326 A SHORT HISTORY OF SCIENCE 



Maclaurin's (1698-1746) Treatise of Fluxions (1742) was " the 

 first logical and systematic exposition of the method of fluxions," 

 and the applications to problems contained in it were characterized 

 by Lagrange as the "masterpiece of geometry, comparable with 

 the finest and most ingenious work of Archimedes." Maclaurin's 

 point of view may be illustrated by the following passage : 



Magnitudes were supposed to be generated by motion; and, by 

 comparing the increments that were generated in any equal successive 

 parts of the time, it was first determined whether the motion was uni- 

 form, accelerated, or retarded. . . . When the motion was accelerated, 

 this increment was resolved into two parts ; that which alone would 

 have been generated if the motion had not been accelerated, but had 

 continued uniform from the beginning of the time, and that which was 

 generated in consequence of the continual acceleration of the motion 

 during that time. The latter part was rejected, and the former only 

 retained for measuring the motion at the beginning of the time. 

 And in like manner, when the motion was retarded, ... so that the 

 motion at the time proposed was accurately measured, and the ratio 

 of the fluxions always accurately represented. In the method of 

 infinitesimals, the element, by which any quantity increases or de- 

 creases, is supposed to be infinitely small, and is generally expressed 

 by two or more terms, some of which are infinitely less than the rest, 

 which being neglected as of no importance, the remaining terms form 

 what is called the difference of the proposed quantity. The terms 

 that are neglected in this manner, as infinitely less than the other 

 terms of the element, are the very same which arise in consequence 

 of the acceleration, or retardation, of the generating motion, during 

 the infinitely small time in which the element is generated. . . . The 

 conclusions are accurately true, without even an infinitely small 

 error. . . . 



Daniel Bernoulli (1700-1782) made such good use of the new 

 mathematical methods in attacking previously unsolved problems 

 of mechanics, that he has been called the founder of mathematical 

 physics. He recognized the importance of the principle of the 

 conservation of force anticipated in part by Huygens. 



Euler (1707-1783), while Swiss by birth, spent most of his life 



