909 



TAKTINI, GIUSEPPE. 



TASMAN, ABEL JANSSEN. 



010 



of hia opponent without receiving ono Bolution from tho latter in 

 returu. 



In 1539, Cardan, who had been informed of the discoveries of 

 Tartaglia, applied to the latter for the solution of certain questions 

 which he proposed, in tho hope of obtaining from him a knowledge of 

 the processes which he employed in obtaining the roots of equations of 

 the kind just mentioned. The application was made at first through 

 a bookseller, and afterwards by letter ; but Tartaglia, who, by the 

 possession of his secret, enjoyed great advantages over the other 

 mathematicians of the time in resolving the questions which were 

 proposed to him, declined making any communication by which his 

 method might become publicly known. Though disappointed in these 

 attempts, Cardan soon afterwards succeeded, by a promise of intro- 

 ducing him to an Italian nobleman, who had the reputation of being a 

 great patron of learned men, in inducing Tartaglia to make a visit to 

 himself at Milan : the latter, while there, yielded to the entreaties of 

 his host, and having exacted a promise of inviolable secrecy, gave him 

 a key to the rule which he had discovered. Cardan immediately 

 found himself embarrassed with what is called the irreducible case, in 



which the expression jQ 2 KyP 3 , entering into the value of tho un- 

 known quantity under the sign of the square root, is negative, and he 

 applied to Tartaglia on the subject : the latter however declined giving a 

 direct answer to his enquiry, being himself unable to conquer the 

 difficulty ; in fact tho solution of the equation in this case is even 

 now usually obtained by the aid of trigonometrical functions. 



In the work of Tartaglia above mentioned there is an account 

 given of a dialogue which took place in 1541 between himself and a 

 Mr. Richard Wentworth, who then resided at Venice, and to whom it 

 appears that Tartaglia had given lessons in mathematics. On being 

 pressed by that gentleman to give him the rules for the solution of 

 equations containing the second and third powers of the unknown 

 quantity, the Italian mathematician declined doing so, on the plea 

 that he was about to compose a work on arithmetic and algebra, in 

 which the rules, he said, were to appear. 



In 1545 Cardan published his work entitled 'Ars Magna,' and in 

 direct violation of his solemn promise, gave in it the rule for the 

 solution of the cubic equation containing the first and third 

 powers of the unknown quantity. He does not assert that he is 

 the discoverer of the rule, but observes that it was first found out 

 about thirty years previously by Scipio Ferreus, of Bologna; and adds 

 that it had since 'that time been independently discovered by Tartaglia. 

 The publication of this work produced, as might be expected, the 

 most animated remonstrances from the man who thus felt himself 

 seriously injured and aggrieved : Tartaglia however revenged himself 

 in no other way than by sending challenges to Cardan and his disciple 

 Lewis Ferrari, to hold with him a disputation on mathematical 

 subjects, by which the public might be judges of their several merits. 

 The discussion actually took place in 1549, in the church of Santa 

 Maria, in Milan, between Tartaglia and Ferrari ; but during the 

 sitting, on the former pointing out an error which had been committed 

 by Cardan in the solution of a problem, the people, who appear to 

 to have taken the side of their townsman, excited a tumult, and the 

 assembly broke up without coming to a decision. Tartaglia has 

 received no more justice from posterity than he experienced from 

 his cotemporaries, and the formula for the value of the unknown 

 quantity in such equations is still designated Cardan's rule. It must 

 be admitted however that Cardan was the first who published its 

 demonstration. 



The works of Tartaglia, all of which were published at Venice, are 

 ' Nuova Scienza ; cioe Invenzione nuovamente trovata, utile per 

 ciascuno speculativo Matematico Bombardiero,' &c., 1537: this is a 

 treatise on tho theory and practice of gunnery, and it was translated 

 into English in 1588. ' Euclide, diligentemente rassettato,' &c., 1543 : 

 this is said to be the first Italian translation of Euclid. ' Archimedes 

 Opera emendata,' &c., 1543. ' Quesiti ed Invenzioui Diverse/ 1550 : 

 this is the work above mentioned, and it is dedicated to Henry VIII. 

 of England : it contains the answers to questions which had been pro- 

 posed to Tartaglia concerning mechanics and hydrostatics ; and to 

 one of the books there is a supplement concerning the art of fortifying 

 places. ' La Travagliata Invenzione, ossia, Regola per sollevare ogni 

 affoudata Nave,' &c., 1551; ' Ragionamenti sopra ia Travagliata 

 Invenzione,' 1551 ; ' General Trattato de' Numeri e Misure,' 1556- 

 1560; ' Trattato di Aritmetica,' 1556; 'Descrizione dell' Artifiziosa 

 Macchina fatta per cavare il Galeone,' 1560 ; ' Archimedis de Insi- 

 dentibus Aquae Libri duo," 1565; 'Jordan! Opusdulum de Pon- 

 derositate,' 1565. A collection of his principal works was published 

 in 1606. 



TARTI'NI, GIUSEPPE, a name celebrated in the annals of music, 

 was born at Pisano, on the coast of Istria, in 1692, and was educated 

 at the university of Padua, for the profession of jurisprudence ; but 

 his love of music triumphed over his graver pursuit, and after some 

 struggles, and several adventures of rather a romantic kind, among 

 which the fighting of many duels, the marrying a cardinal's niece 

 against her uncle's and his father's consent, and his consequent flight 

 to a monastery, where, to avoid the effects of his eminency's resent- 

 ment, he remained during two years secreted, may be mentioned, 

 he became a professed violinist, and the founder of a school which in 



after-times boasted of a Nardini, a Pugnani, a Viotti, and a Baillot 

 among its disciples. 



Tartini was al.-o a composer, and hia productions are much extolled 

 by a very competent j udge, M. Baillot, an eminent French violinist 

 and good critic : but he is more generally known by his writings on 

 the art, among which his ' Trattato di Musica seconda la vera Scienza 

 dell' Armenia' (1754), a strictly scientific work, is still read, and was 

 freely and ably translated and explained in 1771, by Edward Stilling- 

 fleet, under the title of ' Principles and Powers of Harmony,' who 

 cleared it of many of the obscurities which D'Alembert justly com- 

 plained of, and by his additions and illustrations rendered it enter- 

 taining as well as instructive. This treatise in partly founded on the 

 author's theory of a Third Sound, that is the third sound heard when 

 two sounds are given on musical instruments which admit of the tones 

 being held out and strengthened at pleasure, as violins, oboes, horns, 

 &c., a subject which has long engaged the attention of all writers on 

 acoustics, and on which most of Tartini's work is built. This dis- 

 covery of the ' Grave Harmonics,' as these third sounds are called, 

 was made so nearly at tho same time by Tartini and Ilomieu, that 

 both seem to have an undoubted claim to be considered as discoverers. 

 M. Romieu was a member of the Royal Society of Sciences of Mont- 

 pellier. The memoir which he read before the society is entitled ' A 

 New Discovery of Grave Harmonic Sounds, which arc very sensibly 

 produced from the union of Wind Instruments.' (Stillingfleet.) 



Tartini died at Padua in 1770. To the ' Dictionnaire des Musi- 

 ciens ' we are indebted for what relates to his early life : which work 

 also furnished M. Prony with materials for an interesting memoir in 

 the ' Biographie Universelle.' 



TARVER, JOHN CHARLES, was born of English parents at 

 Dieppe, Normandy, March 27th 1790. At the breaking out of the 

 war in 1793, his family, in common with all other English residents 

 at Dieppe, were thrown into prison. At that time the little boy was 

 staying at the country-house of a friend of his mother (M. Fdral, de la 

 Carperie Inge"nieur en chef des ponts et chausse'es du Departement 

 de la Seine Inferieure), and when his family, through the interest of 

 friends, had the means of escape given them, he was left behind in 

 France until an opportunity should offer to send him to England. 

 This never occurred. But M. Fe"ral, faithful to his trust, brought the 

 child up as his own son, educated him partly himself and partly at the 

 government school at Pont-au-de-Mer, and at the age of fifteen took 

 him into his own employment in the several works he was super- 

 intending under the government. In the year 1808 M. Fe"ral got the 

 youth an appointment in the Administration de la Marine, in which 

 service he remained, first as secretary to the admiral of the fleet at 

 Toulon, and afterwards in different ports, as Leghorn, La Spezzia, 

 Genoa, and Brest, till at the cessation of the war in 1814 he was 

 enabled to renew his intercourse with his family. In March 1815 he 

 obtained a short leave of absence, and hastened to England, where he 

 found his mother, brother, and sister living. He returned to Paris at 

 the expiration of his leave in April, where he found that Bonaparte 

 had escaped from Elba, and had put himself at. the head of his army, 

 and that the king, Louis XVIII. had fled. Such being the uncertain 

 state of affairs, and his own desire to return to his family being very 

 strong, Mr. Tarver gave up his situation and in less than a week 

 rejoined his mother. He soon sought and obtained employment as a 

 French master ; first at the grammar-school at Macclesfield in Cheshire 

 where he remained three years. In 1818 he went to live at Windsor, 

 and in 1826 he was appointed French master to Eton school, which 

 situation he held till his death April 15th 1851, aged sixty-one. 



Besides having written several elementary work?, now used at Eton 

 and some other public schools, he published while at Macclesfield a 

 ' Dictionary of French Verbs, showing their government and pecu- 

 liarities.' During his residence at Windsor he wrote his translation 

 of the ' Inferno ' of Dante in French prose, with a volume of notes ; 

 and subsequently ' Lectures on French History,' ' Paris, Ancient and 

 Modern,' and some minor works. He also revised the grammars of 

 Wanostrocht and Levizac, and Nugent's ' Pocket French and English 

 Dictionary.' For the last ten years of hia life he was engaged on his 

 ' Phraseological French and English Dictionary,' an original work of 

 immense labour, and which has given to its author a high place 

 amongat those who have most distinguished themselves in philological 

 studies. 



T ASM AN, ABEL JANSSEN, one of the greatest navigators of 

 the 17th century, whose fame has even yet scarcely equalled his 

 merits, owing to his countrymen, the Dutch, having neglected to make 

 known the important services which he rendered to geography. In 

 the service of the Dutch East India Company he gave such proof of 

 his enterprise and ability as to induce Anthony Van Diemen, the most 

 distinguished governor-general who had presided over the affairs of 

 that company, to commission him, in 1642, to proceed on a voyage, 

 the object of which was to ascertain the extent of the Australian con- 

 tinent, on the western coast of which discoveries had been made by 

 previous Dutch navigators. 



On the 14th August 1642, Tasman sailed from Batavia in command 

 of two vessels, the Heemskirk and the Zeehaan, directing his course 

 first towards the Isle of France, where he put in for provisions and 

 water. From tho Isle of France he set sail on the 3rd October, and 

 proceeded south to about 41 S. lat., afterwards to the south-east, to 



