801 



FERMAT, PIERRE DE. 



FERNANDEZ, NAVARRETE. 



902 



Bcjapore, where he was kindly received by the regent and minister, 

 DUawur Khan, who introduced him to Ibrahim Adil Shah II., the 

 reigning monarch. In this court he spent the remainder of his life 

 in high honour, engaged sometimes in military expeditions, as we 

 learn from his own history, and devoting his leisure time to the 

 composition of his great work. He died, in all probability, soon after 

 1611, at the age of forty-one. He mentions in his history the English 

 and Portuguese factories at Surat, 1611. 



The preceding account has been chiefly taken from the English 

 translation of Ferishta, by Colonel Briggs, which was published in 

 London, in 1829, 4 vols. Svo. Portions of the history had been pre- 

 viously translated. Colonel Dow published a translation of the first 

 two books in his ' History of Hindostan," 2 vols., 4to, London, 1768, 

 which is not considered to be very accurately done. A much better 

 translation of the third book was given by Mr. Jonathan Scott in his 

 * History of the Deccan,' 2 vols., 4to, 1794. Mr. Stewart, in his 

 ' Descriptive Catalogue of the Library of the late Tippoo Sultan of 

 Mysore,' gives an account of the contents of the history, p. 12 ; and 

 also a translation of part of the tenth book, accompanied with the 

 original Persian, pp. 259-267. 



The history of Ferishta is divided into twelve books, with an 

 introduction, which gives a brief and imperfect account of Hindoo 

 bi-tury before the time of the Mohammedans, and also a short account 

 of the conquests of the Arabs in their progress from Arabia to 

 Hindustan. The first book contains an account of the kings of 

 Ohizui and Lahore, 997-1186. Here the detailed portion of his 

 history begins : 2, ' The kings of Delhi, 1205 to the death of Abker, 

 1605;' 3, 'The kings of 'the Deccan, 1347-1596;' 4, 'The kings of 

 Quzerat ; ' 5, ' The kings of Malwa ; ' 6, ' The kings of Kandeish ; ' 

 7, ' The kings of Bengal and Behar ; ' 8, ' The kings of Multan ; ' 9, 

 ' The rulers of Sind ; ' 10,' The kings of Cashmir ; ' 1 1 , ' An Account 

 of Malabar;' 12, 'An Account of the European Settlers in Hin- 

 dostan.' At the conclusion of the work, Ferishta gives a short account 

 of the geography, climate, and other physical circumstances of Hin- 

 dustan. 



Ferishta is certainly one of the most trustworthy, impartial, and 

 unprejudiced of oriental historians. He seems to have taken great 

 pains in consulting authorities. At the close of his preface he gives 

 a list of thirty-five historians to whom he refers, and Colonel Briggs 

 mentions the name) of twenty more who are quoted in the course of 

 the work. 



FEKMAT, PIERRE DE, was bom at Toulouse, about 1595, and 

 was brought up to the profession of the law. We have but few inci- 

 dents of his private lite, except that he became a counsellor of the 

 parliament of his native town, was universally respected for his talents, 

 and lived to the age of seventy years. His works were published in 

 1670 and 1679, in folio : the last volume contains his correspondence, 

 besides some original scientific papers. 



Format restored two books of Apollonius, and published Diophan- 

 tus, with a commentary. The whole of the actual works of Fermat 

 fill an exceedingly small space ; nevertheless they contain the germs 

 of analytical principles which have since come to maturity. In fact 

 they may be regarded, generally speaking, as announcements of the 

 results to which he had arrived, without demonstrations, or any 

 indications of the processes employed. 



The properties of numbers were the subject of his enthusiastic 

 researches, and no single individual has added more that is both 

 curious and u-eful to this branch of mathematics than Fermat : the 

 theorem now commonly called Format's is but a particular case of a 

 much more general one given in his works. 



His method for finding Maxima and Minima has only the merit of a 

 moderate ingenuity, before the differential calculus was discovered ; the 

 analysts of that day hovered on the brink of that beautiful process of 

 analysis which hag been rather ridiculously termed the greatest disco- 

 very of the human mind. A method not very remote from Format's 

 was practised by other analysts of his day; and in spirit also by the 

 ancient geometers; but it certainly is not the differential calculus, and 

 Laplace has no ground for his attempt to snatch from the claims of 

 the English and German nations this grand step of analysis in order 

 to appropriate it to his own. 



In Format's correspondence with Father Mersenne, we find him, in 

 a bungling manner, contesting with Roberval the first principles of 

 mechanics, and maintaining that the weight of bodies is least at the 

 surface of the earth, increasing both within and without, which is the 

 direct opposite to the truth ; and in one of his letters, when greeted 

 by Mersenne with the retraction of his errors, he very disingenuously 

 attempts to deny them, asserting that no body has a centre of gravity, 

 with many similar trifles, which place in bold relief the immortal 

 discovery of Sir Isaac Newton of the law of universal attraction, and 

 add lustre to his predecessor Galileo, who escaped from similar para- 

 doxes, from which common sense ought to have guarded both Fermat 

 and De^artes. 



The correspondence of Fermat ia sufficiently replenished with 

 vanity, which wast also well fed by some of his compatriots, who 

 lauded his DTOpodtlbfll as the finest things which had ever been dis- 

 covered. But it is justly suspected that the discovery of many of his 

 properties of numbers was effected by a tentative process, he himself 

 no demonstration, as no vestige remains in the works 



published by his eon of any peculiar analysis for arriving at them ; 

 while there are abundant proofs that he and Frenacle, a young 

 Parisian, employed the methods of tabulation and trial, to suggest 

 properties, and by further trials observe if they could generalise them. 

 In a subject less barren than the theory of numbers this talent and 

 industry would have produced more useful results; for what are the 

 theorems of Fermat to the laws of Kepler ? 



Fermat conjectured that the path of light, in passing from air to 

 a denser medium, ought to be such as to describe the shortest pos- 

 sible course. This is a particular case of the principle of least action, 

 and requires some remark. First, we see that Format's method for 

 finding maxima and minima was not the differential calculus, for 

 though importuned from various quarters to try this principle he was 

 deterred, as he says himself, for two or three years, by the dread of 

 the asymetries of the process, though any tyro acquainted with the 

 first principles of the differential calculus, with the proper data given, 

 would now do it in five minutes : when Fermat at last did this, it was 

 in a geometrical manner. Secondly, during the life of Descartes, he 

 seems to have disbelieved this law of refraction. The foundations of 

 both their reasonings in natural philosophy were of the slenderest 

 description, if indeed we can at all use such a term as reasoning to 

 the methods of Descartes, whose followers had the greatest faith when 

 he employed the least of that useful faculty. But the law is truly 

 attributable to Suellius, and, though this is well known, many French 

 writers still ridiculously talk of the Cartesian law of refraction. 

 Thirdly, Fermat did not attribute the truth of the principle to any 

 mechanical laws, of which he seems to have known nothing, but to the 

 pseudo-physical principle that nature should take the shortest course 

 in performing its operations for which indeed he was subjected to 

 several cases of objection, to which he has given good answers, 

 considering the position in which such an hypothesis placed him. 



To give a more exact idea of the ' man,' we shall give one of his 

 problems, entitled ' Problem by P. de Fermat. To Wallis, or any other 

 mathematician that England may contain, I propose this problem to 

 be resolved by them. 



' To find a cube number which, added to its aliquot parts, will give 

 a square number ? Example 343. 



' If Wallis and no English mathematician can solve this, nor any 

 analyst of Belgic or Celtic Gaul, then an analyst of Narbonne will 

 solve it.' 



Wallis gives an account of this in the ' Commercium Epistolicum,' 

 the correspondence having been conducted through Sir Kenelui Digby. 

 The works of Fermat contain also the tangents to some known curves, 

 and some centres of gravity. 



Though thus strongly endowed with the faculty of self-esteem, and 

 of that cunning which seeks to hide the tracks of discovery, we must 

 still place Fermat among such men as Pascal, Barrow, Brouncker, 

 Wallis ; but he had none of the masculine mind of Descartes, nor a 

 particle of the penetrating spirit of the glory of his age and nation, 

 Newton. 



It would bo wrong to omit here the most curious of the theorems 

 of Fermat relative to numbers. To make it more generally intelli- 

 gible we may state, that a triangular number means the sum of any 

 number of terms from the first of the natural numbers 1, 2, 3, 4, 5, 

 &c. ; thus 1, 3, 0,10, c., are triangular numbers; the square numbers 

 are 1, 4, 9, 16, &c., and are the sums of the progression 1, 3, 5, 7,&c. ; 

 pentagonal numbers in like manner arc the sums of the numbers 

 1,4, 7, 10, &c., namely, 1, 5, 12, 22, &c. The theorem consists in this, 

 that ' every number ' is the sum of 1, 2, or 3 triangular numbers ; 

 every number is the sum of 1, 2, 3, or 4 square numbers, and so on. 

 In the works of Euler, Legendre, and Barlow, the demonstration of 

 the first two cases may be found ; and though Legendre and Cauchy 

 have both laboured to prove it more generally, yet our impression is 

 that the general theorem is still without proof. 



FERNANDEZ, DENIS, a Portuguese navigator, who, in 1446, 

 discovered the river Senegal and Cape Verde. 



FERNANDEZ, JOAN, a Portuguese, the first European who 

 visited the interior of Africa. In 1446 he joined a Portuguese expe- 

 dition of discovery, and from au ardent desire to procure information 

 for Prince Henry, he got leave to remain among the Assenhaji, or 

 wanderers of the great African desert, in its Atlantic extremity. He 

 stayed there seven mouths till his countrymen returned. His 

 account has been strikingly corroborated in our days by that of 

 Mungo Park. The date of his death appears to be unknown. 

 (KeiT, Systematic Collection of Voyages and Travels, ii. p. 190.) 



FERNANDEZ, FRANCISCO, burn at Madrid, 1604, was, accord- 

 ing to Palomino, one of the most ingenious painters of his time. He 

 was employed by Philip IV. of Spain to execute several considerable 

 works. His chief works were an ' Obsequies of St. Francis," a ' St. 

 Joachim,' and a ' St. Anne.' He was killed by a companion in a 

 drunk' n quarrel in 1646. 



FERNANDEZ, NAVARRETE, surnamed El Mudo (the dumb), 

 born 1526 at Logrofto, on the Ebro, became a distinguished pupil of 

 Titian, and painter to Philip II., who employed him chiefly at the 

 Escurial. His principal works are a ' Nativity of Christ ; ' a ' Martyr- 

 dom of St. James ; ' 'St. Jerome in the Desert,' and especially 

 ' Abraham with the Three Angels." He painted with great ease and 

 despatch. On account of his colouring he was called the Spanish 



