CLA SXIFICA TIOX. 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 riot 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 sav 



Curve of equal curvature = curve of greatest area. 



