IDEAS OF EQUALITY AND SIMILARITY. 153 



idea has evidently arisen by subsequent analysis. And that 

 the notion of equality did thus originate, will, we think, 

 become obvious on remembering that as there were no ar- 

 tificial objects from which it could have been abstracted, it 

 must have been abstracted from natural objects ; and that 

 the various families of the animal kingdom chiefly furnish 

 those natural objects which display the requisite exactitude 

 of likeness. 



The same order of experiences out of which this gene 

 ral idea of equality is evolved, gives birth at the same time 

 to a more complex idea of equality ; or, rather, the process 

 just described generates an idea of equality which further 

 experience separates into two ideas equality of things and 

 equality of relations. While organic, and more especially 

 animal forms, occasionally exhibit this perfection of likeness 

 out of which the notion of simple equality arises, they more 

 frequently exhibit only that kind of likeness which we call 

 similar Hi/ and which is really compound equality. For 

 the similarity of two creatures of the same species but of 

 different sizes, is of the same nature as the similarity of two 

 geometrical figures. In either case, any two parts of the 

 one bear the same ratio to one another, as the homologous 

 parts of the other. Given in any species, the proportions 

 found to exist among the bones, and we may, and zoologists 

 do, predict from any one, the dimensions of the rest ; just as, 

 when knowing the proportions subsisting among the parts 

 of a geometrical figure, we may, from the length of one, 

 calculate the others. And if, in the case of similar geome 

 trical figures, the similarity can be established only by 

 proving exactness of proportion among the homologous 

 parts; if we express this relation between two parts in the 

 one, and the corresponding parts in the other, by the for 

 mula A is to B as a is to b ; if we otherwise write this, A 

 to B= to b ; if, consequently, the fact we prove is that 

 the relation of A to B equals the relation of a to b : then 



