(fl. ad 62),

mathematician and inventor, was known as *ho mechanikos* (‘the inventor’). The following works are associated with his name. (1) Metrica, three books, on the measurement of surfaces and bodies, and their division in a given ratio. (2) Definitions (Horoi), defining geometrical terms and concepts. (3) Geometrica, (4) Stereometrica, and (5) On Measures (Peri Metron, all works of practical mensuration. (6) Pneumatica, on the construction of devices worked by compressed air, steam and water. (7) On Automata-making (Peri automatopoiikes), mostly on the construction of *thaumata* (‘miracle-working’ devices used especially in temples). (8) Mechanica, three books (extant only in Arabic, but extensively excerpted by Pappus book 8), on how to move weights with the least effort, containing (book 1) the foundations of statics and dynamics, (book 2) the five simple machines, (book 3) the building of lifting-machines and presses. (9) Dioptra, on the construction and use of a sighting-instrument for measurement at a distance (with additions describing unrelated instruments, e.g. a hodometer). (10) Catoptrica (extant only in Latin translation), on the theory and construction of plane and curved mirrors. (11) Belopoeica, in the construction of war-catapults. Some of these, notably (3), (4) and (5), can hardly be by Heron in their present form, but all may well be based on treatises by him.

(1) Metrica, three books, on the measurement of surfaces and bodies, and their division in a given ratio. (2) Definitions (Horoi), defining geometrical terms and concepts. (3) Geometrica, (4) Stereometrica, and (5) On Measures (Peri Metron, all works of practical mensuration. (6) Pneumatica, on the construction of devices worked by compressed air, steam and water. (7) On Automata-making (Peri automatopoiikes), mostly on the construction of *thaumata* (‘miracle-working’ devices used especially in temples). (8) Mechanica, three books (extant only in Arabic, but extensively excerpted by Pappus book 8), on how to move weights with the least effort, containing (book 1) the foundations of statics and dynamics, (book 2) the five simple machines, (book 3) the building of lifting-machines and presses. (9) Dioptra, on the construction and use of a sighting-instrument for measurement at a distance (with additions describing unrelated instruments, e.g. a hodometer). (10) Catoptrica (extant only in Latin translation), on the theory and construction of plane and curved mirrors. (11) Belopoeica, in the construction of war-catapults.

Other works by Heron no longer extant include a commentary on Euclid's Elements (substantial remains in an-Nayrīzī's commentary on Euclid); Baroulkos, describing a machine for lifting huge weights by means of a combination of gear-wheels (parts are incorporated into Mechanica 1.1 and Dioptra 37); On Water-clocks (Proclus, Hypotyp. 120); and Cheiroballistra, another type of artillery weapon (fragmentarily preserved). The Geodaesia and Liber geoponicus are later compilations, largely extracts from the Geometrica and other mensurational works.

Heron, although very adept at both mathematics and applied mechanics, was probably not very original in either. But his mensurational works are of great importance as our main source for practical mathematics in Graeco-Roman antiquity. While classical ‘Euclidean’ mathematics aimed at constructing and proving theorems, ‘Heronic’ mathematics was directed towards solving practical problems, if necessary by approximation. Thus, Heron gives examples of approximations to irrational square- and cube- roots. He solves quadratic equations arithmetically, and gives the formula for the area of a triangle, Δ = √ {(s(s – a) (s – b) (s – c)}. The origins of this type of mathematics lie in Mesopotamia. In pneumatics, mechanics, and the other sciences too, though Heron often discusses theoretical matters, his purpose is utility and amusement; hence we get detailed descriptions, with figures, of devices such as siphons, a self-regulating lamp, a water-organ, pulley-systems, and a variety of mechanical toys. Although the discovery of the principles behind these, and perhaps many of the devices too, were due to Heron's predecessors, such as Ctesibius, here too he is of major importance as a source.

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