V I V 



afterwards compared witli that of the Greek matlicmaticiaii, 

 it was difcovered that Viviani had not only formed new 

 theories, but tliat he had difcovered many new properties of 

 the conic fedlions, fo that his work may be confidercd as a 

 fupplement to the ancient theory of thefe curves. In the 

 years 1664 and 1665, he was engaged, in concurrence with 

 Caflini, in concerting means for preventing the inundations 

 of the Tiber, by altering the courfe of certain rivers : and 

 in their furvey of the country for this purpofe, they were 

 led to a variety of collateral obfervations on the inlefts 

 found in the gall-nut, on marine fliells, partly petrilied and 

 partly in their natural Hate, dug up in the mountains, and 

 alfo on Etrufcan vafes and infcriptions. In 1666, the grand 

 duke of Tufcany honoured Viviani with tiie title of his ma- 

 thematician, which had been previoully enjoyed by Galileo ; 

 and in 1673 lie commenced printing the work of Arilleus, 

 an ancient mathematician, the reftoration of which he had 

 at an early period of his life contemplated : but infirmities 

 and other engagements prevented his proceeding with it. 

 In the following year he publidied, in a fniall quarto, fome 

 works of Galileo, and particularly his Trcatife on Propor- 

 tion, for illuftrating the 5th book of Euclid. In 1676, 

 three problems were propofed by M- de Comiers, provoft 

 of the collegiate church of Ternant, two of which related 

 to the trifeftion of an angle, for the folution of which Viviani 

 had difcovered three methods, which he now determined to 

 publifh. His work on this fubjeft, dedicated to the me- 

 mory of his friend Chapelain, appeared in 1677. ^" 1692 

 he propofed, in the Acts of Leipfic, a problem relating to 

 the art of piercnig an hernifphcrical arch with four equal 

 windows, in fuch a manner that the remainder of the turface 

 {hould be abfoUitcly fquarcable. This problem, which he 

 called a geometrical enigma, was folved by Leibnitz, J. 

 BernouiUi at Bade, the marquis de I'Hofpital in France, 

 and by Ur. Wallis and David Gregory in England. Vi- 

 viani himlelf publillied the problem and his own geometric;J 

 folution of it in a work, in which he treats, both as a geo- 

 meter and architect, of the arches of the ancient Romans, 

 and propofes a new arch to be called the Florentine. In 

 1664 Louis XIV. had fettled on him an annual penfion, in 

 confideration of his diilinguilhcd merit: and in 1669 he 

 was appointed one of the eight foreign alTociates ot the 

 Academy of Sciences. Thus noticed, he was led in 1701 to 

 publifh his divination of Arifteus, in three books, dedicated 

 to his bencfaftor. Part of his penfion was devoted by him 

 to the conftruclion of a magnificent edifice at Florence, 

 which he called " VEdes a Deo data," and over the gate 

 he placed a buft of Galileo, with feveral infcriptions in 

 honour of him. In his old age he amufed himfelf with the 

 folution of feveral problems relating to chances on dice. 

 He alfo publiihed, for facilitating the (tudy of geometry, 

 an edition of Euclid's Elements, both plane and folid. Vi- 

 viani, dcfirous of rendering mathematics in connection with 

 the arts praftically nfeful, was confult-'d both by his coun- 

 trymen and foreigners on various public works ; and it is 

 /lated, that, among other benefits which he conferred on his 

 country, he contributed, by the introdu£lion of new terms 

 in his mathematical and philofophical writings, to render the 

 Tufcan language more copious ; but his ftyle is faid to be 

 inferior in elegance to that of his mailer Galileo. After a 

 life of ufefulnefs and honour, prolonged to his 8 1 ft year, he 

 died of an apoplexy, in October 1703. 



Baylc has accufed him of atheifm ; but Fabroni has re- 

 futed the charge. Fonteiielle fays, *' he had that innocence 

 and fimplicity which are commonly prcfervcd by perfons 

 who have more intcrcourfc with books than with men. 



V I V 



without that h-jiighlincls and boiftcrous rudeiiefs which are 

 often acquired by them. He was affable, modelt, fiiicere, 

 and faithful in his friendfhips ; and what includes many 

 virtues in one, he was grateful, in the highell degree, to 

 thofe from whom he received favours." His works were 

 numerous. To fome of them we have already referred. 

 Fabroni. Montucla. Fontenelle Eloges, &c. Gen. Biog. 



VIVIEN, .lo.sEPn, a French painter, who, though a 

 pupil of Le Bruii, pradtifed his art moftly in crayons, and 

 obtained a degree of reputation, which few who ha«e worked 

 in tliofe perifhable materials have arrived at. He was 

 born at Lyons, in 1657. His portraits were frefh and vi- 

 gorous, and obtained for him confiderable employment, 

 and the favour of the eleftor of Bavaria, who made him 

 his flate painter, and gav him a penfion. His portrait is 

 among thofe of diftinguiflied artilis at Florence. He died 

 in 1735. 



VIVIER, La, in Geography, a town of France, in the 

 department of the lUe and Vilaine ; 3 miles N. of Del. 



VIVIERS, a town of France, in the department of the 

 Ardeche, on the right bank of the Rhone. Before the 

 revolution, the fcfe of a bifliop, and capital of a province, 

 called Vivarais, now the department of the Ardeche; 

 16 miles S.S.E. of Privas. N. lat. 44° 20'. E. long- 

 4° 46'. 



VIVIFICATION, in Alfdkine, the art of -vivifying, 

 that is, of contributing to the attion that gives hfe, or 

 maintains life. 



The chemifts alfo ufe the word in fpeaking of the new 

 force, vigour, and lullre, which, by their art, they give to 

 natural bodies, particularly to mercury ; whicii, after having 

 been fixed, or amalgamated, they rellore to its firft ftate. 

 See Revivikication. 



VIVIPAROUS, ViVlPARUS, in Natural Hijlory, an 

 epithet applied to fucli animals as bring forth their young 

 alive and perfeft ; in contradillindtion to fuch as lay eggs, 

 which arc call-d oviparous animals. 



The females of all the quadrupfd clafs are viviparous, and 

 thofe of the bird clafs are all oviparous. 



The laws of nature in the larger animals are, therefore, 

 in 3 great meafure, fixed and certain ; but it is not fo in the 

 infeft tribes, nor in the fiflies ; for of thefe, fome are vivi- 

 parous, and others oviparous ; and thofe of genera nearly 

 allied to one another. 



Among infefts, the much greater number are oviparous ; 

 but there are many which are not fo, as the p.icerons, pro- 

 gall infeds, cochineal, &c. The millepedes and fcorpions 

 are alio well known to be fo ; all the females of the butter- 

 fly, and of fome other clalfes, lay only eggs ; but the mod 

 fingular and remarkable inconllancy in nature, if we may be 

 allowel tiie cxprefiion, is that in the fly kingdom ; the fame 

 clafs ot infeits, aicd even the fame genus, will furnifli us with 

 lome which are viviparous, and others which are oviparous : 

 the two-winged flies give us inllances of this ; but tlufe are 

 not fingular in that ref])eft ; for among the reptile world, 

 there are other creatures whicli are fubje<ft to the fame va- 

 rieties ; and Swammerdam has obferved a viviparous fnail. 



The fpecies of viviparous two-wi.iged flies are niiii;h more 

 rare than the oviparous ; and among the four-winged clafs 

 they are yet more uncommon. It is not certain, that any 

 of the latter, bcfide the winged. pucerons, are of this kind; 

 but among the former there are fix or feven fpeci' s which 

 are known always to produce living worms, an 1 -robably 

 many more will be difcovered, by a more clofe attention 

 ihun has hithcito been given them. 



It is cafy to tlnd about our houfcs one of thefe fpecies of 



viviparous 



