Hello,
I thank you all very much indeed for your detailed and informative replies. It may be the right time to disclose the day of purchase: My grandfather's sister Ludmila (who is the girl in the pictures) bought her Douglas at Arnošt Dietz (Praha II., Novomlýnská 9) on April 2, 1926 (after 5 p.m., according to her diaries). What you've written drives me to the conclusion that it must have been a new machine (or if it had, purely theoretically, been used, certainly it hadn't been worn out too much, thus not influencing the price substantially). She was just twenty-two by then, so it isn't quite clear to me how she could afford buying a motorcycle on her clerical salary.
To answer Wilfried's question, the pictures above were taken on April 4 and 3 (the latter in the backyard of this building:
http://www.mff.cuni.cz/toUTF8.en/fakulta/budovy/f.htm ).
May I ask another question? In a Czech 1927 price list, I can see that electric light for Douglas E.W. was delivered optionally (increasing the price by some 11 %), but can't find it in older ones. Was that already available in early 1926 (or was it a sort of trade-off to stay with a carbide one)? (I am asking because its reliability was to play a critical role later.)
Another reason why friends of mine have suggested it had been a second-hand bike was a relatively high number of defects she was facing. If anybody is interested, I'll try to post their full account here.