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Hero of Alexandria

Hero of Alexandria (/ˈhɪər/; Greek: Ἥρων[1] ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also known as Heron of Alexandria /ˈhɛrən/; fl. 60 AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era. He has been described as the greatest experimentalist of antiquity[2] and his work is representative of the Hellenistic scientific tradition.[3]

Heron of Alexandria

Mathematics
Physics
Pneumatic and hydraulic engineering

Hero published a well-recognized description of a steam-powered device called an aeolipile (sometimes called a "Hero engine"). Among his most famous inventions was a windwheel, constituting the earliest instance of wind harnessing on land.[4][5] He is said to have been a follower of the atomists. In his work Mechanics, he described pantographs.[6] Some of his ideas were derived from the works of Ctesibius.


In mathematics he is mostly remembered for Heron's formula, a way to calculate the area of a triangle using only the lengths of its sides.


Much of Hero's original writings and designs have been lost, but some of his works were preserved including in manuscripts from the Eastern Roman Empire and to a lesser extent, in Latin or Arabic translations.

Life and career

Almost nothing is known about Hero's life, including his ethnicity, parents' names or occupations, birthplace, or dates. The first mention of him in extant secondary sources is a quotation of Mechanics by Pappus's Collection (4th century AD), and scholarly estimates for Hero's dates range from 150 BC to 250 AD. Otto Neugebauer noted a lunar eclipse observed in Alexandria and Rome used as a hypothetical example in Hero's Dioptra, found that it best matched the details of an eclipse in 62 AD, and surmised that Hero personally observed the eclipse from Alexandria; however, Hero does not explicitly say this, his brief mention of the eclipse is vague, and he might instead have used some earlier observer's data or even made up the example.[7]


Alexandria was founded by Alexander the Great in the 4th century BC, and by Hero's time was a cosmopolitan city, part of the Roman Empire. The intellectual community, centered on the institution of the Musaeum (which included the Library of Alexandria), spoke and wrote in Greek; however, there was significant intermarriage between the city's Greek and Egyptian populations.[8] It is assumed that Hero taught at the Musaeum, because his writings seem like course notes or textbooks in mathematics, mechanics, physics and pneumatics.

The first was also one of his constructions; when a coin was introduced via a slot on the top of the machine, it dispensed a set amount of water for ablutions. This was included in his list of inventions in his book Mechanics and Optics. When the coin was deposited, it fell upon a pan attached to a lever. The lever opened up a valve which let some water flow out. The pan continued to tilt with the weight of the coin until it fell off, at which point a counter-weight would snap the lever back up and turn off the valve.[12]

vending machine

A wind-wheel operating an organ, marking the first instance in history of wind powering a machine.[5]

[4]

Hero also invented many mechanisms for the Greek , including an entirely mechanical play almost ten minutes in length, powered by a binary-like system of ropes, knots, and simple machines operated by a rotating cylindrical cogwheel. The sound of thunder was produced by the mechanically-timed dropping of metal balls onto a hidden drum.

theatre

The was widely used in the Roman world, and one application was in a fire engine.

force pump

A -like device was described by Hero to control the delivery of air or liquids.[13]

syringe

In optics, Hero formulated the : If a ray of light propagates from point A to point B within the same medium, the path-length followed is the shortest possible. It was nearly 1,000 years later that Alhacen expanded the principle to both reflection and refraction, and the principle was later stated in this form by Pierre de Fermat in 1662; the most modern form is that the optical path is stationary.

principle of the shortest path of light

A stand-alone fountain that operates under self-contained hydro-static energy; now called .

Heron's fountain

A cart that was powered by a falling weight and strings wrapped around the drive axle.

[14]

Various authors have credited the invention of the to Hero. The thermometer was not a single invention, however, but a development. Hero knew of the principle that certain substances, notably air, expand and contract and described a demonstration in which a closed tube partially filled with air had its end in a container of water.[15] The expansion and contraction of the air caused the position of the water/air interface to move along the tube.

thermometer

A self-filling wine bowl, using a .[16]

float valve

Hero described[9] the construction of the aeolipile (a version of which is known as Hero's engine) which was a rocket-like reaction engine and the first-recorded steam engine (although Vitruvius mentioned the aeolipile in De Architectura some 100 years earlier than Hero). It was described almost two millennia before the industrial revolution. Another engine used air from a closed chamber heated by an altar fire to displace water from a sealed vessel; the water was collected and its weight, pulling on a rope, opened temple doors.[10] Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work, which is not entirely false, air containing a trace of water vapor. However, this engine is far from a pure aeolipile.[11]

Mathematics

Hero described a method, now known as Heron's method, for iteratively computing the square root of a number.[17] Today, however, his name is most closely associated with Heron's formula for finding the area of a triangle from its side lengths. He also devised a method for calculating cube roots.[18] He also designed a shortest path algorithm, that is, given two points A and B on one side of a line, find C a point on the straight line that minimizes AC+BC.


In solid geometry, the Heronian mean may be used in finding the volume of a frustum of a pyramid or cone.

Pneumatica (Πνευματικά), a description of machines working on , steam or water pressure, including the hydraulis or water organ[19]

air

Automata, a description of machines which enable wonders in banquets and possibly also theatrical contexts by mechanical or pneumatical means (e.g. automatic opening or closing of temple doors, statues that pour wine and milk, etc.)

[20]

Mechanica, preserved only in Arabic, written for , containing means to lift heavy objects

architects

Metrica, a description of how to calculate and volumes of diverse objects

surfaces

On the Dioptra, a collection of methods to measure lengths, a work in which the and the dioptra, an apparatus which resembles the theodolite, are described

odometer

Belopoeica, a description of

war machines

Catoptrica, about the progression of , reflection and the use of mirrors

light

The most comprehensive edition of Hero's works was published in five volumes in Leipzig by the publishing house Teubner in 1903.


Works known to have been written by Hero include:


Works that sometimes have been attributed to Hero, but are now thought most likely to have been written by someone else:[21]


Works that are preserved only in fragments:

(in Latin). Venezia: Francesco De Franceschi (senese). 1572.

Liber de machinis bellicis

an ancient Alexandrian engineer[22]

Abdaraxus

Heronian triangle

Drachmann, Aage Gerhardt (1963). . Madison, WI: University of Wisconsin Press. ISBN 0598742557.

The Mechanical Technology of Greek and Roman Antiquity: A Study of the Literary Sources

Drachmann, Aage G. (1972). . In Gillispie, Charles Coulston (ed.). Dictionary of Scientific Biography. Vol. 6 (Hachette–Hyrtl). New York: Charles Scribner's Sons. pp. 310–314. LCCN 69-18090.

"Hero of Alexandria"

Landels, J.G. (2000). (2nd ed.). Berkeley: University of California Press. ISBN 0-520-22782-4.

Engineering in the ancient world

Mahoney, Michael S. (1972). . In Gillispie, Charles Coulston (ed.). Dictionary of Scientific Biography. Vol. 6 (Hachette–Hyrtl). New York: Charles Scribner's Sons. pp. 314–315. LCCN 69-18090.

"Hero of Alexandria: Mathematics"

Marsden, E.W. (1969). . Oxford: Clarendon Press.

Greek and Roman Artillery: Technical Treatises

Roby, Courtney Ann (2023). The mechanical tradition of Hero of Alexandria: strategies of reading from antiquity to the early modern period. Cambridge; New York: Cambridge University Press.  9781316516232.

ISBN

Schellenberg, Hans Michael (2008). Birley, Anthony Richard; Hirschmann, Vera-Elisabeth; Krieckhaus, Andreas; Schellenberg, Hans Michael (eds.). . Foundation for the Development of Gdańsk University. ISBN 978-8375311464.

A Roman Miscellany: Essays in Honour of Anthony R. Birley on His Seventieth Birthday

Webpage about Hero by The Technology Museum of Thessaloniki

(1911). "Hero of Alexandria" . Encyclopædia Britannica. Vol. 13 (11th ed.). pp. 378–379.

Heath, Thomas Little

in online Encyclopædia Britannica

Heron of Alexandria

High resolution images preserved at The Internet Archive

Online Galleries, History of Science Collections, University of Oklahoma Libraries

. New International Encyclopedia. 1905.

"Hero of Alexandria" 

Reconstruction of Heron’s Formulas for Calculating the Volume of Vessels

From the John Davis Batchelder Collection at the Library of Congress

Spiritali di Herone Alessandrino

Critical edition, with translation and partial commentary by Francesco Grillo (PhD thesis, Univ. of Glasgow, 2019)

Automata

From the Collections at the Library of Congress

The Pneumatics of Hero of Alexandria, from the Original Greek. Tr. and ed. by Bennet Woodcroft

Scans of Wilhelm Schmidt's Teubner edition of Hero

scan of a 1905 dissertation on Hero by Rudolph Meier