427 



VIVIANI, VINCENTIO. 



VLADIMIR. 



423 



The work ' De Locfs ' being suspended, Viviani employed some of 

 the leisure which his duties in the service of the Grand-Duke of 

 Tuscany afforded iu the attempt to restore the fifth book of Apollo- 

 nius of Perga on the conic sections, which, with the three remaining 

 books of that writer, was then supposed to be lost. It was well 

 known that the subject of that fifth book was the determination of the 

 longest and shortest right lines in the conic sections ; and Viviani had 

 already made great progress in the work when, in 1656, Borelli dis- 

 covered, among the manuscripts in the Laurentian Library at Flo- 

 rence, a translation in Arabic of the conies of Apollonius, with a Latin 

 inscription denoting that it contained the eight books of the treatise; 

 the last book was however wanting. Having obtained permission, he 

 carried the manuscript to Rome, and caused it to be translated into 

 Latin by a learned Syrian named Abrahamua Ecchellensis : thia trans- 

 lation was published in 1659, and Viviani, who had not then com- 

 pleted his work, apprehending that his labours might become fruitless, 

 obtained a certificate to the effect that he had not been aware of the 

 existence of the manuscript, and that he was unacquainted with the 

 Arabic language. His ' Restoration ' was published in the same year, 

 under the title 'De Maximis et Minimis Geometrica Divinatio in quin- 

 tutn Conicorum Apollonii Pergoci adhuc desideratum,' fol., Florence; 

 and when the work was compared with the translation it was acknow- 

 ledged that Viviani had pursued the subject beyond the point to 

 which it had been carried by Apollonius himself. 



From this circumstance Viviaui immediately attracted the particular 

 notice of his prince, and acquired a high reputation among the mathe- 

 maticians of Europe. In 1672 the Grand-Duke Ferdinand gave him 

 the tihle of chief engineer, and appointed him, to proceed to the 

 frontier of the Papal States for the purpose of consulting with Cassini, 

 who was sent from Rome to meet him, concerning the navigation of 

 the Chiana and the means of preventing the inundations of the 

 Tiber. The measures proposed by the two mathematicians were not 

 put in execution by the governments, but Viviani availed himself of 

 the opportunity which his connection with Cassini afforded to join the 

 latter in making astronomical observations, and even of carrying on 

 some researches in natural history. In 1664, at the request of 

 M. Chapelain, Colbert recommended Viviani to the king of France, 

 Louis XIV., who assigned him a pension, and five years afterwards 

 appointed him one of the foreign associates in the Acade'mie Royale 

 des Sciences. In 1666 he became a member of the Accadeinia del' 

 Cimento at Florence, and in 1696 he was elected a fellow of the Royal 

 Society of London. 



About the year 1666 Viviani commenced a tract on the resistance 

 of solid bodies against the strains to which they are subject, but his 

 numerous occupations preventing him from immediately completing 

 it, he waa anticipated by Marchetti, who in 1669 published a work 

 on the same subject. As in this work the right of Galilei to the dis- 

 covery of the law of the resistance was denied, Viviani took advantage 

 of the delay to introduce into his tract a defence of his friend and 

 preceptor ; and in every respect his work appears to have been far 

 superior to that of his opponent. 



In 1674 he published a work entitled ' Quinto Libro degli Element! 

 d'Euclide, overro la Scienza Universale delle Proportion! spiegata colla 

 Dottrina di Galilei,' to which he joined a tract designated 'Diporto 

 Geometrico ' (Geometrical Amusements), the latter consisting of the 

 solutions, in the spirit of the ancient geometry, of twelve problems 

 which had been anonymously proposed ; and some propositions of a 

 like kind which were proposed by Comiers having been sent to him, 

 he published, in 1677, solutions of them in a work entitled ' Enodatio 

 Problematum universis Propositorum h, Claudio Comiers; pramissis 

 tentamentis variis ad solutionem illustris veterum problematis de 

 anguli trisectione.' This work is dedicated to the memory of his 

 friend Chapelain ; and in the preface he expresses a distaste for such 

 challenges, observing that the problems are enigmas which are seldom 

 proposed except by persons who have previously discovered their 

 solutions ; yet fifteen years afterwards he proposed as a challenge to 

 the mathematicians of Europe a problem whose enunciation was fanci- 

 fully stated in the following manner : "Among the ancient monu- 

 ments of Greece, there is a temple dedicated to geometry ; its plan is 

 circular, and it is covered by a hemispherical dome, in which are four 

 equal apertures of such magnitude that the remainder of the super- 

 ficies is accurately quadrable : it is required to determine the magnitude 

 and the positions of the apertures." The challenge appeared in the 

 ' Acta Eruditorum,' under a designation which is an anagram of the 

 words "A postremo Galilei Discipulo," a title of which Viviani appears 

 to have been always proud. Solutions were almost immediately given, 

 by the aid of the infinitesimal calculus, by Leibnitz and James BernoulM 

 in Germany, by the Marquis de l'H6pital in France, and by Wallis and 

 David Gregory in England : the solution given by Viviani himself is 

 very simple, and it was published by him, but without a demonstration, 

 in a small work entitled 'Formazione e Misura di tutti i Cieli, con la 

 Struttura e Quadratura esatta d'un nuovo Cielo ammirabile,' 4to, 

 Firenze, 1692. 



In 1701 he published, at Florence,^ second and enlarged edition of 

 his restitution of Aristseus, under the title ' De Locis Solidis Seeunda 

 Divinatio Geometrica iu Quinque Libros amissos Aristoei Seuioris, 

 Opus Conicum, continens Elementa Tractatuum ejusdem Viviaui, 

 quibus tune ipse niulta in, Mathesi Theoremata demonstrare cogita- 



verat.' The work is dedicated to Louis XIV., and the author avails 

 himself of the occasion to express his gratitude to his preceptor 

 Galilei. The subject is treated with great elegance and simplicity, and 

 according to the methods of the ancient geometers ; it must be 

 admitted however that the difficulty of the work would have been 

 much diminished by the employment of the modern analysis. 



Viviani was solicited by Casimir, king of Poland, to reside in that 

 country ; but from attachment to his native land, he declined the 

 request, as he did the offer of Louis XIV. to make him his first 

 astronomer. He built for himself, at Florence, a mansion, on the 

 front of which he inscribed the words, JBdes a Deo datte : and from 

 respect to the memory of Galilei, he adorned the entrance with the 

 bust of that philosopher. He died on the 22nd of September 1703, 

 in the eighty-second year of his age, leaving behind him the character 

 of having been a man of simple manners and a faithful friend. 



(Eloge de Viviani, by Fontenelle, in the ' Histoire de 1' Acade'mie des 

 Sciences,' for 1703.) 



VLACQ, ADRIAN", a Dutch mathematician of the 17th century, 

 who distinguished himself by his labours in the computation of loga- 

 rithms. Being a bookseller or printer, he superintended the printing 

 of the tables which he had composed, as well as of almost the first of 

 those which were computed by the mathematicians of this country. 



Logarithms had then been recently invented, and while the employ- 

 ment of them was becoming genera) in Britain through the labours 

 of Briggs, Gunter, and other indefatigable computers, Vlacq in 

 Holland contributed greatly to extend their use and a knowledge of 

 the principles of their construction on the Continent. In 1628 he 

 published at Gouda an edition of the ' Arithmetica Logarithmica ' of 

 Briggs, which contained the logarithms of numbers between 1 and 

 20,000, and also between 90,000 and 100,000, to fourteen places of 

 decimals; but having computed the logarithms of the 70,000 inter- 

 mediate numbers, he published at the same place, in folio, a French 

 translation of the above work, including in it the seventy chiliads, 

 under the title of ' Arithmetique Logarithmetique : ' all the logarithms 

 are given to ten places of decimals. It appears that part of the 

 edition of the ' Arithmetica Logarithmica,' which had been published 

 by Vlacq, waa sold in England, contrary to the intention of the 

 author ; for Norwood, in his ' Trigometria,' which was published in 

 1631, complains of such sale, and designates it an unfair practice. 



Briggs having just before his death completed his great table of 

 logarithmic sines and tangents, his friend Gellibraud wrote for it a 

 preface and an account of the application of the logarithms to the 

 purposes of plane and spherical trigonometry. This work, which was 

 designated ' Trigonometrica Britannica,' was printed at Gouda by 

 Vlacq in 1633. In the same year Vlacq printed a work, composed by 

 himself, which is entitled ' Trigonometria Artificialis, sive magnus 

 canon Triangulorum Logarithmicus, ad dena scrupula secuuda,' &c. ; 

 it contains the logarithmic sines and tangents to ten places of fitrures, 

 with differences, and to these is added Briggs's table of the first 20,000 

 logarithms with their applications, chiefly extracted from the 'Trigo- 

 nometrica Britannica.' 



In 1636 Vlacq published an abridgment of the 'Trigonometria 

 Artificialis,' under the title of ' Tabula Sinuum, Tangentium, et 

 Secantium, et Logarithmorum Sinuum, Tangentium, et Nunieroruui 

 ab 1 ad 10,000,' in 8vo. These tables have passed through several 

 editions in French and German, and on the Continent they continued 

 long to be a manual for persons employed in making trigonometrical 

 computations. 



VLADIMIR (the First), Grand-Duke of Russia, surnamed the 

 Great, was the son of Sviatoslav by a slave, or at least a woman of low 

 condition. 



His father, meditating the conquest of Bulgaria, divided in 1790 his 

 empire between his two legitimate sons Yaropolk and Oleg. Vladimir 

 was sent to Novgorod, as that unruly place, disdained by the legiti- 

 mate princes, was considered a government only fit for an illegitimate 

 son. After Sviatoslav's death, 972, his sous remained at peace for 

 five years ; but in 977 Yaropolk, who ruled at Kiev, quarrelled with 

 his younger brother Oleg. and having slaiu him in battle, took his 

 share of the paternal heritage. Vladimir, expecting an attack from 

 his brother, fled beyond the sea to the Varingians (i.e. the Scandi- 

 navians), and Yaropolk occupied Novgorod by his officers. 



Vladimir returned after two years from Scindinavia with a formidable 

 body of adventurers, and was joined by the inhabitants of Novgorod. 

 He formally declared war against his brother, and demanded the hand 

 of Rogneda, daughter of the Varingian Rogvold, prince of Polotsk. 

 Rogneda, who was betrothed to his brother, rejected Vladimir's suit, 

 saying that she would not marry the son of a slave. Vladimir attacked 

 Polotsk ; Rogvold was killed with his two sons, and Rogneda was com- 

 pelled to marry Vladimir. 



Vladimir marched on Kiev, and Yaropolk, perceiving that he was 

 betrayed by his own people, fled from his capital, but being soon after- 

 wards induced to surrender, he was treacherously murdered by his 

 brother's command. Vladimir now became monarch of the empire of 

 his father, which extended from the vicinity of the Baltic to that of 

 the Black Sea. It was however by no means a regularly constituted 

 empire, like that of the western monarchs of that time. The sove- 

 reignty of the grand-dukes of Russia, who had established their 

 capital at Kiev, was limited to a tribute levied on the various Slavo- 



