Online Encyclopedia
Search over 40,000 articles from the original, classic Encyclopedia Britannica, 11th Edition.
HERO OF ALEXANDRIA
Online EncyclopediaEncyclopedia Home :: HEG-HIG
del.icio.us it!
|
See also:HERO OF See also:ALEXANDRIA , See also:Greek geometer and writer on See also:mechanical and See also:physical subjects, probably flourished in the second See also:half of the 1st See also: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: 55, (3) an allusion by See also:Plutarch (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 See also: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 See also:close approximations to the square roots of See also: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:land-See also:surveying, so called from the See also: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's See also:fountain," " See also:penny-in-theslot " See also:machines, a See also:fire-See also:engine, a water-organ, and arrangements employing the force of See also: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 See also: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 See also:war) is extant in Greek, and both this and the Mechanics contain Hero's See also: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 See also: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:Admiral 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 See also: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 See also:critical researches on Hero were G. B. Venturi's Commentari sopra la storia e la teoria dell'ottica (See also: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 See also: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 See also: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 See also:Journal asiatique (ix. serie, ii., 1893). In 1899 began the publication in Teubner's See also: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 See also:Hermann Schone) contains the Meirica (in three books) and the Dioptra. A See also: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 See also:arithmetic by See also: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 See also:fur Math. and Physik, xxxix., 1894 Bulletin des sciences math., ii. serie, xviii., 1894). A See also:good See also: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. Additional information and CommentsThere are no comments yet for this article.
» Add information or comments to this article.
Please link directly to this article:
Highlight the code below, right click, and select "copy." Then paste it into your website, email, or other HTML. Site content, images, and layout Copyright © 2006 - Net Industries, worldwide. |
|
|
[back] HERO AND LEANDER |
[next] HERO, THE YOUNGER |