The definite article has developed from the Old English demonstrative pronoun that and in some cases it has preserved this demonstrative meaning in Modern English: nothing of the (that) kind, under the (those) circumstances.
These two articles are related to other determiners in the following way: the = this, that, the same; a (an) = some, any, such.
THE INDEFINITE AND THE DEFINITE ARTICLES COMPARED The indefinite article is used before a noun in the singular to show that the object denoted by the noun is one of a class. Therefore it may be qualified as a classifying article.
The indefinite article is generally used with countable nouns. As a rule, it is not used with nouns of abstract or material meaning.
The noun used with the indefinite article may have a non-restrictive attribute. Such an attribute describes the person or thing denoted by the noun by giving additional information about it. This information only narrows the class to which the object belongs.
She was wearing a necklace of red beads (one of such neck-laces). A young girl of about sixteen wants to see you (no mote information is given to distinguish her from all other girls). Father gave me a ten-dollar bill (but not a pound). The President holds office during a term of four years (but not for life).
The main cases of the use of the indefinite article are these:
(1) With a predicative noun, when the speaker refers the object to a certain class.
My husband is a sailor.
(2) With nouns in other functions, when the speaker states that the object denoted by the 'noun is one of a class (один, какой-то, некий).
A lady is calling you up, Sir.
(3) When a noun serves as a typical example of a class: what is said of one representative of a class can be applied to any representative of the same class; here the article has the meaning of “every”.
A policeman is always a policeman.
(4) When the indefinite article preserves its original numerical meaning of "one":
A week or two passed.
