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"Repräsentation der Imaginären der Plangeometrie" by Sophus Lie

  1. Oct 18, 2014 #1
    I am looking for the translation in English of the "Representation der Imaginiren der Plangeometrie" by Sophus Lie. If any one knows where can I find it I will very much appreciate it. Thank you.
  2. jcsd
  3. Oct 18, 2014 #2
    I speak fluent german, so I believe I have detected a mistake in your title. If you mean something with imaginary like the root of one then you the german word is imaginaer!? Or is Imaginiren just a accident of yours?
  4. Oct 18, 2014 #3
    It should be "Imaginaren". That is the closest I can type on the forum as it does not have the required fonts. I also looked up the message from the library which sent me the original paper in German, and they have also used the spelling in the title. It does represent the root of (minus) one. Thanks.
  5. Oct 18, 2014 #4
    I used the ae to represent the a with the dots over.
  6. Oct 18, 2014 #5


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    The paper was published by Crelle's Journal in 1869. It is available in the internet, in German, at least...

  7. Oct 18, 2014 #6
    Thanks. As I mentioned I also have the original in German, however as I am labouring through the translation in English, I am not sure that I will be able to grasp all the nuances, hence the request.
  8. Oct 18, 2014 #7


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    As you can see in Crelle's, the exact title of that paper is:

    'Ueber eine Darstellung des imaginären in der Geometrie'. It's somewhat different from what you mentioned...
  9. Oct 18, 2014 #8
    This is quite interesting. I looked up the paper you have mentioned and compared with the paper I received from University of Oslo. The title of the paper from University of Oslo is what I had posted earlier, which is different than the paper available at http://gdz.sub.uni-goettingen.de/. Also the text seems to be a little different. So may be there are different versions.
  10. Oct 18, 2014 #9


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    According to this biographical sketch of Sophus Lie:


    The paper entitled, "Representation der Imaginaeren der Plangeometrie" was Lie's first published work, appearing in 1869. The original paper was published privately by Lie himself and circulated to the Collegium Academicum at Christiania with an application for a travelling fellowship. Any other versions, such as that which appeared in Crelle's Journal, would probably have been edited from the original. The original paper should be in Lie's Collected Works, which were published with state assistance after Lie's death.
  11. Oct 18, 2014 #10


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    I see... The word 'representation' sounds a little weird in German... A clear 'Fremdwort'...
  12. Oct 23, 2014 #11


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    Various websites, including Google books, list the publication as "Repräsentation der Imaginären der Plangeometrie", a construction you would not use in German today, but all words are German. I changed the thread title as this really improves google search results.

    If your keyboard does not support "ä" (note the dots), "ae" is a valid replacement, "a" is wrong (that is a completely different letter).
  13. Oct 26, 2014 #12
    The original article is available at http://www.ijspace.org/Download/Download.html [Broken] for reference.
    Last edited by a moderator: May 7, 2017
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