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RUFFORD

sequently still further amalgamated with Rudolf's version and ampUfied by various continuators, notably one Heinrich von Miinchen (fourteenth century). In this form the work became very popular and was finallv resolved into prose.

•'Der gute Gerhard" was edited by Haupt (Leip- zig. 1S40); "Barlaam und Josaphat" by PfeifTer (Leipzig. 1843). Of the other works there are as yet no critical editions. A MS. reprint of a "Willehalm von Orlens" was given by Victor Junk in "Deutsche Texte des Mittelalters" (Berlin, 1905), II; selections from "Alexander" bv Junk in "Beitriige zur Ge- schichte der deutschen Sprache" (1904). 29, 369-469; from "Woltchronik", by Vilmar, "Die zwei Rezen- sionen und die HandschriftenfamiUen der Weltchronik Rudolfs V. E." (Marburg, 1839).

KrCger, Stilis:lische Unlersuchungen iiber R. v. E. als Nachahmer Gottfrifds (Lubeck. 1896); Zingerle, Die Quellen zum Alex, des R. V. E. in Weinhold and Vogt, Germanistische Abhand- lungen, IV (Breslau, 1885); Zeidler, Die Quellen von Rtidolfs r. E. Wilhelm ron Orient (Berlin, 1894) ; Junk, Die Epigonen des hofischen Epos in Sammlung Goschen, no. 289 (Leipzig, 1906), 16-<)2.

Arthur F. J. Remy.

Rudolph Acquaviva, Blessed. See Cuncolim,

Martyrs of.

Rueckers, Family of, famous organ and piano- forte builders of Antwerp. Hans Rueckers, the founder, lived in Amsterdam at the end of the sixteenth and the beginning of the seventeenth century, where he became a member of the Guild of St. Luke and was ac- tive principally as organ-builder. He died in 1640 or 1641. In what year the house which he estabhshed in Amsterdam was transferred to Antwerp is not known, but it was in the latter city that it attained its renown. Hans Rueckers originated a spinet (fore- runner of the piano-forte) with two keyboards, which could be played singly or simultaneously. They could be coupled, a higher octave on one keyboard, with a lower octav^e on the other, thereby doubling the sonority. Hans Rueckers' son, Andreas, b. in 1579, still further perfected the mechanism of their instruments, which gained world-wide celebrity under Andreas the Younger during the second half of the seventeenth century, their importance continuing under his successors throughout the greater part of the eighteenth. Rueckers' pianos were exported to foreign countries, particularly to England, and sold for the price, in tho.se days fabulous, of 3000 francs. Many of these instruments were decorated by famous painters, which caused some of them to be destroyed .so that the paintings might be preserved.

RiMBADLT, The Pianoforte, its Origin, Progress, and Construc- tion (London, 1860) ; Hopkins, Old Keyboard Instruments ( Ixjndon, 1887) ; Musikaliaches Konversationslexikon (Berlin,

1877).

Joseph Otten.

Rufliii, Paolo, physician and mathematician, b. at Valentano in the Duchy of Castro, 3 Sept., 1765; d. at Modena, 10 May, 1822. At first he intended to enter Holy orders and went so far as to receive the tonsure, but changing his mind, he began the study of mathematics and medicine in the University of Moflena, where he receiv<-d the degree of doctor. At the age of twenty-three he was appointed professor of analysis after having substituted for a year for his ff-acher, Cassiani. In 1791, the chair of elementary mathematics wa« entrusted to him. In the meantime, he did not neglect the stud^ and practice of medicine. .•\t the time of the French mvasion of Italy (1796), he wiiF unfxpe(te<ily appointed a member of the Juniori in the legi.slativc bo^ly at Milan. It was not without difficulty that he succeeded in returning to his lectures at Moflena. Becauw; he refused to take the rei)ubli- can oath without \hf conditional declaration dictatxid by his con.scienc;e, he was dismisstid from his jiosition as a public lecturer; but with the return of the AuHtrians in 1799 he waa restored to hia former poet

and maintained therein by succeeding governments. A call to the chair of higher mathematics in Pavia he declined, because he did not wish to give up his medi- cal practice among his dear Modenese. The univer- sity having been degraded to the rank of a lyceum, he accepted (1S06) the chair of applied mathematics at the newly established military school. In 1814 Francesco IV re-established the university and ap- pointed Ruffini rector for life, and at the same time professor of practical medicine and applied mathe- matics. By his lectures with the patients actually present he revived the clinical studies which had been neglected for several years. During the t\T)hus epidemic of 1817 he sacrificed himself for his fellow citizens, and finally succumbed. Although he re- covered, he never regained his strength. He was buried in the Church of Santa Maria di Pomposa, between the tombs of Sigonio and Muratori.

Ruffini's sole medical treatise is a "Memoria sul tifo contagioso". As a mathematician his name is inseparably associated with the proof of the im- possibility of solving algebraically the quintic equa- tion, on which subject he wrote several treatises ("Teoria generale delle equazioni, in cui si dimostra impossibile la soluzione algebraica delle equazioni generali di grado superiore al 4°", 2 vols., Bologna, 1798; "Delia soluzione delle equazioni alg. determi- nate particolari di grado sup. al 4°" in "Mem. Soc. Ital.", IX, 1802, which was awarded a prize by the National Institute of Milan; "Delia insolubilita delle eq. alg. etc.", ibid., X, 1803; "Delia insolubilita etc. qualunque metodo si adopori, algebraico esso sia o trascendente " in "Mem. Inst. Naz. Ital.", I, 1806). He also proved the impossibility of the quadrature of the circle ("Riflessioni intorno alia rettificazione ed alia quadratura del circolo" in "Mem. Soc. Ital.", IX, 1802). Less known, however, is the fact that Ruffini published the now familiar "Horner's method " of approximation to the roots of numerical equations fifteen years before Horner's fii-st paper on it appeared in the "Philosophical Transactions" of 1819 (pt. I, pp. 308-35). In 1802 the Italian Society of Forty offered a gold medal for the best method of deter- mining the root of a numerical equation of any de- gree. In 1804 the medal was awarded to Ruffini, and the dissertation was ])ublished under the title "Sopra la determinazione delle radice nelle equazioni nume- riche di qualunque grado". In a paper read before the Southwestern Section of the American Math. Soc. (26 Nov., 1910), Professor Florian Cajori pointed out that the computation demanded by Ruffini is identical with that in "Horner's method", and that this method is elaborated by Ruflnni with a clearness and thoroughness not surpassed in Horner's own ex- position of 1819. In view of this fact. Professor Cajori insists that the name of Ruffini should be associated with that of Horner in the designation of the method. Ruffini again wrote on this subject in 1807 (Algebra elementare, cap. iv, v), and in 1813 (Memori(! Soc. It., X\^I, XVII). Ruffini was during his whole life a zealous Catholic. His convictions find expression in his a])ologetic works: "Dell' immortality deir anima" (Modena, 1806), dedicated to I'ius VII, who sent him a gold medal; "Riflessioni critichc sopra il saggio filosofico intorno alle probability, del Sig. Conte de la Place-" (Modena, 1821), in which he proves himscdf to be as familiar with metaphysics as with questions of religion.

Fantonetti, Note Slorirfir sopra i socj defunti: Paolo Ruffini in Mem. Imp. Reg. hi. ,IH Regno Lomb. Ven., V (1838), 40-41; LoMBAHDi, Notizie nulla vita di Paolo Ruffini (Florence, 1S24); PooaENDOiiKF, Biogr.-Litl. IlandwOrterb. zur Gesch. der Exact. Wiss. (18.58-<j.'5); Cajori, Horner's Method of Approxi- mation Anticipated by Ruffini in Bull, of American Math. Soc (May, 1911).

J. Stein.

Ruflord Abbey, a monastery of the Cistercian Order, situated on the left bank of the Rainworth