Algebra equivalent to Euclid’s Elements?

[mathwhizpro]

I want to get a copy of historical Algebra literature that essentially the equivalent of Euclid’s Elements for Algebra. Does anyone have any recommendations?

 

[jedishrfu]

Prof Keith Devlin in his blog mentions Al Kwarizmi as the author of one of the earliest books on Algebra:

https://profkeithdevlin.org/2011/12/13/when-did-algebra-begin/

Here's a translated version of the book that you can buy:

http://www.saqibooks.com/book/al-khwarizmi/

and you might find more links here in my google search using the terms: " al-khwarizmi book "

https://www.google.com/search?q=al-...hrome.0.0l6.2062j0j8&sourceid=chrome&ie=UTF-8

 

[Stephen Tashi]

I want to get a copy of historical Algebra literature that essentially the equivalent of Euclid’s Elements for Algebra.

What do you mean by "equivalent"? Are you looking for a textbook of algebra that follows the same step-by-step intuitive style of presenting algebra as Euclid used in his Elements to present geometry and number theory? I don't think such a textbook exists for abstract alglebra. Algebra is a different ball game than plane geometry.

 

[e-pie]

Might be of historical value as it is written by one of the greatest mathematicians.

Here Elements of Algebra Leonard Euler

https://books.google.co.in/books/about/Elements_of_Algebra.html?id=X8yv0sj4_1YC&redir_esc=y

Also Diophantus' Arithmatica.
English version.
https://www.amazon.com/dp/0387906908/?tag=pfamazon01-20

Other parts may be available in the internet.

 

[mathwhizpro]

Thank you for the suggestions!

 

[brainpushups]

I like the Euler suggestion. One issue with the search for a book analogous with Euclid is that, though Euclid imposed the logical structure, many of the results were well-known from earlier mathematicians.

Though Arab scholars did systematize algebra a bit, Al Kwarizmi's book (according to Katz – I have not seen the text) is more of a practical manual rather than a theoretical treatise as the Elements is. Further, I believe all of the justification for the algebraic relations were still proven using geometry.

You could look at works of Francois Viete who made steps toward more abstract symbolism. Descartes also moved things forward with the introduction of analytic geometry. Beyond this and we're probably up to Euler. But, in a sense, if you want something that is analogous to Euclid for algebra it is probably best to find a modern algebra text because all of these earlier works are akin to geometrical works that came before Euclid (attempted) to rigorously systematize it. It's just that none of them (to my knowledge) survived, probably, at least in part, due to the success of the Elements. Reading Al Kwarizimi or Viete would be like reading Thales or Theaetetus instead of Euclid.