INTRODUCTION. 7 



use to form to ourselves a general idea of the sciences and arts which are to 

 be placed among them. 



Upon the advantages of mathematical and philosophical investigation in 

 general it is unnecessary to enlarge, because no liberal mind can require 

 any arguments to be convinced how much the judgment is strengthened, ! 

 and the invention assisted, by habits of reasoning with caution and accu- 

 racy. The public opinion is rather, on the contrary, in danger, at least in 

 some parts of the world, of being too exclusively biassed in favour of 

 natural philosophy ; and has sometimes been inclined to a devotion too 

 much limited to science, without a sufficient attention to such literature as 

 an elegant mind always desires to see united with it. As to the practical 

 importance of philosophical theories of thqf arts, it may have been overrated 

 by some, but no person is authorised to amrm that it has been too highly 

 estimated, unless he has made himself master of every thing that theory is 

 capable of doing ; such a one, although he may in some cases be obliged to 

 confess the insufficiency of our calculations, will never have reason to com- 

 plain of their fallacy. 



The division of the whole course of lectures into three parts was origi- 

 nally suggested by the periodical succession in which the appointed hours 

 recur : but it appears to be more convenient than any other for the regular 

 classification of the subjects. The general doctrines of motion, and their 

 application to all purposes variable at pleasure, supply the materials of the 

 first two parts ; of which the one treats of the motions of solid bodies, and 

 the other of those of fluids, including the theory of light. The third part 

 relates to the particular history of the phenomena of nature, and of the 

 affections of bodies actually existing in the universe, independently of the 

 art of man ; comprehending astronomy, geography, and the doctrine of the 

 properties of matter, and of the most general and powerful agents that 

 influence it. 



The synthetical order of proceeding, from simple and general principles, 

 to their more intricate combinations in particular cases, is by far the most 

 compendious for conveying information with regard to sciences that are at 

 all referable to certain fundamental laws. For these laws being once 

 established, each fact, as soon as it is known, assumes its place in the 

 system, and is retained in the memory by its relation to the rest as a con- 

 necting link. In the analytical mode, on the contrary, which is absolutely 

 necessary for the first investigation of truth, we are obliged to begin by 

 collecting a number of insulated circumstances, which lead us back by 

 degrees to the knowledge of original principles, but which, until we arrive 

 at those principles, are merely a burden to the memory. For the pheno- 

 mena of nature resemble the scattered leaves of the Sibylline prophecies ; 

 a word only, or a single syllable, is written on each leaf, which, when sepa- 

 rately considered, conveys no instruction to the mind ; but when, by the 

 labour of patient investigation, every fragment is replaced in its appropriate 

 connexion, the whole begins at once to speak a perspicuous and a harmoni- 

 ous language. 



Proceeding, therefore, in the synthetical order, we set out from the ' 

 abstract doctrines of mathematics, relating to quantity, space, and number, 



