Till. PROGRESS OK 



unmerited epithets uhich they reciprocally be- 

 itowed upon each other, to the eternal disgrace 

 of both parties, and the humiliation of mathema- 

 tical science. The dispute was of a nature not 

 capable of being decided by reasoning. Had 

 New ton made know n the nature of the lluxionary 

 calculus when it first occurred to him, his claim 

 as a discoverer would have been universally 

 allowed, and he would have conferred n boon 

 of the greatest magnitude on mathematicians, 

 l.eiluiit/ may have been informed that Newton 

 was in possession of an unknown calculus of the 

 greatest power this information may have set 

 his invention at work, and his exertions were 

 rrowned by the discovery of the differential 

 calculus. This discovery, as soon as made, he 

 gave to the public ; and, with the assistance of 

 the Bernoullis, soon brought it to a considerable 

 degree of perfection. This proceeding^ was 

 much more calculated for the improvement of 

 science than the morbid timidity of Newton. The 

 algorithm of Leibnitz was better ; his method 

 was taken up by men of first rate abilities, and 

 prosecuted with astonishing success. For it 

 would be difficult to find a series of mathemati- 

 cians to be compared with the two Bernoullis, 

 Euler, and Lagrange, who devoted in succession 

 their unrivalled powers to the improvement and 

 extension of the differential and integral calculus. 



In England, at, or before the time of New ton, 

 the number of profound mathematicians was 

 great. Wallis, Brounker, Wren, James Gregory, 

 Barrow, were his immediate predecessors or 

 contemporaries. Newton himself stands unri- 

 valed, as, perhaps, the greatest mathematical 

 genius that ever existed. Of his successors, the 

 most remarkable is Cotes, whose Harmonia 

 Mensurarum appeared in 1722. It contained 

 the method of finding the fluents of fractional 

 expressions, greatly generalized, and highly im- 

 proved, by means of a property of the circle dis- 

 covered by himself, and justly reckoned among 

 the most remarkable propositions in geometry. 

 It is curious, that this book, notwithstanding its 

 merit, has never acquired, among English ma- 

 thematicians the popularity which it deserves, 

 while, on the continent, it seems to be very little 

 known. 



Another very original and profound writer of 

 this period, was Dr Brook Taylor, who, in nis 

 Method of Increments, published in 1715, added 

 a new branch to the analysis of variable quan- 

 tity. A single analytical formula in his Me- 

 thod of Increments, has conferred a celebrity on 

 its author which very voluminous works have 

 often failed to bestow. It is known by the name 

 of Taylor's theorem, and expresses the value of 

 any function of a variable quantity, in terms oi 

 the successive orders of increments, whether finite 



or infinitely small. It is perhaps, without excep- 

 tion, the most comprehensive proposition in the* 

 whole range of mathematical science. 



Maclaurin may bo mentioned as another ma- 

 thematician, who did credit to his country. 



The mathematicians of Britain, and on the 

 continent, though the algorithm used by cacti 

 was different, yet kept pace with each other for 

 :i considerable time, except in one branch, the 

 integration of differential or fluxional equations. 

 In this the British mathematicians had fallen 

 considerably behind. And the <1 Utancff between 

 them, and those on the continent, continued to 

 increase in proportion to the number and impor- 

 tance of the questions, physical and mathematical, 

 which depended upon these integrations. The 

 habit of reading only British mathematical 

 works, produced at first by the admiration of 

 Newton, and afterwards continued, in consequence 

 of the difference of notation, prevented the 

 British mathematicians from partaking in the 

 pursuits of the mathematicians on the continent. 

 Prodigious improvements were made in Italy, 

 France, and Germany, in which the natives of 

 Great Britain had little or no share. 



Other causes, perhaps, may have contributed to 

 draw away our men of science from mathematical 

 investigations. But by the middle of the last 

 century, the race of British mathematicians, at 

 one time so numerous and so splendid, was 

 reduced to a very small number indeed. It is 

 true that mathematics still continued to be 

 cultivated in Cambridge: but they satisfied them- 

 selves with studying the Principia of Newton, 

 and neglected or despised the splendid improve- 

 ments and discoveries of the continental mathe- 

 maticians. 



A little after the middle of the last century, 

 Mr West was appointed to teach the mathematical 

 class in the university of St Andrews, in conse- 

 quence of the illness of professor Vilant. West 

 possessed an uncommon mathematical genius, as 

 is evident from the slightest inspection of his 

 Elementary System of Geometry, which he pub- 

 lished while a teacher. His mode of teaching 

 seems to have been admirable, and he had the 

 merit of infusing his own spirit into a num- 

 ber of young men who have contributed not a 

 little to the recovery of that high rank in mathe- 

 matical science which formerly belonged to 

 the British mathematicians. The late professor 

 Playfair was not indeed the pupil of West, but 

 he was his friend and contemporary, and both 

 had been educated at the same university. It is 

 not unlikely, therefore, that he may have been 

 indebted for his passion for the science, to his 

 intimacy with West. The late Sir John Leslie 

 was a pupil of West, and indebted to him for all 

 his mathematical knowledge. He was possessed 



