Hero of Alexandria

Heron of Alexandria

Ἥρων

Depiction in the Codex of Saint Gregory Nazianzus, Greek manuscript, 9th cent.

Born|

Alexandria, then part of Roman Egypt

Known for|

* Aeolipile
* Heron's fountain
* Heron's formula
* Heron's method
* Vending machine
* Hero's principle

Scientific career
Fields|

* Mathematics
* Physics
* Pneumatic and hydraulic engineering

Hero of Alexandria (/ˈhɪəroʊ/; Ancient Greek: Ἥρων[lower-alpha 1] 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 and a representative of the Hellenistic scientific tradition.[1][2]

Hero published a well-recognized description of a steam-powered device called an aeolipile, also known as "Hero's 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 in manuscripts from the Byzantine Empire and, to a lesser extent, in Latin or Arabic translations.

## Contents

* 1 Life and career
* 1.1 Inventions
* 1.2 Mathematics
* 2 Bibliography
* 3 See also
* 4 Notes
* 5 References
* 6 Further reading
* 7 External links

## Life and career

Almost nothing is known about Hero's life, including his birthplace and background. The first extant mention of him is references to his works found in Book VIII of Pappus's Collection (4th century AD), and scholarly estimates for Hero's dates range from 150 BC to 250 AD.[7] Otto Neugebauer (1938) noted a lunar eclipse observed in Alexandria and Rome used as a hypothetical example in Hero's Dioptra, and found that it best matched the details of an eclipse in 62 AD; A. G. Drachmann subsequently surmised that Hero personally observed the eclipse from Alexandria.[8] 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.[9]

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 around the Mouseion (which included the Library of Alexandria), spoke and wrote in Greek; however, there was considerable intermarriage between the city's Greek and Egyptian populations.[10] It has been inferred that Hero taught at the Mouseion because some of his writings appear to be lecture notes or textbooks in mathematics, mechanics, physics and pneumatics.[11] 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]

### Inventions

Hero's aeolipile

A number of devices and inventions have been ascribed to Hero, including the following:

* 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, presumably earlier than Hero).[13] 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]
* A vending machine that dispensed a set amount of water for ablutions when a coin was introduced via a slot on the top of the machine. This was included in his list of inventions in his book Mechanics. 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 documented instance of wind powering a machine.[3][4]
* Many mechanisms for the Greek theatre, including an entirely mechanical play almost ten minutes in length, powered by a 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.
* A force pump that 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]
* 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]
* A kind of thermometer has been credited to Hero. Although the thermometer was not a single invention 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]

### Mathematics

Hero described an iterative algorithm for computing square roots, now called Heron's method, in his work Metrica, alongside other algorithms and approximations.[21] Today, however, his name is most closely associated with Heron's formula for the area of a triangle in terms of its side lengths. Hero also reported on a method for calculating cube roots.[22] In solid geometry, the Heronian mean may be used in finding the volume of a frustum of a pyramid or cone.

Hero also described a shortest path algorithm, that is, given two points A and B on one side of a line, find a point C on the straight line that minimizes AC + BC. This led him to formulate 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 (Hero's principle). In the Middle Ages, Ibn al-Haytham 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.[23]

## Bibliography

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[24]
* 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.)[25]
* Belopoeica, a description of war machines[26]
* Dioptra, a collection of methods to measure lengths, where the odometer and the dioptra (an apparatus resembling the theodolite) are described
* Metrica, a work describing how to calculate surface areas and volumes of diverse geometrical objects

Works that have been preserved only in Arabic translations:

* Mechanica, written for architects, containing means to lift heavy objects
* Catoptrica, 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:[11]

* Geometrica, a collection of problems similar to the first chapter of Metrica[27]
* Stereometrica, examples of three-dimensional calculations similar to the second chapter of Metrica[27]
* Mensurae, tools which can be used to conduct measurements for problems based on Stereometrica and Metrica
* Cheiroballistra, about catapults
* Definitiones, containing definitions of terms for geometry

Works that are preserved only in fragments:

* Geodesia
* Geoponica
* A commentary to Euclid's Elements, attested by Arabic authors but no longer extant

## See also

* Abdaraxus, an ancient Alexandrian engineer[28]
* Heronian triangle

## Notes

1. ↑ The genitive in Ancient Greek: Ἥρωνος

## References

1. ↑ Abbott, David, ed (1986). "Hero of Alexandria". The Biographical Dictionary of Scientists. New York: Peter Bedrick Books. p. 81. https://archive.org/details/biographicaldict00abbo_0/page/81/mode/1up?q="greatest+experimentalist". "Hero of Alexandria lived c. AD 60, variously described as an Egyptian scientist and a Greek engineer, was the greatest experimentalist of antiquity."
2. ↑ Boas, Marie (1949). "Hero's Pneumatica: A Study of Its Transmission and Influence". Isis 40 (1): 38 and supra.
3. ↑ 3.0 3.1 Drachmann, A. G. (1961). "Heron's Windmill". Centaurus 7: 145–151.
4. ↑ 4.0 4.1 Lohrmann, Dietrich (1995). "Von der östlichen zur westlichen Windmühle". Archiv für Kulturgeschichte 77 (1): 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. https://books.google.com/books?id=UmBnVMA5ri4C.
6. ↑ Tybjerg, Karin (December 2004). "Hero of Alexandria's Mechanical Geometry" (in en). Apeiron 37 (4): 29–56. doi:10.1515/APEIRON.2004.37.4.29. ISSN 2156-7093. https://www.degruyter.com/document/doi/10.1515/APEIRON.2004.37.4.29/html.
7. ↑ Heath, Thomas (1921). "XVIII: Mensuration: Heron of Alexandria". A History of Greek Mathematics. 2. Oxford University Press. "Controversies as to Heron's Date", Template:Pgs. https://archive.org/details/historyofgreekm02heat/page/298/.
8. ↑ 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" (in de). Kgl. Danske Videnskabernes Selskab, Historisk-Filologiske Meddelelser 26 (2).

Drachmann, A. G. (1950). "Heron and Ptolemaios". Centaurus 1: 117–131.
9. ↑ 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". Centaurus 53: 55–61. doi:10.1111/j.1600-0498.2010.00203.x. http://individual.utoronto.ca/acephalous/Sidoli_2011.pdf.

Masià, Ramon (2015). "On dating Hero of Alexandria". Archive for History of Exact Sciences 69 (3): 231–255.
10. ↑ 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."
11. ↑ 11.0 11.1 O'Connor, John J.; Robertson, Edmund F., "Heron of Alexandria", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Heron.html .
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. https://archive.org/details/outofcontrolnewb00kell.
13. ↑ "Pneumatika, Book ΙΙ, Chapter XI" (in el, de). Herons von Alexandria Druckwerke und Automatentheater. Wilhelm Schmidt (translator). Leipzig: B.G. Teubner. 1899. pp. 228–232. https://archive.org/stream/heronsvonalexandhero#page/228/mode/2up.
14. ↑ Hero of Alexandria (1851). "Temple Doors opened by Fire on an Altar". Pneumatics of Hero of Alexandria. London: Taylor Walton and Maberly (online edition from University of Rochester, Rochester, NY). http://www.history.rochester.edu/steam/hero/section37.html.
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 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.; Oleson, John P.; Sherwood, Andrew N. (1998). Greek and Roman technology: A Sourcebook. London: 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. http://www.history.rochester.edu/steam/hero/section57.html. Retrieved January 27, 2010. "No. 57. Description of a Syringe"
18. ↑ Sharkey, Noel (7 July 2007). "The programmable robot of ancient Greece". New Scientist (2611). https://www.newscientist.com/article/mg19526111-600-the-programmable-robot-of-ancient-greece/.

Crystall, Ben (July 4, 2007). "A programmable robot from AD 60: Noel Sharkey traces the technology way back to ancient Alexandria". https://www.newscientist.com/blog/technology/2007/07/programmable-robot-from-60ad.html. (Video also available from YouTube)
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". https://engines.egr.uh.edu/episode/1038.
21. ↑ Heath, Thomas (1921). A History of Greek Mathematics. 2. Oxford: Clarendon Press. {{pgs|323–324}}. https://archive.org/details/ahistorygreekma00heatgoog.
22. ↑ Smyly, J. Gilbart (1920). "Heron's Formula for Cube Root". Hermathena 19 (42): 64–67.
23. ↑ A.I. Sabra, 1981, Theories of Light: From Descartes to Newton (London: Oldbourne Book Co., 1967), pp. 137–139 reprinted Cambridge University Press, 1981, ISBN 0-521-28436-8.
24. ↑ McKinnon, Jamies W. (2001). "Hero of Alexandria and Hydraulis". in Root, Deane L.. The New Grove Dictionary of Music and Musicians. Oxford University Press.
25. ↑ 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.
26. ↑ (in la) Liber de machinis bellicis. Venice: Francesco De Franceschi (senese). 1572. https://gutenberg.beic.it/webclient/DeliveryManager?pid=117154.
27. ↑ 27.0 27.1 Høyrup, Jens (1997). "Hero, Ps-Hero, and Near Eastern practical geometry". Antike Naturwissenscha und ihre Rezeption 7: 67–93. http://akira.ruc.dk/~jensh/Publications/1996{f}_Hero.pdf.
28. ↑ Russo, Lucio (2004). The Forgotten Revolution: How Science Was Born in 300 BC and Why it Had to Be Reborn. Berlin: Springer. ISBN 978-3-642-18904-3.

## Further reading

* Drachmann, A. G. (1963). The Mechanical Technology of Greek and Roman Antiquity: A Study of the Literary Sources. Madison: University of Wisconsin Press. ISBN 0598742557. https://books.google.com/books?id=8jQzwAEACAAJ.
* Drachmann, A. G. (1972). Gillispie, Charles Coulston. ed. Dictionary of Scientific Biography. 6 (Hachette–Hyrtl). New York: Charles Scribner's Sons. pp. 310–314. https://archive.org/details/dictionaryofscie6gill/page/310/mode/1up?q="Hero+(or+Heron)".
* Landels, J. G. (2000). Engineering in the ancient world (2nd ed.). Berkeley: University of California Press. ISBN 0-520-22782-4. https://archive.org/details/isbn_9780520227828.
* Mahoney, Michael S. (1972). Gillispie, Charles Coulston. ed. Dictionary of Scientific Biography. 6 (Hachette–Hyrtl). New York: Charles Scribner's Sons. pp. 314–315. https://archive.org/details/dictionaryofscie6gill/page/314/mode/1up?q="Hero+of+Alexandria:+Mathematics".
* Marsden, E.W. (1969). Greek and Roman Artillery: Technical Treatises. Oxford: Clarendon Press.
* 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. ISBN 9781316516232.
* Schellenberg, Hans Michael (2008). "Anmerkungen zu Heron von Alexandria und seinem Werk ueber den Geschuetzbau". A Roman Miscellany: Essays in Honour of Anthony R. Birley on His Seventieth Birthday. Foundation for the Development of Gdańsk University. ISBN 978-8375311464. https://books.google.com/books?id=DBQMAQAAMAAJ.

## External links

| Wikisource has the text of the 1911 Encyclopædia Britannica article Hero of Alexandria.

|

* Heron of Alexandria in online Encyclopædia Britannica
* Works by Hero of Alexandria at Project Gutenberg
* Online Galleries, History of Science Collections, University of Oklahoma Libraries High resolution images preserved at The Internet Archive
* "Hero of Alexandria". New International Encyclopedia. 1905.
* Webpage about Hero by The Technology Museum of Thessaloniki[Usurped!]
* Reconstruction of Heron's Formulae for Calculating the Volume of Vessels
* Spiritali di Herone Alessandrino From the John Davis Batchelder Collection at the Library of Congress
* Automata Critical edition, with translation and partial commentary by Francesco Grillo (PhD thesis, Univ. of Glasgow, 2019)
* The Pneumatics of Hero of Alexandria, from the Original Greek. Tr. and ed. by Bennet Woodcroft From the Collections at the Library of Congress
* Scans of Wilhelm Schmidt's Teubner edition of Hero at wilbourhall.org
* Also includes a scan of a 1905 dissertation on Hero by Rudolph Meier

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Ancient Greek mathematics

Mathematicians
(timeline)|

* Anaxagoras
* Anthemius
* Archytas
* Aristaeus the Elder
* Aristarchus
* Apollonius
* Archimedes
* Autolycus
* Bion
* Bryson
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* Dionysodorus
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* Eratosthenes
* Eudemus
* Euclid
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* Eutocius
* Geminus
* Heron
* Hipparchus
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* Isidore of Miletus
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* Sosigenes
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* Theodorus
* Theodosius
* Theon of Alexandria
* Theon of Smyrna
* Thymaridas
* Xenocrates
* Zeno of Elea
* Zeno of Sidon
* Zenodorus

Treatises|

* Almagest
* Archimedes Palimpsest
* Arithmetica
* Conics (Apollonius)
* Elements (Euclid)
* On the Sizes and Distances (Aristarchus)
* On Sizes and Distances (Hipparchus)
* On the Moving Sphere (Autolycus)
* The Sand Reckoner

Problems|

* Problem of Apollonius
* Squaring the circle
* Doubling the cube
* Angle trisection

Centers|

* Cyrene
* Library of Alexandria
* Platonic Academy

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