TAR 



71 



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twelfth 'century Benjamin of Tudela speaks of it as the 

 limit of the Greek empire (i. 58, Asher's translat.) ; and in 

 the thirteenth, during the caliphate of Mostazem, the Arabs 

 attempted to recover Tarsus, but failed. (Abulpharagius, 

 p. ICO, ed. Poeocke, Oxon., 1673.) It was finally taken 

 by Mohammed II., in 1458. (Von Hammer's Geschichte 



f )s>na>iischen Retches, ii. 35.) 



Very few remains of the antient city of Tarsus exist : at 

 the north-west end of the antient town is part of an old 



fateway, and near it a very large mound, apparently arti- 

 cial, with a flat top, from which is an extensive view 

 of the adjacent plain : on an eminence to the south-west 

 are the ruins of a spacious circular edifice, probably the 

 tryinnasium. Lucas, who visited it in 1704, only noticed 

 one inscription, which he gives (i. 271-2, Amster., 1714). 

 For the probable situation of the tomb of Julian, see 

 Rennel, Western Asia, 88, &c. On a rock three or four 

 ,cs from Tarsus is a fortress, called the Castle of 

 Giants. Kazalu, the port of Tarsus, is now about twelve 

 distant, iind is closed up by a sand-bar. (Beaufort's 

 i nf f':i/-'">mni(i, '^76.) The population of Tarsus is 

 about 6000, chiefly Greeks and Armenian Christians, 

 governed by a Moosellim : its site is unhealthy. For 

 further information, see Michaud and Poujoulat's Corre- 

 snoiiikiirr- d'Orii-nt, vii., 146. 



TARTA'GLIA, NICHOLAS, a learned Italian mathe- 

 matician, who was born at Brescia about the beginning of 

 the sixteenth century. When he was six years of a<:e his 

 father, who followed the humble occupation of a nK-scn- 

 >r carrier, died, leaving him in indigent circumstances, 

 and without education. Even his family name is unknown, 

 and that which he bore (designating one who stammers) 

 .'iven him in derision by his young companions in 

 queiice of an impediment in his speech arising from 

 a wound which he received on his lips from a soldier, 

 when the French army under Gaston de Foix relieved 



a in 1512. 



No account has been transmitted of the means by which 

 Tartairlia obtained a knowledge of the rudiments of science, 

 and it is probable that he owed but little to a preceptor. 

 His oun i aided only by a mind endowed with 



the power of readily comprehending the processes of ma- 

 thematical investigation, enabled him at. length to attain 

 the highest rank among the geometers of his time. Having 

 i'1'iil years as a teacher at Verona and Vicenza, 

 he was appointed professor of mathematics at Brescia, and 

 in 15,'U he removed to Venice, where he held the like 

 pn.->t till his death, which took place in 1557. 



Tartaglia wrote on military engineering and on natural 



philosophy, but it is on his talents as an algebraist that his 



fame principally rests. In that age it was the custom for 



mathematicians to send difficult propositions to each other 



for solution, as trials of skill ; and in the work entitled 



'Quesiti ed Invention! Diverse,' which Tartaglia published 



in 1546, there are contained some interesting accounts of 



the circumstances connected with the algebraic questions 



which he had received and answered. Among these are 



his investigations relating to equations of the third degree; 



and the solutions of two eases, in which both the second 



'hird powers of (lie unknown quantity are involved, 



arc shown to have been discovered in 1530, on the oeca- 



if ;; iiuestion proposed by a person who kept a school 



at Brescia: Tartaglia states also that, in the year 1533, he 



! out the solutions of two equations, in which the first 



and third powers of the unknown quantity enter without 



the second, while preparing himself for a public contest 



with Aiitonia Maria 1'iore, who then resided at Venice, 



liallenged him to a competition, in which 



Ive a-, many as he could of thirty questions 



: by the other. It is added that larttiglia, 



iswered all those of his opponent without 



lution from the hitter in return. 



:in, who had been informed of the disco- 



ia, applied to the latter for the solution of 



:i (mentions which he proposed, in the hope of ob- 



' from him a knowledge of the processes which he 



employed iii obtaining the roots of equations of the kind 



H'ntioned. The application was made at first through 



:! afterwards by letter; but Tartaglia, who, 



MI of his secret, enjoyed great advantages 



iie other mathematicians of the time in resolving the 



MIS which wtre proposed to him, declined \\- 

 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 reputa- 

 tion 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 hav- 

 ing exacted a promise of inviolable secrecy, gave him a 

 key to the rule which he had discovered. Cardan imme- 

 diately found himself embarrassed with what is called the 



irreducible case, in which the expression jQ a P 8 [IR- 

 REDUCIBLE CASE], entering into the value of the unknown 

 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 inquiry, 

 being himself unable to conquer the difficulty ; in fact the 

 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 be- 

 tween 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 1 545 Cardan published his work entitled 'ArsMagna,' 

 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 30 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 

 lelt'himself seriously injured and aggrieved : Tartaglia how- 

 ever 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 actuallytook place in 1549,in the church of Santa 

 Maria, in Milan, bet ween 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 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 

 cotemporarles, and the formula for the value of the un- 

 known quantity in such equations is still designated Car- 

 dan'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 ; eioe Invenzione nuovamente 

 trovata, utile per ciascuno speculative Matematico Bom- 

 bardiero," &c., 1537 : this is a treatise on the theory and 

 practice of gunnery, and it was translated into English in 

 1588. ' Eucfide, difigentemente rassettato,' &c., 1543 : this 

 is said to be the first Italian translation of Euclid. 'Archi- 

 medes Opera emendata,' &c., 1543. 'Quesiti ed Invcnzioni 

 Diverse,' 1550 : this is the work above mentioned, and it is 

 dedicated to Henry VIII. of England: it contains the an- 

 swers to questions which had been proposed to Tartaglia 

 concerning mechanics and hydrostatics; and to one of the 

 books there is a supplement concerning the art of fortify- 

 ing places. ' La Travagliata Invenzione, ossia, Regola per 

 sollevare ogni atfondata Nave,' &c.. 1551: 'Ragionamenti 

 -o])i:i la Travagliata Invenzione,' 1551; 'General Trattato 

 lie' Numcri e Misure,' 1556-1560 ; 'Trattato di Aritmetica,' 

 155(i: Dcseri/.ione dell' Artih'ziosa Macchina fatta per ca- 

 varc il Galeone,' 1560 ; ' Archimedis de Insidentibns Aqua 

 Lihri duo,' 1565; '.Tordani Opusculum de Ponderositate,' 

 1565. A collection of his principal works was published 



in 1606. 

 TARTAN. 



[\VKAVINO.] 



TARTAR. [POTASSIUM.] 

 TARTAR1C ACID. This acid was first obtained in a 

 separate state by Scheele ; it exists in several vegetable 



