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PROCEEDINGS 



CAMBRIDGE PHILOSOPHICAL SOCIETY. 



November 14, 1853. 



A paper was read by Mr. Dobson on the Theory of Cyclones. See 

 Philosophical Magazine, vol. vi. p. 438. 



Also, on the Storm- tracks of the South Pacific Ocean. See Phi- 

 losophical Magazine, vol. vii. p. 268. 



A communication was made by Mr. C. C. Babington on the use 

 that has been made of the mode of growth to distinguish nearly 

 allied Species. 



November 28, 1853. 



A paper was read by Mr. Wedgwood on the Geometry of the first 

 three books of Euclid, synthetically demonstrated from premises 

 consisting exclusively of definitions. 



In a treatise* published by the author a few years ago, definitions 

 founded on relations of direction were indicated as exhibiting the 

 ultimate analysis of the conceptions of straightness and parallelism 

 in lines, and of planeness in surface ; and in proof of the adequacy of 

 these definitions as the basis of a complete system of geometry 

 without the aid of axioms or any other assumption whatever, they 

 were employed in demonstrating the principal propositions necessary 

 to place the student on the ground occupied by the definitions and 

 axioms of the ordinary system. If the basis thus built in underneath 

 the old foundations of the science had been complete in every nook 

 and corner, nothing more would have been required in order to rest 

 the entire demonstration on the single principle of definitions. So 

 long, however, as any step in the process, however subordinate, was 

 left to be supplied by others, there always would be room for sus- 

 picion that the assumption in reasoning which was speciously plas- 

 tered over in one place might be secretly undermining the system in 

 another. The reform, moreover, of the premises in geometry is a. 

 problem on which such an infinity of thought has been spent, and 



* The Principles of Geometrical Demonstration deduced from the ori- 

 ginal conception of Space and Form. Taylor and Walton. 1844. 

 No. X. — Proceedings of the Cambridge Phil. Soc. 



