Heron of Alexandria by Evangelos Papadopulos.pdf

HERON OF ALEXANDRIA

(c. 10–85 AD)

Evangelos Papadopoulos

Department of Mechanical Engineering, National Technical University of Athens,

15780 Athens, Greece

E-mail: egpapado@central.ntua.gr

Abstract. Heron of Alexandria was a mathematician, physicist and engineer who lived

around 10–85 AD. He taught at Alexandria’s Musaeum and wrote many books on Mathemat-

ics, Geometry and Engineering, which were in use till the medieval times. His most important

invention was the Aeolipile, the ﬁrst steam turbine. Other inventions include automated ma-

chines for temples and theaters, surveying instruments, and military machines and weapons.

Introduction

The ancient Greek technology developed mostly in the period 300 BC to 150

AD and was in use for more than one thousand years. It had a profound im-

pact both on Western and Muslim civilization. Notable inventions include

cranes, screws, gears, organs, odometer, dial and pointer devices, wheelbar-

rows, diving bells, parchment, crossbows, torsion catapults, rutways, show-

ers, roof tiles, breakwaters, and many more. Greek engineers were pioneers

in three of the ﬁrst four means of non-human propulsion known prior to the

Industrial Age: watermills, windmills, and steam engines, although only wa-

ter power was used extensively, (Lahanas, Web). Among the Ancient Greek

Engineers, the most prominent include Archimedes, Ktesibios, Heron, and

Pappos.

Heron (or Hero) of Alexandria (in Greek H

λεξανδρε νς

), see

Figure 1, was a mathematician, physicist and engineer who lived in the Hel-

lenistic times in Alexandria, Egypt, at that time part of the Roman empire. He

was made famous for documenting the ﬁrst steam turbine, the aelolipile .He

also invented many mechanisms for temples and theaters while he advanced

or improved inventions by others, for example the hydraulis , originally in-

ρων

Evangelos Papadopoulos

Fig. 1. Heron of Alexandria (O’Connor, 1999).

vented by Ktesibius. Heron was also called Michanikos (M

ηχανικ ´

), the

Greek word for Engineer.

It is important to stress that in the Ancient World, technology was not

considered as very important for the growth of philosophy and science. The

dominant motive in philosophy was understanding or wisdom, while the con-

nection between science and technology was not as extensive as it is today.

In this context, Heron, as well as the other engineers, were on the exception

side (Lloyd, 1991).

Biographical Notes

The chronology of Heron’s works is disputed and not absolutely certain to

date. Many contradictory references on Heron exist, partly because the name

was quite common. However, historians cite that he came after Apollonius,

whom he quotes, and before Pappos, who cites him. This suggests that he

must have lived between 150 BC and 250 AD (Thomas, 2005). In 1938,

Neugebauer, based on a reference in Heron’s Dioptra book of a moon eclipse,

he found that this must have happened on March 13, 62 AD, (Neugebauer,

1938). Since the reference was made to readers who could easily remember

the eclipse, this suggests that Heron ﬂourished in the late ﬁrst century AD.

According to Lewis (2001), and assuming that Cheirobalistra , a powerful

catapult, is genuinely his, Heron should have been alive at least till 84 AD,

the year in which the Cheirobalistra , was introduced.

Because most of his writings appear as lecture notes for courses in math-

ematics, mechanics, physics and pneumatics, it is almost certain that Heron

Heron of Alexandria

taught at the Musaeum of Alexandria, an institution for literary and scientiﬁc

scholars supported by the Ptolemies, which included the famous Library of

Alexandria. Many scholars believe that not only he taught at the Musaeum,

but that in addition he served as its Director and that he developed it as the

ﬁrst Polytechnic School, or Technical Institute. He is the last recorded mem-

ber of the School, and the best known (Lewis, 2001).

According to Drachmann (1963), Heron was a man who knew his busi-

ness thoroughly, who was a skillful mathematician, astronomer, engineer and

inventor of his time. Based on the content of the book Pneumatica , a number

of researchers expressed doubts about his capabilities. However, this book

appears to be an unﬁnished collection of notes and may have been altered

through the years.

An important characteristic of Heron’s work was clarity in expressing

his ideas, something not common in ancient writings. As Drachmann (1963)

states, “a man who is always able to present his subject in such a way that is

readily understood, is a man who understands it himself, and he is certainly

not a fool or a bungler.”

Mahoney notes the following about Heron, “In the light of recent schol-

arship, he now appears as a well-educated and often ingenious applied math-

ematician, as well as a vital link in a continuous tradition of practical math-

ematics from the Babylonians, through the Arabs, to Renaissance Europe”

(Drachmann and Mahoney, 1970). Furthermore, Heath writes that, “The prac-

tical 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 education for centuries” (Heath, 1931).

In many of his works, Heron would start by reviewing past works. How-

ever, he would not always give credit to previous inventors and would tend to

dismiss easily the work of others, before presenting his own solutions.

Heron recognized the value of experimental work. The example passage,

taken from Lloyd (1973), attacks ﬁrst those (like Aristotle) who denied ab-

solutely that a void can exist, accusing them of following their faith as op-

posed to evidence:

Those then who assert generally that there is no vacuum are satisﬁed

with inventing many arguments for this and perhaps seeming plausi-

ble with their theory in the absence of sensible proof. If, however, by

Evangelos Papadopoulos

referring to the appearances and to what is accessible to sensation,

it is shown that there is a continuous vacuum, but only one produced

contrary to nature; that there is a natural vacuum, but one scattered in

tiny quantities; and that bodies ﬁll up these scattered vacua by com-

pression; then those who put forward plausible arguments on these

matters will no longer have any loop-hole.

Following this statement, Heron described an apparatus designed to show the

existence of vacuum. This is basically a metal hollow sphere with a small

hole and a thin tube of bronze attached to the hole. Heron argued that if one

blows air into the sphere, then air enters it and therefore it must be compress-

ible. This compressibility was attributed to the existence of small pockets of

vacuum. He also continued his argument by saying that one can also draw

air out of the sphere by inhaling air. Once this is done, then the sphere must

contain more vacuum than before.

Although arguments of this sort may be commonplace today, they were

not necessarily the norm two thousand years before, and therefore, this atti-

tude towards experiments is considered to be very important.

List of Main Works

The main works of Heron are published in ﬁve volumes in the Teubner Series,

(Heiberg, 1912; Schmidt, 1899). Among them, the most well-known books

related to engineering include

•

Pneumatica (Pneumatics), a treatise on the use of air, water, or steam, in

Greek.

ερ ´ ιαυτ

ιητικ ης

•

Automatopoietica (Gr.

, i.e. about making au-

tomatic devices), a description of automated machines using mechanical

or pneumatical means, most for temples, in Greek.

µατ

•

βελ

ι ω

Belopoeica (from the Greek

, meaning arrow, and

, meaning to

make), on the constructions of machines of war, in Greek.

•

Mechanics , which covers mechanisms and simple machines and has sur-

vived in Arabic, with a few fragments in Greek preserved by Pappos.

o υλκ

βαρ υς

, meaning heavy and ελκω

•

Barulkos (Gr. B

, mean-

ing to pull), that discusses methods of lifting heavy weights. Perhaps this

is the same as Mechanics .

αρ

from

Heron of Alexandria

•

Dioptra , which describes a theodolite-like instrument used in surveying

and methods to measure length, in Greek and Arabic.

•

Catoptrica (Catoptrics), on light propagation and reﬂection, and on the

use of mirrors.

•

Cheirobalistra (On Catapults), about catapults, in Greek.

Heron has also contributed to Mathematics and Geometry. Although some of

them are of disputed authorship, his works in this area include

•

Metrica , describes how to calculate surfaces and volumes of diverse ob-

jects, in Arabic.

•

Geometrica (Geometria), a collection of equations based on the ﬁrst chap-

ter of Metrica, in Greek.

•

Stereometrica (i. and ii.), examples of three-dimensional calculations

based on the second chapter of Metrica, in Greek.

•

Geodaesia , surveying analysis, in Greek.

•

Mensurae , tools which can be used to conduct measurements based on

Stereometrica and Metrica (disputed authorship), in Greek.

•

Deﬁnitiones (Deﬁnitions), containing deﬁnitions of terms for geometry, in

Greek, (disputed authorship).

Unlike other ancient works in Greek, the language in Heron’s book is quite

easy to be read by non-scholars, even today. Except the Deﬁnitiones , these

books mostly consist of methods for obtaining the areas and volumes, of plane

or solid ﬁgures. In these, Heron gave methods for computing very close ap-

proximations to the square roots of numbers, which are not complete squares

and even cubic roots of numbers, which are not complete cubes. Heron also

provided expressions for computing the areas of regular polygons of ﬁve to

twelve sides in terms of the squares of the sides that lead to important trigono-

metrical ratio approximations. In general, it is believed that these books were

based on Heron’s works, but also that they were altered by people after him.

Heron’s most important work on geometry, Metrica , was missing until it was

discovered in Constantinople in 1896 by R. Schöne. This work is the closest

to its original form.

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