copy / specimen
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copy
A single item or individual copy from a set of similar things, especially books, magazines, or works of art.
Ich habe mir ein vom Autor signiertes Exemplar des Romans gekauft.
I bought a copy of the novel signed by the author.
'Das Exemplar' (copy/specimen) is a loanword from Latin. This explains its often slightly formal or scientific sound, especially compared with more everyday words.
Von diesem Manuskript existiert nur noch ein einziges Exemplar.
Only one single copy of this manuscript still exists.
The context reveals the meaning: if it is about books or newspapers, a copy is meant. In connection with animals or plants in science, an individual or specimen is meant. If it refers to a person, it is colloquial and often ironic.
Ich suche noch ein Exemplar dieser seltenen Briefmarke.
I'm still looking for a copy of this rare stamp.
When 'Exemplar' (character/specimen) is used for a person, it is always colloquial and has a particular tone. It can be admiring ('Prachtexemplar' — fine specimen), but it is often slightly mocking and emphasizes that the person is unusual.
Er ist wirklich ein seltsames Exemplar, aber irgendwie sympathisch.
He really is a strange character, but somehow likable.
book
'das Buch' and 'das Exemplar' can both have to do with books. 'Buch' names the work itself or the object that you read. 'Exemplar' means a single item or an individual copy of a work. You use 'Exemplar' especially when there are several identical or similar items, for example in a library or at a publishing house. The confusion arises because an 'Exemplar' can often be a book. But not every 'Exemplar' is a book, and 'Exemplar' emphasizes the individual copy, not the content.
Wegen der großen Nachfrage hat die Bibliothek ein zweites Exemplar bestellt.
Because of the high demand, the library ordered a second copy.
Meine Mutter liest abends ein Buch über Kräuter.
My mother reads a book about herbs in the evenings.