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Rh undertaking a further journey to Greece in 1862, Curtius was appointed (in 1863) ordinary professor at Berlin. In 1874 he was sent to Athens by the German government, and concluded an agreement by which the excavations at (q.v.) were entrusted exclusively to Germany. Curtius died at Berlin on the 11th of July 1896. His best-known work is his History of Greece (1857–1867, 6th ed. 1887–1888; Eng. trans. by A. W. Ward, 1868–1873). It presented in an attractive style what were then the latest results of scholarly research, but was criticized as wanting in erudition. It is now superseded (see : History, Ancient, § Bibliography). His other writings are chiefly archaeological. The most important are: Die Akropolis von Athen (1844); Naxos (1846); Peloponnesos, eine historisch-geographische Beschreibung der Halbinsel (1851); Olympia (1852); Die Ionier vor der ionischen Wanderung (1855); Attische Studien (1862–1865); Ephesos (1874); Die Ausgrabungen zu Olympia (1877, &c.); Olympia und Umgegend (edited by Curtius and F. Adler, 1882); Olympia; Die Ergebnisse der von dem deutschen Reich veranstalteten Ausgrabung (with F. Adler, 1890–1898); Die Stadtgeschichte von Athen (1891); Gesammelte Abhandlungen (1894). His collected speeches and lectures were published under the title of Altertum und Gegenwart (5th ed., 1903 foll.), to which a third volume was added under the title of Unter drei Kaisern (2nd ed., 1895).

A full list of his writings will be found in L. Gurlitt, Erinnerungen an Ernst Curtius (Berlin, 1902); see also article by O. Kern in Allgemeine deutsche Biographie, xlvii. (1903), to which may be added ''Ernst Curtius. Ein Lebensbild in Briefen, by F. Curtius (1903); T. Hodgkin, Ernest Curtius'' (1905).

His brother, (1820–1885), philologist, was born at Lübeck on the 16th of April 1820. After an education at Bonn and Berlin he was for three years a schoolmaster in Dresden, until (in 1845) he returned to Berlin University as privat-docent. In 1849 he was placed in charge of the Philological Seminary at Prague, and two years later was appointed professor of classical philology in Prague University. In 1854 he removed from Prague to a similar appointment at Kiel, and again in 1862 from Kiel to Leipzig. He died at Hermsdorf on the 12th of August 1885. His philological theories exercised a widespread influence. The more important of his publications are: Die Sprachvergleichung in ihrem Verhältniss zur classischen Philologie (1845; Eng. trans. by F. H. Trithen, 1851); Sprachvergleichende Beiträge zur griechischen und lateinischen Grammatik (1846); Grundzüge der griechischen Etymologie (1858–1862, 5th ed. 1879); Das Verbum der griechischen Sprache (1873). The last two works have been translated into English by A. S. Wilkins and E. B. England. From 1878 till his death Curtius was general editor of the Leipziger Studien zur classischen Philologie. His Griechische Schulgrammatik, first published in 1852, has passed through more than twenty editions, and has been edited in English. In his last work, Zur Kritik der neuesten Sprachforschung (1885), he attacks the views of the “new” school of philology.

Opuscula of Georg Curtius were edited after his death by E. Windisch (Kleine Schriften von E. C., 1886–1887). For further information consult articles by R. Meister in Allgemeine deutsche Biographie, xlvii. (1903), and by E. Windisch in C. Bursian’s Biographisches Jahrbuch für Alterthumskunde (1886).

CURTIUS, MARCUS, a legendary hero of ancient Rome. It is said that in 362 a deep gulf opened in the forum, which the seers declared would never close until Rome’s most valuable possession was thrown into it. Then Curtius, a youth of noble family, recognizing that nothing was more precious than a brave citizen, leaped, fully armed and on horseback, into the chasm, which immediately closed again. The spot was afterwards covered by a marsh called the Lacus Curtius. Two other explanations of the name Lacus Curtius are given: (1) a Sabine general, Mettius (or Mettus) Curtius, hard pressed by the Romans under Romulus, leaped into a swamp which covered the valley afterwards occupied by the forum, and barely escaped with his life; (2) in 445 the spot was struck by lightning, and enclosed as sacred by the consul, Gaius Curtius. It was marked by an altar which was removed to make room for the games in celebration of Caesar’s funeral (Pliny, Nat. Hist. xv. 77), but restored by Augustus (cf. Ovid, Fasti, vi. 403), in whose time there was apparently nothing but a dry well. The altar seems to have been restored early in the 4th century In April 1904, on the N. side of the Via Sacra and 20 ft. N.W. of the Equus Domitiani, remains of the buildings were discovered.

See Livy i. 12, vii. 6; Dion Halic. ii. 42; Varro, De lingua Latina, v. 148; Ch. Hülsen, The Roman Forum (Eng. trans. of 2nd ed., J. B. Carter, 1906); O. Gilbert, Geschichte und Topographie der Stadt Rom im Altertum, i. (1883), 334–338.

 CURTIUS RUFUS, QUINTUS, biographer of Alexander the Great. Of his personal history nothing is known, nor can his date be fixed with certainty. Modern authorities regard him as a rhetorician who flourished during the reign of Claudius ( 41–54). His work (De Rebus gestis Alexandri Magni) originally consisted of ten books, of which the first two are entirely lost, and the remaining eight are incomplete. Although the work is uncritical, and shows the author’s ignorance of geography, chronology and military matters, it is written in a picturesque style.

There are numerous editions: (text) T. Vogel (1889), P. H. Damste (1897), E. Hedicke (1908); (with notes), T. Vogel (1885 and later), M. Croiset (1885), H. W. Reich (1895), C. Lebaigue (1900), T. Stangl (1902). There is an English translation by P. Pratt (1821). See S. Dosson, Étude sur Quinte-Curce, sa vie, et ses &oelig;uvres (1887) a valuable work; F. von Schwarz, Alexander des Grossen Feldzüge in Turkestan (1893), a commentary on Arrian and Curtius based upon the author’s personal knowledge of the topography; C. Wachsmuth, Einleitung in das Studium der alten Geschichte (1895), p. 574, cf. p. 567, note 2; Schwarz, “Curtius Rufus” No. 31 in Pauly-Wissowa (1901).

 CURULE (Lat. currus, “chariot”), in Roman antiquities, the epithet applied to the chair of office, sella curulis, used by the “curule” or highest magistrates and also by the emperors. This chair seems to have been originally placed in the magistrate’s chariot (hence the name). It was inlaid with ivory or in some cases made of it, had curved legs but no back, and could be folded up like a camp-stool. In English the word is used in the general sense of “official.” (See, and .)

 CURVE (Lat. curvus, bent), a word commonly meaning a shape represented by a line bending continuously out of the straight without making an angle, but only properly to be defined in its geometrical sense in the terms set out below. This subject is treated here from an historical point of view, for the purpose of showing how the different leading ideas were successively arrived at and developed.

1. A curve is a line, or continuous singly infinite system of points. We consider in the first instance, and chiefly, a plane curve described according to a law. Such a curve may be regarded geometrically as actually described, or kinematically as in the course of description by the motion of a point; in the former point of view, it is the locus of all the points which satisfy a given condition; in the latter, it is the locus of a point moving subject to a given condition. Thus the most simple and earliest known curve, the circle, is the locus of all the points at a given distance from a fixed centre, or else the locus of a point moving so as to be always at a given distance from a fixed centre. (The straight line and the point are not for the moment regarded as curves.)

Next to the circle we have the conic sections, the invention of them attributed to Plato (who lived 430–347 ); the original definition of them as the sections of a cone was by the Greek geometers who studied them soon replaced by a proper definition in plano like that for the circle, viz. a conic section (or as we now say a “conic”) is the locus of a point such that its distance from a given point, the focus, is in a given ratio to its (perpendicular) distance from a given line, the directrix; or it is the locus of a point which moves so as always to satisfy the foregoing condition. Similarly any other property might be used as a definition; an ellipse is the locus of a point such that the sum of its distances from two fixed points (the foci) is constant, &c., &c.

The Greek geometers invented other curves; in particular, the (q.v.), which is the locus of a point such that its distance from a given line, measured along the line drawn through 