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PREFACE. 



The first part of this volume, consisting of the mathematical elements of 

 natural philosopliy, is in part reprinted from the syllabus of the lectures, 

 but considerable additions have been made to it, both of elementary 

 matter and of original investigations. These elements are perfectly in- 

 dependent of every other work introductory to any branch of the ma- 

 thematics, and they comprehend all the propositions which are required 

 for forming a complete series of demonstrations, leading to every case of 

 importance that occurs in natural philosophy, with the exception of 

 some of the more intricate calculations of astronomy. It was therefore 

 absolutely necessary that they should be expressed in the most concise 

 manner that was possible ; yet except a few propositions which have been 

 cursorily introduced in sonic of the scholia, no essential step of a demon- 

 stration has ever been omitted. The best use, that a student could 

 make of these elements, would be to read over each theorem or problem 

 superficially, then to endeavour to form for himself a more particular 

 demonstration, and to compare this again with that which is here given: 

 for the exertion of a certain degree of invention is by far tlic surest 

 mole of fixing any principle of science in the mind. 



The catalogue of references has been methodically subdivided, as faras 

 it was possible to do it with convenience and accuracy, and the works and 

 passages belonging to each subdivision have in general been arranged in 

 chrono'ogical order; except that the different productions of the samo 

 author have been placed together. The divisions of the catalogue fol- 

 low very nearly the same order as the text of the lectures, so that there 

 has been no occasion for any references from one to the other. This ar- 



