On the Principles of Motion, <$c 299 



more practical arguments were necesssary for the less pene- 

 trating and profound, the disciples of Berkeley and others. 

 These, when the science was attacked, were abundantly af- 

 forded by the most superior minds. I need only mention the 

 names of Robins, Jurin, and Maclaurin. Their writings 

 have so completely established the foundations of the higher 

 calculus, that scarcely a doubt on the subject of its true logic, 

 had arisen for more than half a century. Since their time, 

 however, Lagrange, an eminent mathematician, has pro- 

 claimed certain dogmas relative to this subject, and in them 

 has afforded what by some is considered as a demonstration, 

 which, if not satisfactory, is less exceptionable, than those of 

 his predecessors ; the substance of which appears to be, 



1. That Newton's illustrations and demonstration of the 

 science by motion or flowing, and the limits of ratios, are 

 improper and unmathematical, as every science ought to be 

 based on its own principles, and that that of motion is not 

 mathematical but physical. 



2. The method of Leibnitz too, which consists in the com- 

 parison of dependent variables when infinitely small, he pro- 

 nounces as very objectionable, and not founded on any clear 

 principles. 



3. He considers the subject as peculiarly and exclusively 

 belonging to algebra or analysis, and the theory of the de- 

 velopment of functions. 



Now from these positions, it would seem that those great 

 geniuses who originated the science in question, and by 

 whose reflected light only, Lagrange has shone as a mathe- 

 matician, are considered by him as not having established it 

 on a legitimate foundation, or as not having given to it the 

 true metaphysique. Before he had found out a new one of 

 his own, when there was no other than that of Newton or 

 Leibnitz, did he mistrust the foundation of the calculus ? On 

 the contrary, did he not use it with great success and much 

 to the improvement of science 1 



We have already shown that the idea of motion origina- 

 ted this science, and that it is truly a mathematical idea, as 

 being inherently essential to that of quantity. As a cause 

 producing effects, it is a physical attribute, but no otherwise 

 than existing in matter. Motion itself, independent of its 

 existence in body, and productive of physical action, is sus- 

 ceptible of more or less, and the ratio of one motion to ano- 



