28 DISSERTATION SECOND. fr«T n. 



remain constant, or to belong to all the individuals of the 

 species, and, according to the second, another property is to 

 be the greatest or the least possible ; and as, in some of the 

 simplest of such questions, 1 the constant quantity is the cir- 

 cumference or perimeter of a certain curve, so problems of 

 this kindy-have had the name of Isoperimelrkal given them, 

 a term which has thus come to denote one of the most curi- 

 ous and difficult subjects of mathematical investigation. 



The new analysis, especially according to the view taken 

 of it by Newton, is peculiarly adapted to physical researches, 

 as the hypothesis of quantities being generated by continu- 

 ed motion, comes there to coincide exactly with the fact. 

 The momentary increments or the fluxions represent so pre- 

 cisely the forces by which the changes in nature are produc- 

 ed, that this doctrine seemed created for the express purpose 

 of penetrating into the interior of things, and taking direct 

 cognizance of those animating powers which, by their sub- 

 tility, not only elude the observation of sense, but the ordi- 

 nary methods of geometrical investigation. The infinitesi- 

 mal analysis alone affords the means of measuring forces, 

 when each acts separately, and instantaneously under condi- 

 tions that can be accurately ascertained. In comparing the 

 effects of continued action, the variety of time and circum- 

 stance, and the continuance of effects after their causes have 

 ceased, introduce so much uncertainty, that nothing but 

 vague and unsatisfactory conclusions can be deduced. The 

 analysis of infinites goes directly to the point ; it measures 

 the intensity or instantaneous effort of the force, and, of 



1 The most simple problem of the kind is strictly and literally 

 Isoperimetrical, viz. of all curves having the same perimeter to 

 find that which has the greatest area. Elementary geometry 

 had pronounced this curve to be the circle long before there 

 was any idea of au entire class of problems characterized by 

 similar conditions. Fid. Pappi Alcxandrini Collect Math. Lib. 

 V. Prop. 2. &c. 



