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Hero of Alexandria

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Heron of Alexandria
17th-century German depiction of Heron
CitizenshipAlexandria, Roman Egypt
Known for
Scientific career
  • Mathematics
  • Physics
  • Pneumatic and hydraulic engineering

Hero of Alexandria (/ˈhɪər/; Greek: Ἥρων[a] ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also known as Heron of Alexandria /ˈhɛrən/; probably 1st or 2nd century 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[1] and his work is representative of the Hellenistic scientific tradition.[2]

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.[3][4] In his work Mechanics, he described pantographs.[5] Some of his ideas were derived from the works of Ctesibius.

In mathematics, he wrote a commentary on Euclid's Elements and a work on applied geometry known as the Metrica. He is mostly remembered for Heron's formula, a way to calculate the area of a triangle using only the lengths of its sides.[6]

Much of Hero's original writings and designs have been lost, but some of his works were preserved including in manuscripts from the Byzantine 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 – which may have been[1][7] Greek or Hellenized Egyptian – 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.[8] Otto Neugebauer (1938) 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 Aage Drachmann [de] surmised that Hero personally observed the eclipse from Alexandria;[9] 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.[10]

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.[11] It is assumed that Hero taught at the Musaeum because his writings appear to be lecture notes for courses or textbooks in mathematics, mechanics, physics and pneumatics. Although the field was not formalized until the twentieth century, it is thought that works of Hero, in particular those on his automated devices, represented some of the first formal research into cybernetics.[12]


Hero's aeolipile

Hero described[13] 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.[14] Some historians have conflated the two inventions to assert that the aeolipile was capable of useful work.[15]

Hero's wind-powered organ (reconstruction)
  • The first vending machine 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.[16]
  • A wind-wheel operating an organ, marking the first instance in history of wind powering a machine.[3][4]
  • Hero also invented many mechanisms for the Greek theatre, 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.
  • The force pump was widely used in the Roman world, and one application was in a fire engine.
  • A syringe-like device was described by Hero to control the delivery of air or liquids.[17]
  • In optics, Hero formulated the principle of the shortest path of light: 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.
  • 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.[18]
  • Various authors have credited the invention of the thermometer 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.[19] The expansion and contraction of the air caused the position of the water/air interface to move along the tube.
  • A self-filling wine bowl, using a float valve.[20]



Hero described a method, now known as Heron's method, for iteratively computing the square root of a number.[21] 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.[22] 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.


The book About automata by Hero of Alexandria (1589 edition)

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:

  • Pneumatica (Πνευματικά), a description of machines working on air, steam or water pressure, including the hydraulis or water organ[23]
  • 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.)[24]
  • Belopoeica, a description of war machines
  • Dioptra, a collection of methods to measure lengths, a work in which the odometer and the dioptra, an apparatus which resembles the theodolite, are described
  • Metrica, a description of how to calculate surfaces and volumes of diverse objects
  • Mechanica, preserved only in Arabic, written for architects, containing means to lift heavy objects
  • Catoptrica, preserved only in Arabic, about the progression of light, reflection and the use of mirrors

Works that sometimes have been attributed to Hero, but are now thought most likely to have been written by someone else:[25]

  • Geometrica, a collection of equations based on the first chapter of Metrica
  • Stereometrica, examples of three-dimensional calculations based on the second chapter of Metrica
  • Mensurae, tools which can be used to conduct measurements based on Stereometrica and Metrica
  • Cheiroballistra, about catapults
  • Definitiones, containing definitions of terms for geometry

Works that are preserved only in fragments:

  • Geodesia
  • Geoponica


  • Liber de machinis bellicis (in Latin). Venezia: Francesco De Franceschi (senese). 1572.

See also



  1. ^ The genitive in Greek: Ἥρωνος


  1. ^ a b Abbott, David, ed. (1986) [1985]. "Hero of Alexandria". The Biographical Dictionary of Scientists. New York: Peter Bedrick Books. p. 81. Hero of Alexandria lived c. AD 60, variously described as an Egyptian scientist and a Greek engineer, was the greatest experimentalist of antiquity.
  2. ^ Marie Boas (February 1949). "Hero's Pneumatica: A Study of Its Transmission and Influence", Isis, Vol. 40, No. 1, p. 38 and supra
  3. ^ a b A.G. Drachmann (1961). "Heron's Windmill", Centaurus, 7, pp. 145–151
  4. ^ a b Dietrich Lohrmann (1995). "Von der östlichen zur westlichen Windmühle", Archiv für Kulturgeschichte, Vol. 77, Issue 1, pp. 1–30 (10f.)
  5. ^ Ceccarelli, Marco (2007). Distinguished Figures in Mechanism and Machine Science: Their Contributions and Legacies. Springer. p. 230. ISBN 978-1-4020-6366-4.
  6. ^ Karin Tybjerg (2004-12-01). "Hero of Alexandria's Mechanical Geometry". Apeiron. 37 (4): 29–56. doi:10.1515/APEIRON.2004.37.4.29. ISSN 2156-7093.
  7. ^ Sarton, George (1936). "The Unity and Diversity of the Mediterranean World". Osiris. 2: 406–463. [429].
  8. ^ Heath, Thomas (1921). "XVIII: Mensuration: Heron of Alexandria". A History of Greek Mathematics. Vol. 2. Oxford University Press. "Controversies as to Heron's Date", pp. 298–307.
  9. ^ Keyser, Paul (1988). "Suetonius 'Nero' 41. 2 and the Date of Heron Mechanicus of Alexandria". Classical Philology. 83 (3): 218–220.
    Neugebauer, Otto (1938). "Über eine Methode zur Distanzbestimmung Alexandria–Rom bei Heron" [On a method for determining the distance between Alexandria and Rome by Heron]. Kgl. Danske Videnskabernes Selskab, Historisk-Filologiske Meddelelser (in German). 26 (2).
    Drachmann, Aage Gerhardt (1950). "Heron and Ptolemaios". Centaurus. 1: 117–131.
  10. ^ Heron's text is (translation by Masià):
    "Then, let it be necessary to measure, say, the path between Alexandria and Rome along a line – or rather along a great-circle arc on the earth – if it has been agreed that the circumference of the earth is 252,000 stades – as Eratosthenes, having worked rather more accurately than others, showed in his book entitled On the Measurement of the Earth. Now, let <the> same lunar eclipse have been observed at Alexandria and Rome. If one is found in the records, we will use that, or, if not, it will be possible for us to state our own observations because lunar eclipses occur at 5 and 6 month intervals. Now let an eclipse be found <in the records> – this one, in the stated regions: in Alexandria in the 5th hour of the night, and the same one in the 3rd hour in Rome – obviously the same night. And let the night – that is, the day circle with respect to which the sun moves on the said night – be 9 (or 10) days from the vernal equinox in the direction of the winter solstice."
    Sidoli, Nathan (2011). "Heron of Alexandria's Date" (PDF). Centaurus. 53: 55–61. doi:10.1111/j.1600-0498.2010.00203.x.
    Masià, Ramon (2015). "On dating Hero of Alexandria". Archive for History of Exact Sciences. 69 (3): 231–255. JSTOR 24569551.
  11. ^ Katz, Victor J. (1998). A History of Mathematics: An Introduction. Addison Wesley. p. 184. ISBN 0-321-01618-1. But what we really want to know is to what extent the Alexandrian mathematicians of the period from the first to the fifth centuries C.E. were Greek. Certainly, all of them wrote in Greek and were part of the Greek intellectual community of Alexandria. And most modern studies conclude that the Greek community coexisted [...] So should we assume that Ptolemy and Diophantus, Pappus and Hypatia were ethnically Greek, that their ancestors had come from Greece at some point in the past but had remained effectively isolated from the Egyptians? It is, of course, impossible to answer this question definitively. But research in papyri dating from the early centuries of the common era demonstrates that a significant amount of intermarriage took place between the Greek and Egyptian communities [...] And it is known that Greek marriage contracts increasingly came to resemble Egyptian ones. In addition, even from the founding of Alexandria, small numbers of Egyptians were admitted to the privileged classes in the city to fulfill numerous civic roles. Of course, it was essential in such cases for the Egyptians to become "Hellenized", to adopt Greek habits and the Greek language. Given that the Alexandrian mathematicians mentioned here were active several hundred years after the founding of the city, it would seem at least equally possible that they were ethnically Egyptian as that they remained ethnically Greek. In any case, it is unreasonable to portray them with purely European features when no physical descriptions exist.
  12. ^ Kelly, Kevin (1994). Out of control: the new biology of machines, social systems and the economic world. Boston: Addison-Wesley. ISBN 0-201-48340-8.
  13. ^ Hero (1899). "Pneumatika, Book ΙΙ, Chapter XI". Herons von Alexandria Druckwerke und Automatentheater (in Greek and German). Wilhelm Schmidt (translator). Leipzig: B.G. Teubner. pp. 228–232.
  14. ^ Hero of Alexandria (1851). "Temple Doors opened by Fire on an Altar". Pneumatics of Hero of Alexandria. Bennet Woodcroft (trans.). London: Taylor Walton and Maberly (online edition from University of Rochester, Rochester, NY). Archived from the original on 2008-05-09. Retrieved 2008-04-23.
  15. ^ For example: Mokyr, Joel (2001). Twenty-five centuries of technological change. London: Routledge. p. 11. ISBN 0-415-26931-8. Among the devices credited to Hero are the aeolipile, a working steam engine used to open temple doors and Wood, Chris M.; McDonald, D. Gordon (1997). "History of propulsion devices and turbo machines". Global Warming. Cambridge, England: Cambridge University Press. p. 3. ISBN 0-521-49532-6. Two exhaust nozzles ... were used to direct the steam with high velocity and rotate the sphere ... By attaching ropes to the axial shaft Hero used the developed power to perform tasks such as opening temple doors
  16. ^ Humphrey, John W.; John P. Oleson; Andrew N. Sherwood (1998). Greek and Roman technology: A Sourcebook. Annotated translations of Greek and Latin texts and documents. Routledge Sourcebooks for the Ancient World. London and New York: Routledge. pp. 66–67. ISBN 978-0-415-06137-7.
  17. ^ Woodcroft, Bennet (1851). The Pneumatics of Hero of Alexandria. London: Taylor Walton and Maberly. Bibcode:1851phal.book.....W. Archived from the original on 1997-06-29. Retrieved January 27, 2010. No. 57. Description of a Syringe
  18. ^
  19. ^ T.D. McGee (1988) Principles and Methods of Temperature Measurement ISBN 0-471-62767-4
  20. ^ "Hero of Alexandria | The Engines of Our Ingenuity". engines.egr.uh.edu.
  21. ^ Heath, Thomas (1921). A History of Greek Mathematics, Vol. 2. Oxford: Clarendon Press. pp. 323–324.
  22. ^ Smyly, J. Gilbart (1920). "Heron's Formula for Cube Root". Hermathena. 19 (42). Trinity College Dublin: 64–67. JSTOR 23037103.
  23. ^ McKinnon, Jamies W. (2001). "Hero of Alexandria and Hydraulis". In Sadie, Stanley; Tyrrell, John (eds.). The New Grove Dictionary of Music and Musicians (2nd ed.). London: Macmillan Publishers. ISBN 978-1-56159-239-5.
  24. ^ On the main translations of the treatise, including Bernardino Baldi's 1589 translation into Italian, see now the discussion in Francesco Grillo (2019). Hero of Alexandria's Automata. A Critical Edition and Translation, Including a Commentary on Book One, PhD thesis, Univ. of Glasgow, pp. xxviii–xli.
  25. ^ O'Connor, J.J. & E.F. Robertson. "Heron biography". MacTutor History of Mathematics archive. Retrieved 2006-06-18.
  26. ^ Russo, Lucio (2004). The Forgotten Revolution : How Science Was Born in 300 BC and Why it Had to Be Reborn. Translated by Levy, Silvio (1 ed.). Berlin, Heidelberg: Springer Berlin Heidelberg. ISBN 978-3-642-18904-3.

Further reading