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I am looking for a specific book on non-Euclidean geometry that I read in my undergraduate years.

The unique characteristic of this book is that the first part of the book started by re-proving in modern notation the entirety of the first book of Euclid's Elements – given that all the geometry up until Euclid used the parallel postulate would be common to Euclidean and non-Euclidean geometries. The second part of the book treats a few equivalent formulations of the parallel postulate and the ways in which non-Euclidean geometry modifies them.

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    $\begingroup$ Do you remember when you read it? Knowing the year, one can eliminate some options. For example Geometry: Euclid and Beyond is quite recent, while The elements of non-Euclidean geometry is much more older. $\endgroup$
    – user6530
    Commented Oct 15, 2022 at 15:01
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    $\begingroup$ I have the feeling that you might be referring to Marvin J. Greenberg's "Euclideand and Non-Euclidean Geometries: Development and History": bibotu.com/books/2013/History%20and%20Philosophy%20of%20Science/… $\endgroup$
    – José Hdz. Stgo.
    Commented Oct 16, 2022 at 17:36
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    $\begingroup$ @JoséHdz.Stgo. You are absolutely correct! This is precisely the book I was looking for! Do you want to make your comment an official answer to give you credit? $\endgroup$
    – ltcomdata
    Commented Nov 4, 2022 at 5:40
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    $\begingroup$ @user6530 : Thank you for the reference of Geometry: Euclid and Beyond. It looks like a very worthwhile read! $\endgroup$
    – ltcomdata
    Commented Nov 4, 2022 at 6:01
  • $\begingroup$ ltcomdata: I have done so! Hope you "accept" it later on... $\endgroup$
    – José Hdz. Stgo.
    Commented Nov 18, 2022 at 23:39

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The book is none other than Marvin Jay Greenberg's "Euclidean and Non-Euclidean Geometries: Development and History" (the fourth edition of which is available wherever fine books are sold).

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