See also:mechanical and
See also:physical subjects, probably flourished in the second
See also:half of the 1st century . This is the more
See also:modern view, in contrast to the earlier theory most generally accepted, according to which he flourished about Too B.C . The earlier theory started from the superscription of one of his
See also:works, "Hpcovos KTrlvc(3iov (3eXosroiisa, from which it was inferred that Hero was a
See also:pupil of Ctesibius .
See also:Martin, Hultsch and Cantor took this Ctesibius to be a
See also:barber of that name who lived in the reign of
See also:Ptolemy Euergetes II . (d . 117 B.C.) and is credited with having invented an improved
See also:organ . But this
See also:identification is far from certain, as a Ctesibius mechanicus is mentioned by
See also:Athenaeus as having lived under Ptolemy II . Philadelphus (285-247 B.C.) . Nor can the relation of
See also:master and pupil be certainly inferred from the superscription quoted (observe the omission of any article), which really asserts no more than that Hero re-edited an earlier
See also:treatise by Ctesibius, and implies nothing about his being an immediate predecessor . Further, it is certain that Hero used physical and mathematical writings by
See also:Posidonius, the Stoic, of
See also:Cicero's teacher, who lived until about the
See also:middle of the 1st century B.C . The
See also:positive arguments for the more modern view of Hero's date are (I) the use by him of Latinisms from which Diels concluded that the 1st century A.D. was the earliest possible date, (2) the description in Hero's
See also:Mechanics iii. of a small
See also:press with one
See also:screw which is alluded to by Pliny (Nat . Hist. viii.) as having been introduced since A.D .
55, (3) an allusion byPlutarch (who died A.D . 120) to the proposition that
See also:light is reflected from a
See also:surface at an
See also:angle equal to the angle of incidence, which Hero proved in his Catoptrica, the words used by Plutarch fitting well with the corresponding passage of that
See also:work (as to which see below) . Thus we arrive at the latter half of the 1st century A.D. as the approximate date of Hero's activity . The geometrical
See also:treatises which have survived (though not interpolated) in Greek are entitled respectively Definitiones, Geometric, Geodaesia, Stereometrica (i. and ii.), Mensurae,
See also:Liber Geoponicus, to which must now be added the Metrica recently discovered by R . Sch8ne in a MS. at Constantinople . These books, except the Definitiones, mostly consist of directions for obtaining, from given parts, the areas or volumes, and other parts, of
See also:plane or solid figures . A remarkable feature is the
See also:bare statement of a number of very close approximations to the square roots of numbers which are not
See also:complete squares . Others occur in the Metrica where also a method of finding such approximate square, and even approximate
See also:cube, roots is shown . Hero's expressions for the areas of
See also:regular polygons of from 5 to 12 sides in terms of the squares of the sides show interesting approximations to the values of trigonometrical ratios . Akin to the geometrical works is that On the Dioptra, a remarkable
See also:book on
See also:surveying, so called from the instrument described in it, which was used for the same purposes as the modern
See also:theodolite . It is in this book that Hero proves the expression for the
See also:area of a triangle in terms of its sides . The Pneumatica in two books is also extant 'fn-Greek as is also the Automatopoietica .
In the former will be found such things as siphons, " Hero'sfountain," "
See also:penny-in-theslot "
See also:machines, a
See also:fire-engine, a water-organ, and arrangements employing the force of steam . Pappus quotes from three books of Mechanics and from a work called Barulcus, both by Hero . The three books on Mechanics survive in an Arabic
See also:translation which, however, bears a title "On the lifting of heavy
See also:objects." This corresponds exactly to Barulcus, and it is probable that Barulcus and Mechanics were only alternative titles for one and the same work . It is indeed not credible that Hero wrote two
See also:separate treatises on the subject of the mechanical
See also:powers, which are fully discussed in the Mechanics, ii., iii . The Belopoiica (on engines of war) is extant in Greek, and both this and the Mechanics contain Hero's solution of the problem of the two mean proportionals . Hero also wrote Catoplrica (on reflecting surfaces), and it seems certain that we possess this in a Latin work, probably translated from the Greek by Wilhelm
See also:van Moerbeek, which was long thought to be a fragment of Ptolemy's
See also:Optics, because it
See also:bore the title Ptolemaei de speculis in the MS . But the attribution to Ptolemy was shown to be wrong as soon as it was made clear (especially by Martin) that another translation by an
See also:Eugenius Siculus (I2th century) of an
See also:optical work from the Arabic was Ptolemy's Optics . Of other treatises by Hero only fragments remain . One was four books on Water Clocks (llepi bbpiwv ,povxoird ou), of which
See also:Proclus (Hypotyp. astron., ed .
See also:Halma) has preserved a fragment, and to which Pappus also refers . Another work was a commentary on Euclid (referred to by the
See also:Arabs as " the book of the
See also:resolution of doubts in Euclid ") from which quotations have survived in an-Nairizi's commentary . The Pneumatica, Automatopoietica, Belopoiica and Cheiroballistra of Hero were published in Greek and Latin in Thevenot's Veterum mathematicorum
See also:opera graece et latine pleraque nunc primum edita (
See also:Paris, 1693) ; the first important critical researches on Hero were G .
B . Venturi's Commentari sopra la storia e la teoria dell'ottica (Bologna, 1814) and H . Martin's " Recherches sur la
See also:vie et
See also:les ouvrages d'
See also:Heron d'Alexandrie
See also:disciple de Ctesibius et sur tous les ouvrages mathematiques grecs conserves ou perdus,publies ou inedits, 9ui ont ete attribues a un auteur nomme Heron " (Mein. presentee a t Academie
See also:des Inscriptions et Belles-Lettres, i. serie, iv., 1854) . The geometrical works (except of course the Metrica) were edited (Greek only) by F . Hultsch (Heronis Alexandrini geometricorum et stereometricorum reliquiae, 1864), the Dioptra by Vincent (Extraits des manuscrits relatifs a la geometrie pratique des Grecs, Notices et extraits des manuscrits de la Bibliothr'que Imperiale, xix . 2, 1858), the treatises on Engines of War by C . Wescher (Poliorcetique des Grecs, Paris, 1867) . The Mechanics was first published by Carra de
See also:Vaux in the Journal asiatique (ix. serie, ii., 1893) . In 1899 began the publication in Teubner's series of Heronis Alexandrini opera quae supersunt omnia . Vol. i. and Supplement (by W .
See also:Schmidt) contains the Pneumatica and Automata, the fragment on Water Clocks, the De ingeniis spiritualibus of
See also:Philon of
See also:Byzantium and extracts on
See also:Pneumatics by
See also:Vitruvius . Vol. ii. pt. i., by L .
Nix and W . Schmidt, contains the Mechanics in Arabic, Greek fragments of the same, the Catoplrica in Latin with appendices of extracts from
See also:Olympiodorus, Vitruvius, Pliny, &c . Vol. iii . (by Hermann Schone) contains the Meirica (in three books) and the Dioptra . A German translation is added throughout . The approximation to square roots in Hero has been the subject of papers too numerous to mention . But reference should be made to the exhaustive studies on Hero's arithmetic by Paul Tannery, " L'Arithmetique des Grecs dans Heron d'Alexandrie " (Mem. de la
See also:Soc. des sciences phys. et math. de
See also:Bordeaux, ii. serie, iv., 1882), " La Stereometrie d'Heron d'Alexandrie " and " Etudes Heroniennes (ibid. v., 1883), " Questions Heroniennes " (Bulletin des sciences math., ii. serie, viii., 1884), " Un Fragment des Metriques d'Heron " (Zeitschrift fur Math. and Physik, xxxix., 1894 Bulletin des sciences math., ii. serie, xviii., 1894) . A
See also:good account of Hero's works will be found in M . Cantor's eschichte der Mathematik, i.$ (1894), chapters 18 and 19, and in G . Loria's studies, Le Scienze esatte nell' antica Grecia, especially libro iii . (
See also:Modena, 1900), pp . 103-128 .
(T . L .
HERO AND LEANDER
THE YOUNGER HERO
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