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 separate treatises on the subject of the mechanical 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 Catoptrica (on reflecting surfaces), and it seems certain that we possess this in a Latin work, probably translated from the Greek by Wilhelm van Moerbeek, which was long thought to be a fragment of Ptolemy’s Optics, because it 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 Admiral Eugenius Siculus (12th century) of an optical work from the Arabic was Ptolemy’s Optics. Of other treatises by Hero only fragments remain. One was four books on Water Clocks ( ), of which Proclus (Hypotyp. astron., ed. Halma) has preserved a fragment, and to which Pappus also refers. Another work was a commentary on Euclid (referred to by the Arabs as “the book of the resolution of doubts in Euclid”) from which quotations have survived in an-Nairīzī’s commentary.

The Pneumatica, Automatopoietica, Belopoiica and Cheiroballistra of Hero were published in Greek and Latin in Thévenot’s Veterum mathematicorum opera graece et latine pleraque nunc primum edita (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 vie et les ouvrages d’Héron d’Alexandrie disciple de Ctésibius et sur tous les ouvrages mathématiques grecs conservés ou perdus, publiés ou inédits, qui ont été attribués à un auteur nommé Héron” (Mém. presentés à l’Académie des Inscriptions et Belles-Lettres, i. série, 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 à la géométrie pratique des Grecs, Notices et extraits des manuscrits de la Bibliothèque Impériale, xix. 2, 1858), the treatises on Engines of War by C. Wescher (Poliorcétique des Grecs, Paris, 1867). The Mechanics was first published by Carra de Vaux in the Journal asiatique (ix. série, ii., 1893). In 1899 began the publication in Teubner’s series of Heronis Alexandrini opera quae supersunt omnia. Vol. i. and Supplement (by W. Schmidt) contains the Pneumatica and Automata, the fragment on Water Clocks, the De ingeniis spiritualibus of Philon of Byzantium and extracts on Pneumatics by Vitruvius. Vol. ii. pt. i., by L. Nix and W. Schmidt, contains the Mechanics in Arabic, Greek fragments of the same, the Catoptrica in Latin with appendices of extracts from Olympiodorus, Vitruvius, Pliny, &c. Vol. iii. (by Hermann Schöne) contains the Metrica (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’Arithmétique des Grecs dans Héron d’Alexandrie” (Mém. de la Soc. des sciences phys. et math. de Bordeaux, ii. série, iv., 1882), “La Stéréométrie d’Héron d’Alexandrie” and “Études Héroniennes” (ibid. v., 1883), “Questions Héroniennes” (Bulletin des sciences math., ii. série, viii., 1884), “Un Fragment des Métriques d’Héron” (Zeitschrift für Math. und Physik, xxxix., 1894; Bulletin des sciences math., ii. série, xviii., 1894). A good account of Hero’s works will be found in M. Cantor’s Geschichte der Mathematik, i.2 (1894), chapters 18 and 19, and in G. Loria’s studies, Le Scienze esatte nell’ antica Grecia, especially libro iii. (Modena, 1900), pp. 103-128.

 HERO,, the name given without any sufficient reason to a Byzantine land-surveyor who wrote (about 938) a treatise on land-surveying modelled on the works of Hero of Alexandria, especially the Dioptra.

See “Géodésie de Héron de Byzance,” published by Vincent in Notices et extraits des manuscrits de la Bibliothéque Impériale, xix. 2 (Paris, 1858), and T. H. Martin in Mémoires présentés à l’ Académie des Inscriptions, 1st series, iv. (Paris, 1854).

HEROD, the name borne by the princes of a dynasty which reigned in Judaea from 40

(surnamed ), the son of Antipater, who supported Hyrcanus II. against Aristobulus II. with the aid first of the Nabataean Arabs and then of Rome. The family seems to have been of Idumaean origin, so that its members were liable to the reproach of being half-Jews or even foreigners. Justin Martyr has a tradition that they were originally Philistines of Ascalon (Dial. c. 52), and on the other hand Nicolaus of Damascus (apud Jos. Ant. xiv. 1. 3) asserted that Herod, his royal patron, was descended from the Jews who first returned from the Babylonian Captivity. The tradition and the assertion are in all probability equally fictitious and proceed respectively from the foes and the friends of the Herodian dynasty.

Antipas (or Antipater), the father of Antipater, had been governor of Idumaea under Alexander Jannaeus. His son allied himself by marriage with the Arabian nobility and became the real ruler of Palestine under Hyrcanus II. When Rome intervened in Asia in the person of Pompey, the younger Antipater realized her inevitable predominance and secured the friendship of her representative. After the capture of Jerusalem in 63 Pompey installed Hyrcanus, who was little better than a figurehead, in the high-priesthood; and when in 55 the son of Aristobulus renewed the civil war in Palestine, the Roman governor of Syria in the exercise of his jurisdiction arranged a settlement “in accordance with the wishes of Antipater” (Jos. Ant. xiv. 6. 4). To this policy of dependence upon Rome Antipater adhered, and he succeeded in commending himself to Mark Antony and Caesar in turn. After the battle of Pharsalia Caesar made him procurator and a Roman citizen.

At this point Herod appears on the scene as ruler of Galilee (Jos. Ant. xiv. 9. 2) appointed by his father at the age of fifteen or, since he died at seventy, twenty-five. In spite of his youth he soon found an opportunity of displaying his mettle; for he arrested Hezekiah the arch-brigand, who had overrun the Syrian border, and put him to death. The Jewish nobility at Jerusalem seized upon this high-handed action as a pretext for satisfying their jealousy of their Idumaean rulers. Herod was cited in the name of Hyrcanus to appear before the Sanhedrin, whose prerogative he had usurped in executing Hezekiah. He appeared with a bodyguard, and the Sanhedrin was overawed. Only Sameas, a Pharisee, dared to insist upon the legal verdict of condemnation. But the governor of Syria had sent a demand for Herod’s acquittal, and so Hyrcanus adjourned the trial and persuaded the accused to abscond. Herod returned with an army, but his father prevailed upon him to depart to Galilee without wreaking his vengeance upon his enemies. About this time (47–46 ) he was created strategus of Coelesyria by the provincial governor. The episode is important for the light which it throws upon Herod’s relations with Rome and with the Jews.

In 44 Cassius arrived in Syria for the purpose of filling his war-chest: Antipater and Herod collected the sum of money at which the Jews of Palestine had been assessed. In 43 Antipater was poisoned at the instigation of one Malichus, who was perhaps a Jewish patriot animated by hatred of the Herods and their Roman patrons.

With the connivance of Cassius Herod had Malichus assassinated; but the country was in a state of anarchy, thanks to the extortions of Cassius and the encroachments of neighbouring powers. Antony, who became master of the East after Philippi, was ready to support the sons of his friend Antipater; but he was absent in Egypt when the Parthians invaded Palestine to restore Antigonus to the throne of his father Aristobulus (40 ). Herod escaped to Rome: the Arabians, his mother’s people, had repudiated him. Antony had made him tetrarch, and now with the assent of Octavian persuaded the Senate to declare him king of Judaea.

In 39 Herod returned to Palestine and, when the presence of Antony put the reluctant Roman troops entirely at his disposal, he was able to lay siege to Jerusalem two years later. Secure of the support of Rome he was concerned also to legitimize his position in the eyes of the Jews by taking, for love as well as policy, the Hasmonaean princess Mariamne to be his second wife. Jerusalem was taken by storm; the Roman troops withdrew to behead Antigonus the usurper at Antioch. In 37 Herod was king of Judaea, being the client of Antony and the husband of Mariamne.

The Pharisees, who dominated the bulk of the Jews, were content to accept Herod’s rule as a judgment of God. Hyrcanus returned from his prison: mutilated, he could no longer hold office as high-priest; but his mutilation probably gave him the prestige of a martyr, and his influence—whatever it was worth—seems