PHILOSOPHICAL WRITINGS OF THE LATE DE. DALTON. 3 



furnished solutions to five questions in the mathematical de- 

 partment of that interesting work, but owing probably to 

 inexperience in the art of "getting up** his solutions, the 

 editor, Dr. Hutton, did not think fit to insert any of them at 

 length. He was destined to a similar disappointment in the 

 succeeding Diary, and his name in consequence disappears 

 altogether from the list of correspondents to the Diary for 

 1786. In the solution of geometrical questions two methods 

 of proceeding obviously present themselves, viz.: the alge- 

 braical and the geometrical. The former method consists 

 principally in symbolizing the given data^ and in forming 

 between these and the qucesita a^ many independent equations 

 as there are unknown symbols. The solution of these equa- 

 tions determine the unknowns in terms of the given quantities, 

 and the final results usually suggest a geometrical process by 

 which the given proposition may be constructed. In the 

 latter method the given proposition is supposed to be solved 

 and the requisite diagram constructed : — the various relations 

 between the data and the qucesita are then examined, and 

 by a process of reasoning somewhat similar to that used in 

 Euclid's Data, other relations are determined to be given, or 

 can be found, until we finally arrive at a simple known truth 

 which requires no proof. When such is the case the pro- 

 position is said to be analyzed, and the various steps of the 

 process usually point out a much more simple construction 

 to a given problem than that furnished by the algebraical 

 method.* At the time of which we are now speaking the 



* " Par Vanalyse, on regarde comme vraie la proposition que Ton yeat 

 d^mootrer, ou comme resolu le probleme propose, et Ton marche de con- 

 sequence en consequence, jusqu*^ ce qu'on arrive a quelque verite connue, qui 

 autorise ^ conclurc que la chose admise comme vraie Test reelement, ou qui 

 comporte la constr^ion du probleme ou son impossibilite. 



" Par la synthcse, on part de verites connues pour arriver, do consequence en 

 consequence, h la proposition que Ton veut demontrer, ou k la solution du prob- 

 leme propose." — (Chnsles, Oeometrie Superievre, Discovrs, p. 4()._) 



