Talk:Euclid

What are the first 4 postulates?

See Euclid's Elements. - dcljr

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I could not verify the name "Euclides". Everybody seems to call him "Euclid of Alexandria", and the original Greek name was Eukleides. AxelBoldt 20:39 Feb 23, 2003 (UTC)

Deleted text

In the edit I just made (to Euclid), I removed the following text:

[[Janos Bolyai]] (and probably [[Carl Friedrich Gauss]] before him) realized that its negation leads to consistent [[non-euclidean geometries]], which were later developed by [[Nikolai Ivanovich Lobachevsky|Lobachevsky]], [[Riemann]] and [[Jules-Henri Poincaré|Poincaré]].

Along with some other stuff about the Parallel postulate that's nearly duplicated in Euclid's Elements. I was planning to merge this information into the latter article, where I think most of the discussion of mathematical issues related to the Elements should go, when I noticed that the former one (on the PP) and Non-euclidean geometry#History both talk about these matters, as well. Someone should try to separate out what info belongs in what article and insert links in place of non-germaine text in each, as I have done in this article.

I also excised:

In addition to a treatment of plane geometry, including proofs of the [[Pythagorean theorem]] and a version of the more general [[law of cosines]], Euclid's book also contains the beginnings of elementary [[number theory]], such as the notion of divisibility, the [[greatest common divisor]] and the [[Euclidean algorithm]] to determine it, and the infinity of [[prime number|prime numbers]]. Later chapters deal with three-dimensional geometry and the [[platonic solid]]s. The book also contains proofs that the [[area]] of a [[circle]] is [[proportional]] to the square of its [[radius]], and that the [[volume]] of a [[sphere]] is proportional to the cube of its radius.

Since it clearly belongs in the Elements article.

- dcljr 10:02, 14 Aug 2004 (UTC) (<code> tags changed to <tt> by dcljr on 03:35, 5 Sep 2004 (UTC) — no other changes)

I think a little of the first sentence should be included in the Euclid article. Brutannica 22:39, 14 Aug 2004 (UTC)

Keep Euclid and Elements separate

There has been some discussion in Talk:Euclid's Elements about possibly merging the articles Euclid and Euclid's Elements. I say that's a bad idea.

The Euclid article should be used for biographical information (and there is a little more of this than is here) and some discussion of his general importance in math and science, as is currently touched on in this article. What should be added here is information about Euclid's other works (4 other extant works and 4 lost ones). See, for example, this paper I wrote in college (http://www.obkb.com/dcljr/euclid.html) and the references therein.

Euclid's Elements, OTOH, should be mainly about the contents, structure and impact of that work. Again, see my paper for ideas. (I don't have much about the impact of the Elements — I didn't have time to get into it!) I'll write on some of this when I feel inspired, but I don't want to end up just recapitulating my paper here. ;) (But feel free to use it as a source. Just put a link to it if you use it to a significant degree.)

- dcljr 10:23, 14 Aug 2004 (UTC)

I agree. Euclid should be about the man and should include an overview of his works. The Elements article should be more in-depth. Thanks for the clean-up! Brutannica 22:41, 14 Aug 2004 (UTC)

Algebra

I removed the mention of algebra in:

The text also includes sections on algebra, number theory, and three-dimensional geometry.

There is much debate as to whether Euclid actually had anything like algebra in mind when he presented the techniques sometimes referred to as geometrical algebra (I wish there were an article there!). Certainly, there is no symbolic algebra or explicit solving of equations anywhere in the work. It's only in retrospect (looking back from our post-Renaissance perspective) that one can see in the purely geometrical ideas of the work premonitions of "modern" algebraic notions. Simply put: I think it's misleading to say the work contains algebra. - dcljr 03:53, 5 Sep 2004 (UTC)

Should it be replaced with "geometrical algebra" then? Brutannica 02:07, 8 Sep 2004 (UTC)