XXVI INTRODUCTION. 



themselves, in some measure, masters of the Cal 

 culus, the help of which is required in most of the 

 investigations ; and may follow these so as to under 

 stand the whole of the propositions, by satisfying 

 themselves of their demonstrated truth. That this 

 also can be done with only a previous knowledge of 

 elementary geometry and algebra, has been proved 

 upon trial, that knowledge sufficing to attain an 

 acquaintance with the rules explained in those 

 parts of this treatise above recommended to be 

 passed over by the more general reader. It is by 

 no means intended to affirm that a complete know 

 ledge of the Principia can be attained without much 

 further study. An intimate famiHarity with the 

 Calculus, or with the analogous method of 

 Limits, is required by those who desire to follow 

 the whole of the demonstrations, and to perceive 

 the connexion between the different steps as 

 clearly as they can trace those of any elementary 

 process in geometry or algebra. Other helps than 

 this work are required, and are not wanting, to 

 facilitate the entire mastery of the subject by such 

 as would thoroughly understand the Principia in 

 all its parts. The present treatise is not designed 

 for their use, further than as it may aid them in 

 the earliest part of their studies. It is intended for 

 those who may not be able, or may not be disposed, 

 to go beyond acquiring such a knowledge of the 



