CLASSIFICATION. 377 



either in intension or extension ; in the former respect 

 it is more than the Genus as containing one more quality, 

 the Difference : in the latter respect it is less than the 

 Genus as containing only a portion of the group consti- 

 tuting the Genus. We may say then, with Aristotle, that 

 in one sense the Genus is in the Species, namely in inten- 

 sion, and in another sense the Species is in the Genus, 

 namely in extension. The Difference, it is evident, can 

 be interpreted in intension only. 



A Property is a quality which belongs to the whole of 

 a class, but does not enter into the definition of that class. 

 Thus if it be a generic property it belongs to every indi- 

 vidual object contained in the genus. It is a property of 

 the genus Parallelogram that the opposite angles are 

 equal. If we regard a Rectangle as a species of parallel- 

 ogram, the difference being that one angle is a right angle, 

 it follows as a specific property that all the angles are 

 right angles. Though a property in the strict logical 

 sense must belong to each of the objects included in the 

 class of which it is a property, it may or may not belong 

 to other objects. The property of having the opposite 

 angles equal may belong to many figures besides parallel- 

 ograms, for instance, regular hexagons. It is a property 

 of the circle that all triangles constructed upon the dia- 

 meter with the apex upon the circumference are right 

 angled triangles, and vice versa, all closed curves of 

 which this is true must be circles. We might with ad- 

 vantage distinguish properties which thus belong to a 

 class, and only to that class, as peculiar properties. They 

 enable us to make statements in the form of simple iden- 

 tities (vol. i. p. 44). Thus we know it to be a peculiar 

 property of the circle that for a given length of perimeter 

 it encloses a greater area than any other possible curve ; 

 hence we may say 



Curve of equal curvature = curve of greatest area. 



