I am trying to access the following work online, but I'm having no luck finding it:
Krüger, Dietrich. 1959. "Die Bildersprache des Demosthenes." Ph.D., Classics, Göttingen.
Any idea where I could access it?
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Any online resources may be unlikely for a dissertation that old, but there are some possibilities. Try these.
The Classics department at Göttingen.
The university library at Göttingen.
Proquest, which was founded as "University Microfilms", published a lot of dissertations in that era. This may be a longshot for a German dissertation, but it was used by many universities to "publish" dissertations.
The author is unlikely to still be alive, but it is just possible that one of his students is and can provide a copy, or at least an abstract. If you have a citation of the work, the author who cites it may have a copy.
A good research librarian at an academic library can probably help a lot in such a search.
I'd always expect the university library where the dissertation was done to have at least one exemplar in their archives.
The national library is also supposed to have at least one exemplar of every book published in Germany.
For searching books within Germany, the university libraries of several German Länder have a common online catalgoue (Gemeinsamer Verbundkatalog, GVK), see also https://www.bszgbv.de/ which also include Baden-Württemberg and Saarland.
GVK lists 3 exemplars of the dissertation at the Göttingen University library: https://kxp.k10plus.de/DB=2.1/PPNSET?PPN=146113365
https://www.worldcat.org/ is an online catalogue covering even more libraries from around the globe.
In addition to the references mentioned in the answers (national library, library of the university) I recommend the Karlsruher Virtual Cataloge (Karlsruher Virtueller Katalog, KVK) http://kvk.bibliothek.kit.edu. This cataloge composes all important catalogs of scientific and national libraries in Germany (and optionally also many catalogs of foreign countries).
Searching there for your book results in 5 locations (don't get irritated - some results shown are duplicates):
2 copies in the Deutsche Nationalbibliothek in Leipzig and Frankfurt
1 copy and 1 mircofiche in the library of the Freie Universität Berlin
1 copy in the Bayerische Staatsbibliothek München
2 copies and 1 microfiche in the Niedersächsische Staats- und Universitätsbibliothek Göttingen
Most of these copies can also be accessed via interlibrary loan.