’ PHYSICAL AND MATHEMATICAL SCIENCES. 36 9
and more complex questions arose to be determined, thework of solving them, and reducing them into a system,would not be capable of being performed by the samemeans, or presented in the same form.
The methods of ultimate ratios and fluxions seem tohave been, as it were, created for the express purpose ofconducting Newton to the analysis of the motions ofbodies acted upon by gravitating and central forces,and the solution of the great problems arising out of it;but they were not so applicable when the limits of thesebranches of enquiry became extended : and, to inves-tigate more complex relations in the physical system ofthe world, more refined, more general and comprehensivemethods were required. Hence an exclusive devotionto the methods, however excellent, invented and appliedby Newton, was not likely to assist his disciples incarrying farther the discoveries he had begun; andwhile they confined their attention and acquirements tothe knowledge of his writings and methods, they werenot in a condition to enlarge the boundaries of science,and were not availing themselves of those more powerfulinstruments which were required for the work, in pro-portion as it became more difficult and extensive.
Newton had stretched the powers of geometry to anunprecedented degree, and had successfully applied itin extending the dominion of science over the system ofthe universe ; but such a mode of proceeding would byno means be applicable in all cases: the generality ofthose engaged in such researches would require easiermethods, and more certain and systematic rules, to assistthem in their investigations and computations. Geo-metry, as wielded by Newton, was like the sling andthe stone in the hand of David ; a weapon with whichno ordinary combatant would choose to attack a giant.
Adhering, then, to such methods, the British phi-losophers in general did but little in the way of prose-cuting dynamical enquiries ; while we find the conti-nental analysts busily engaged, and rapidly extending
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