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 CLAVIUS

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CLAVUS

ters on America, who wrote after the expulsion of the order, hke Molina for instance, maintained in their books an attitude of dignified impartiahty, Clavigero has not been able to conceal his resentment against the Spaniards for that measure. He does not allude to it, but criticizes the conquerors harshly, extolling at the same time, beyond measure, the character and culture of the Indians. The writings of De Pauw, Adair, and Robertson are severely criticized. The two former have, in their hypercritical tendencies, gone entirely too far in denying to the Indians of Mexico a certain kind and degree of polity, but' Rob- ertson was much more moderate, hence nearer the truth, and more reliable than Clavigero himself. The latter is an unsafe guide in American et hnology, on ac- count of his exaffffi'ration of the aboriginal culture of the Mexican sedentary tribes. But the systematic ar- rangement of his work, his style, and the sentimental interest taken in the conquered peoples ensured to his book a popular sympathy that for a long time con- trolled the opinions of students as well as of general readers. The "Storia antica del Messico" was trans- lated into English by Cullen (London, 17S7); there is a German translation of the English version (Leipzig, 1789); Spanish editions (London, 1826; Mexico, 1844 and 1853).

BerIoTain de vSouza, Biblioteca hispano-americana septentrio- nal (Mexico, 1S16 and 1883); Diccionario universal de Hislona y Geografla (Mexico, 1853).

■ Ad. F. B.^NDELIER.

Clavius, Christopher (Christoph Clau), mathe- matician and astronomer, whose most important achievement related to the reform of the calendar vmder Gregory XIII; b. at Bamberg, Bavaria, 15.38; d. at Rome, 12 February, 1(112. The German form of his name was latinized into "Clavius". He entered the Society of Jesus in 1.5.55 and his especial talent for mathematical research showed itself even in his preliminary studies at Coimbra. Called to Rome by his superiors as teacher of this branch of science at the well-known CoUegiimi Romanum, he was engaged uninterruptedly there until his death. The greatest scholars of his time, such men as Tycho Brahe, Johann Kepler, Galileo Galilei, and Giovanni Antonio Magini, esteemed him highly. He was called the "Euclid of the sixteenth century"; and even his scientific opponents, like Scaliger, said openly that they would rather be censured by a Clavius than praised by another man. There has, however, been no lack of persistent disparagement of Catholic scholars even down to our own times; and therefore much that is inexact, false, and mythical has been put into circulation about Clavius, as for example that he was originally named "Schhissel" (clavis, "key"), that he was appointed a cardinal, that he met his death by the thrust of a mad bull, etc. His rela- tions with Galilei, vAXh. whom he remained on friendly terms until his death, have also been often misrepre- sented. The best evidence of the actual achieve- ments of the great man is presented by his numerous writings, which at the end of his life he reissued at Mainz in five huge folio volumes in a collective edi- tion under the title, "Christophori Clavii e Societate Jesu opera mathem.atica, quinque tomis distributa". The first contains the Euclidean geometry and the "Spheric" of Theodosius (Sphiericonmi Libri III); the second, the practical geometry and algebra; the third is composed of a complete commentary upon the " .Sphajra ' ' of Joannes de Sacro Bosco (John Holy- wood), and a dissertation upon the astrolabe; the fourth contains what was up to that time the most detailed and copious discussion of gnomonics, i. e. the art of constructing all possible sun-dials; finally, the fifth contains the best and mo.st fundamental exposi- tion of the reform of the calendar accomplished under Gregory XIII.

Many of these writings had already appeared in

numerous previous editions, especially the "Com- mentarius in Sphaeram Joannis de Sacro Bosco" (Rome, 1570, 1575, 1581, 1585, 1606; Venice, 1596, 1601, 1602, 1603, 1607; Lyons, 1600, 1608, etc.); likewise the "Euclidis Elementorum Libri XV" (Rome, 1574, 1589, 1591, 1603, 1605; Frankfort, 1612). After his death also these were republished in 1617, 1627, 1654, 1663, 1717, at Cologne, Frankfort, and Amsterdam, and were even translated into Chi- nese. In his "Geometria Practica" (1604) Clavius states among other things a method of dividing a measuring scale into subdivisions of any desired smallness, which is far more complete than that given by Nonius and must be considered as the precursor of the measuring instrument named after Vernier, to which perhaps the name Clavius ought accordingly to be given. The chief merit of Clavius, however, lies in the profound exposition and masterly defence of the Gregorian calendar reform, the execution and final victory of which are flue chiefly to him. Cf. " Romani calendarii a Gregorio Xlllrestituti explicatio"(Rome, 1603); "Novi calendarii Romani apologia (adversus M. Maestlinum in Tubingensi Academia mathemati- cum)" (Rome, 15SS). Distinguished pupils of Clavius were Grienberger and Blancanus, both priests of the Society of Jesus.

SnMMEKvoGEL, Bihl. de la c. de J. (Brussels, 1891). II. col. 1212; Lalande, Bibliofj. astrnn. (IS03); Delambre, Histoire de I'nMronomie moderne (Paris, 1821); Wolf, Geschichte der Aslronomie (Munich, 1S77); Bulletin aslron. (Paris. 190.5), sqq.; Revue des Questions Scientifiques (Louvain, 1908), series III, XIII, 324-331.

Adolf MtJLLER.

Clavus, Ci^AUDiTis (or Nicholas Niger), the latin- ized form of tlie name of the old Danish cartographer Claudius ClaussOn Swart, b. in the village of Sailing, on the Island of Funen, 14 September, 1388; date of death unknown. He was the first man to make a, map of North-Western Europe, which, moreover, included the first map of Greenland. He was appar- ently an ecclesiastic. In the course of his frequent journeys he went to Italy, where in 1424 he aroused much intiTcst among the Humanists of Rome by announcing that in the Cistercian monastery of Soroe, near Roeskilde, he had seen three large volumes which contained the "Ten Decades" of Livy; according to his own statement he had read the titles of the chap- ters (decern Livii decades, quarum capita ipse legisset). Through his intercourse with the Humanists he became acquainted with the maps and descriptions of Ptolemy, and was thus led to supplement the work of Ptolemy by adding to it a chart and description of the North-West coimtry. Clavus first turned his knowl- edge of Scandinavia and Greenland to accoimt in the geographical drawing antl description which has been preserved in the Ptolemy MS. of 1427 of Cardinal Filiaster. The manuscript is now in the public library of Nancy. Descrijitions of it have been repeatedly given by Waitz, Nordenskjold, Storm, and others. The facsimile of Clavus's map and his description of the parts contained, which were published by Norden- skiold and Storm, show that he gave Greenland and Iceland the correct geographical position, namely, west of the Scandinavian Penin.sula.

Far more important, however, for the history of cartography is the second map and description of North-Western Europe and Greenland that Clavus produced. As yet, unfortunately, the original of this work has not been found, nor does any copy contain both the map and the description. This second map has been preserved in the works of the German car- tographers. Donnus Nicholas Germanus and Henricus Martellus Germanus. who lived at Florence in the second half of the fifteenth century. Until recently, the descriptive text belonging to the map has only been known by the citations of Schoner and Friedlieb (Irenicus): the complete text was not known until it was found by Bjornbo in two codices in the imperial