and three dimensional geometry, and Definitions (Horismoi),
a geometrical handbook, gives definitions for an array of geometrical objects. These have
not survived in their original form and it is hard to separate Heronic material from later
additions.
Lastly a few fragments are preserved from a treatise on Water-Clocks (Hudria Horoskopeia)
and a commentary on Euclid’s Elements. There are reports of treatises on balances, vaults
and astrolabes, but nothing further is known about these works.
Sources and Character of Work: He ̄ro ̄n’s work has, in the past, been used in a
fragmentary fashion mainly as a source for a few selected technologies or for authors con-
sidered more significant. Thus Diels assigned large parts of the introduction of He ̄ro ̄n’s
Pneumatics to Strato ̄n; whereas Drachmann and Heiberg associated most of the discussion
on centers of gravity in Mechanics with Archime ̄de ̄s. More generally He ̄ro ̄n is often viewed as
HE ̄RO ̄N OF ALEXANDRIA