III. AN ESSAY 



ON 



CYCLOIDAL CURVES, 



WITH INTRODUCTORY OBSERVATIONS. 



From the British Magazine, for April 1800. 



ON MATHEMATICAL SYMBOLS. 



Many of the most celebrated mathema- 

 ticians of the present day have been disposed 

 to pride themselves on the very great supe- 

 riority, which they altribiUe to the mo- 

 dern methods of calculation, over those 

 which were known to the ancients. That, 

 in the course of so many centuries, mathe- 

 matical sciences, hke all others, should have 

 been very considerably advanced, is no more 

 than must have been expected, from the great 

 number of persons who have employed iheir 

 talents in the cultivation of those sciences. 

 But, if we examine the matter impartially, 

 we shall have reason to believe, not only 

 that mathematics have been as slow in their 

 real advancement as any other part of phi- 

 losophy, but that the moderns have very fre- 

 quently neglected the more essential, for fri- 

 volous and superficial advantages. To say 



nothing of the needless incumbrances of new 

 methods of variations, of combinatorial ana- 

 lyses, and of many other similar innovations, 

 the strong inclination which has been shown, 

 especially on the continent, to prefer the al- 

 gebraical to the geometrical form of repre- 

 sentation, is a sufficient proof, that, instead 

 of endeavouring to strengthen and enliglitea 

 the reasoning faculties, by accustoming thetn 

 to such a consecutive train of argument as 

 can be fidly conceived by the mind, and 

 represented with all its links by the recol- 

 lection, they have only been desirous of spar- 

 ing themselves as much as possible the pains 

 of thought and labour, by a kind of mecha- 

 nical abridgment, which at best only serves 

 the office of a book of tables in facilitatinar 

 computations, but which very often fails 

 even of this end, and is, at the same time, 

 tlie most circuitous and the least intelligible. 

 These philosophers are like the young^Eng- 



