PART II 



SYSTEMATICS AND HISTORY 



A. THE PRINCIPLES OF SYSTEMATICS 



RATIONAL SYSTEMATICS 



ALL systematics which deserves the predicate " rational " is 

 founded upon a concept or upon a proposition, by the aid of 

 which a totality of specific diversities may be understood. 

 That is to say : every system claiming to be rational gives 

 us a clue by which we are able to apprehend either 

 that there cannot exist more than a certain number of 

 diversities of a certain nature, or that there can be an 

 indefinite number of them which follow a certain law with 

 regard to the character of their differences. 



Solid geometry, which states that only five regular 

 bodies are possible, and points out the geometrical nature of 

 these bodies, is a model of what a rational system should be. 

 The theory of conic sections is another. Take the general 

 equation of the second degree with two unknowns, and 

 study all the possible forms it can assume by a variation 

 of its constants, and you will understand that only four 

 different types of conic sections are possible the circle, the 

 ellipse, the hyberbola, and the parabola. 



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