71 



RHETICUS. 



EIBALTA, FRANCISCO. 



72 



nt Paris he had been employed in the office of the learned printer 

 fi. Stephens, and ho occupied himself in a similar manner in the 

 printing establishment of Froben at BaseL In 1520 his father died, and 

 left him all Lis property ; but although Rhenanus retired to Schlettstadt, 

 he continued his favourite study of the ancients with the same zeal ; 

 and in order not to be disturbed, he requested and obtained from the 

 Emperor Charles V. an exemption from all public offices. He had 

 always objected to marrying, but at last his friends prevailed upon 

 him, and at the advanced ago of sixty-one he married. A few months 

 afterwards ho was attacked by a disease, from which he sought relief 

 in the baths of Baden, but as they only increased his sufferings, he 

 returned home, and on his way thither, be died, at Strasbourg, on the 

 20th of May 1547. His body was carried to his native place, and 

 buried there. 



Rheuanus is chiefly celebrated as the editor of many ancient authors, 

 on whom ho bestowed great care, with the view of giving a correct 

 text. The following is a chronological list of most of hia editions : 

 4 Quintus Curtius,' Basel, 1517; 'Maximus Tyrius,' Basel, 1519; 'Vel- 

 leius Paterculus,' Basel, 1520 (this is the editio princeps of that 

 historian) ; ' Tertulliani Opera,' Basel, 1521 ; 'Auctores Histories Eccle- 

 siasticao,' containing Eusebius, Pamphilus, Nicephorus, Theodoret, &c., 

 152325 (reprinted at Paris in 1541); '.Plinius, Historia Naturalis,' 

 Basel, 1526; 'Procopius Csesariensia, De Rebus Gothorum,' Basel, 

 1531 ;' Tacitus,' Basel, 1533 ; reprinted in 1544 ; ' Livii Decades Tres,' 

 Basel, 1535. 



Among the original works of Rhenanus we may mention 'Prsefatio 

 in Marsilii Deft- nsionem Pacis pro Ludovico IV. Imperatore, adversus 

 iniquas Ecclesiasticorum Usurpationes,' Basel, 1522. This work was 

 published under the assumed name of Liceutius Euangelus, sacerdos. 

 4 Illyrici proviuciaruni utrique Imperio cuin Romano turn Constant!- 

 nopolitano servicntis Descriptio,' published at Paris in 1602, together 

 with the ' Notitia dignitatum imperil Romani.' ' Rerum German!- 

 carum,' libri iil, Basel, 1531 : this work has often been reprinted. 

 The edition of Sturm (Basel, 1551) contains a good Life of Rhenanus. 

 He also translated several works from the Greek into Latin, such as 

 some works of S. Gregorius Nazianzeuus, part of the writings of 

 Origines, in the edition of Erasmus, &c. 



RHE'TICUS. The real name of this individual was George 

 Joachim. He was born February 16, 1514, at Feldkirch, a small 

 town situated a few miles south of Lake Constance, and was surnamed 

 Rheticus from the circumstance of this part of the Tyrol having been 

 anciently inhabited by the Rhseti. When twenty-three years old he 

 was appointed professor of elementary mathematics in the university 

 of Wittenberg, the higher chair being at that time filled by Reinhold ; 

 but after teaching there with some repute for about two years, he 

 relinquished his appointment in order to become the disciple and 

 assistant of Copernicus, whose doctrines he advocated with much zeal 

 and personal risk. His letter to Schoner, entitled ' Narratio de 

 Libris Revolutionum Copernici,' wherein he endeavoured to show that 

 the rotation of the earth about the sun is not a mere probable hypo- 

 thesis, as Copernicus had thought fit to announce it, but an incon- 

 testable truth, and asserts that if Aristotle himself were living, he 

 would be the first to acknowledge his error, excited against him the 

 ill-will of the leading advocates of the Ptolemaic system. This letter 

 appeared in 1540, Danzig, 4to ; was reprinted the following year at 

 Basel, and appended to the work of Copernicus, ' De Revolutionibus,' 

 Basel, 1566; and to Kepler's 'Prodromus Dissertat.,' Tubing., 1596. 

 He resumed his professorship in 1541-42 ; and in the latter year were 

 published his 'Orationes de Astronomic, Geographia, et Physica,' 

 Niirnb. He subsequently visited different parts of Germany, taught 

 for some time at Leipzig, and died of apoplexy at Cashau, in the north 

 of Hungary, the 4th of December 1576. (Zedler.) 



Rheticus has left an indisputable proof of extraordinary industry 

 and devotedness to science in a posthumous work, entitled ' Opus 

 Palatinum de Triangulis a Georgio-Joachimo-Rhetico cceptum, L. Valen- 

 tinus Otho, principis palatini Frederici IV., electoris mathematicus 

 consummavit, Neostadii in Palatinatu,' folio, 1596. The least import- 

 ant part of this work is the introductory treatise on Trigonometry, in 

 nine books, of which the first four, relating to right-angled triangles, 

 were written by Rheticus, and the other five, on oblique triangles, by 

 his pupil Otho. They comprise four hundred and eighty-one folio 

 pages, which, observes Delambre, might be compressed into ten. 



As authors, Delambre declares that Rheticus and Otho were the 

 most prolix and obscure that he had ever met with. After the intro- 

 ductory treatise follows a table of sines, cosines, tangents, cotangents, 

 secants, and cosecants, to every ten seconds of the quadrant, and to 

 a radius of 10,000,000,000. Nearly the whole of this extensive table, 

 which must have been of inestimable value to the astronomer, was the 

 work of Rheticus, though the contrary might be inferred from the 

 statements of Montucla and Lalande. The sines were originally com- 

 puted by him to fifteen places of figures, and were correct to the 

 fourteenth, as was shown by M. Prony, in the fifth volume of the 

 ' Me"inoires de 1'Institut ; ' but only the first ten were inserted in 

 the ' Opus Palatinum.' The table of tangents and secants was not 

 quite complete when Rheticus died. Those which were wanting 

 were added by Otho. The whole were computed to ten places of 

 figures, of which only the first eight could be relied on. Pitiscus 

 subsequently computed the tangents and secants aa far as eleven 



places of figures (Montucla says sixteen), which, with the rest of the 

 table of Rheticus, he published in 1613, under the title of ' Thesaurus 

 Mathematicus.' 



It is to the labours of Pitiscus that Montucla ascribes most praise, 

 designating them " the most remarkable monument of human patience, 

 the more meritorious as it was accompanied by so little glory," which 

 observes Delambre, would be true if the name of Rheticus were sub- 

 stituted for that of Pitiscus, whom he considers to have been little 

 more than the editor of the 'Thesaurus Mathematicus.' (See the 

 'Astronomic Moderne,' ii., p. 34.) The only terms employed in the 

 'Opus Palatinum' to express the several functions of an arc, are base, 

 perpendicular, and hypothenuse ; the terms tangent and secant had 

 not then been introduced, and the appellation sine, which had been 

 generally employed by Miiller and others, was rejected by Rheticus. 

 The construction of the canon is understood to have commenced in 

 the year 1540. 



Rheticus had intended to publish two treatises in German on 

 astronomy and philosophy generally, and 'had announced a work on 

 chemistry, in seven books, none of which have appeared. In these 

 his chief aim was to abolish hypothesis, and to rest exclusively on 

 observation. 



(Zedler, Grosses Universal Lexicon, xiv. 812; Kiistner, Qeschickte 

 der Mathematik, L 561-62; Delambre, Astron. Mod., ii. 1-25; Weiss, 

 Biog. Univ., art. ' Joachim ; ' see also Adani, Vit. Pltilos. Germ. ; and 

 Vossius, De Mathem.) 



RHIA'NUS, a Greek poet, was a native of Bena hi Crete, and lived 

 about the time of Eratosthenes. He was originally a slave who had a 

 kind of superintendence over a palaestra, but he subsequently became 

 a learned grammarian, and wrote several poems : one of them was a 

 'Hpa.K\fta, consisting of four books. Another of his poems, called 

 Mfffffr]viaKd, contained a poetical description of the second Messenian 

 war, of which we probably possess the substance in the account given 

 by Pausanias in his fourth book. Other poems of Rhianus were the 

 ((Tffa\iKd, "AxaiKa, and 'HAicuca. Athenseus (xi. p. 499) also mentions 

 epigrams of Rhianus. The Emperor Tiberius is said to have been 

 very fond of the poems of Rhianus, and even to have imitated them. 

 (Sueton., 'Tiber.,' c. 70.) The few extant fragments of his works are 

 collected in Brunck's 'Analecta,' in Jacob's 'Anthologia Gra>ca,' in 

 Gaisford's ' Poet. Grseci Minor,' and separately in a little book by N. 

 Saal, under the title 'Rhiani qua; supersunt,' Bonn, 1831. Compare 

 A. Meineke's essay, ' Ueber den Dichter Rhianos,' in the ' Transac- 

 tions of the Berlin Academy,' 1834, and his 'Analecta Alexandria, 

 Berlin, 1843. 



RHIZOS RHANGAVIS. [Rizo RANGABE.] 



RHODOMANNUS, LAURENTIUS, was born in 1546, at Sassa- 

 werft, on the estates of the counts of Stolberg. His parents were 

 poor, and as the boy early displayed great talents, Count Stolberg sent 

 him at his own expense to the gymnasium at Ilfeld. Greek literature, 

 which was then reviving in Germany, had most attractions for him, 

 and he made it his principal study at the University of Rostock. 

 After the completion of his studies, he held several offices as teacher, 

 but was afterwards invited to the professorship of Qreek literature in 

 the University of Jena, and subsequently to that of history at Wittem- 

 berg, where he died on the 8th of January 1606. 



Rhodomannus is said to have been extremely ugly, but his learning 

 and amiable qualities soon effaced the unfavourable impression created 

 by his appearance. His greatest merits consist in his efforts to diffuse 

 a taste for Greek poetry, and he endeavoured to attain this object by 

 making Greek verses himself, in which he is said to have been very 

 successful. We still possess a number of works by Rhodomannus, in 

 Greek verse with Latin translations, viz. : ' Vita Lutheri, Groeco car- 

 mine descripta et Latine reddita,' Ursel, 1579; 'Descriptio historic 

 ecclesise, &c., Grseco carmine cum versione Latina, e regione textus 

 Grseci,' Frankfurt, 1581 ; ' Poesis Christiana, id est, Palsestina, sou 

 Historic Sacrse, Graeco-Latinae, libri ix.,' Marpurg, 1589 ; Theologiee 

 Christianas Tyrocinia, carmine heroico Grseco-Latino, libri v.,' Lipsiae, 

 1597, &c. Rhodomannus also made some Latin translations of Greek 

 authors, as of Diodorus Siculus, which is printed in the edition of H. 

 Stephens (1604) ; of the ' Posthomerica ' of Quintus Calaber; he also 

 made a translation of extracts from ' Photii Bibliotheca ' and Diodo- 

 rus Siculus, under the title of 'Memnouis Historia de Republica 

 Heracleensium et Rebus Ponticis Eclogse,' Helmstadii, 1591, and 

 reprinted at Geneva in 1593. Rhodomannus edited the following 

 collection of Greek poems : ' Anonymi Poetae Gracci : Argonautica, 

 Thebaica, Troica, Ilias parva, Arion, Narratio de Bello Trojauo e Cou- 

 stantini Manassis Annal.,' &c., Lips., 1588. His Life has been written 

 in Latin, by Ch. H. Lang, Liibeck, 1741. 



RIBALTA, FRANCISCO, a distinguished Spanish painter of the 

 school of Valencia, was born at Castellon de la Plana in 1551. When 

 very young he fell in love with his master's daughter, but the father 

 (his name is not mentioned) would not consent to a marriage, on the 

 plea that Ribalta was not sufficiently advanced in his profession. 

 Upon this he determined to go to Rome, and his mistress plighted her 

 faith to him. At Rome he studied the works of Raffaelle, and par- 

 ticularly of Sebastian del Piombo. Upon his return to Valencia after 

 an absence of three or four years his professional improvement at 

 once procured him the hand of his mistress. Ribalta eoon obtained 

 great reputation. His first public work was the Last Supper, ordered 



