The single objects are called Individuals, because the division cannot be carried farther. The highest class is technically the Summum Genus, or Genus generalissimum; the next highest class to any species is the Proximum Genus; the lowest group before you descend to individuals is the Infima Species, or Species specialissima.
The attribute or attributes whereby a species is distinguished from other species of the same genus, is called its differentia or differentiæ. The various species of houses are differentiated by their several uses, dwelling-house, town-house, ware-house, public-house. Poetry is a species of Fine Art, its differentia being the use of metrical language as its instrument.
A lower class, indicated by the name of its higher class qualified by adjectives or adjective phrases expressing its differential property or properties, is said to be described per genus et differentiam. Examples: "Black-bird," "note-book," "clever man," "man of Kent," "eminent British painter of marine subjects". By giving a combination of attributes common to him with nobody else, we may narrow down the application of a name to an individual: "The Commander-in-Chief of the British forces at the battle of Waterloo".
Other attributes of classes as divided and defined, have received technical names.
An attribute common to all the individuals of a class, found in that class only, and following from the essential or defining attributes, though not included among them, is called a Proprium.
An attribute that belongs to some, but not to all, or that belongs to all, but is not a necessary consequence of the essential attributes, is called an Accident.
The clearest examples of Propria are found in mathematical figures. Thus, the defining property of an equilateral triangle is the equality of the sides: the equality of the angles is a proprium. That the three angles of a triangle are together equal to two right angles is a proprium, true of all triangles, and deducible from the essential properties of a triangle.
Outside Mathematics, it is not easy to find propria that satisfy the three conditions of the definition. It is a useful exercise of the wits to try for such. Educability—an example of the proprium in mediæval text-books—is common to men, and results from man's essential constitution; but it is not peculiar; other animals are educable. That man cooks his food is probably a genuine proprium.