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This is more of a question for Arabic stack exchange if there was such a thing, but anyways:

The OED suggests as the etymology of the term "algebra"

Etymology: < post-classical Latin algebra algebraic computation (12th or 13th cent.), surgical treatment of fractures (c1300) < Arabic al-jabr < al the + jabr restoration (of anything which is missing, lost, out of place, or lacking), reunion of broken parts, (hence specifically) surgical treatment of fractures < jabara to restore, to reunite, (hence specifically in a medical context) to set broken bones.

The Arabic term al-jabr probably originally referred specifically to the method of solving quadratic equations by completing the square

However, more likely etymology seems to be

Proto-Semitic * gabr- "strong man" (or related word) > Arabic jabara "force, compel" > "set [broken bones]" > "reunite broken parts, restore [anything which is missing, lost, out of place, or lacking]" > Arabic al-jabr "the reunion of broken parts, the restoration [of anything which is missing, lost, out of place, or lacking]" > ...

Is there any clear answer on which is correct? I.e., was the meaning of restoration or the meaning of setting and reuniting broken bones more basic?

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  • English algebra is from Latin algebra which is from Arabic al-jabr. Perhaps the question of the etymology of al-jabr is not suited for ELU.
    – GEdgar
    Mar 24, 2021 at 0:09
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    it is faintly relevant to English to know whether the term "al-jabr" as used by early Arab mathematicians more basically meant "restoration of something missing" or "reunion of broken bones/parts." Somewhat different metaphors with the latter being more vivid and referring to fusion or union.
    – Colin
    Mar 24, 2021 at 0:20
  • There are votes to close this question, but I think one of the answers provides significant additional information beyond the depth provided by the OED, and is therefore a valuable addition to the EL&U library. I'm therefore voting to leave this question open. Apr 1, 2021 at 23:59

2 Answers 2

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The answer in my book, Mathematics A Curious History p.96 by Joel Levy confirms your general understanding.

The word "algebra" comes from the title of a book by the medieval Arab mathematician Al-Kitab-mukhtasar fi hisab al-have w'al-muqabal, which was written around 825CE - the Arabic word al-jabr became "aljebra". The title is usually translated as "The Compendious Book on Calculation by Completion and Balancing", although the last phrase can also be translated as "Reunion and Opposition".

In other words, according to Levy, al-jabr meanscompletion or reunion. He goes on to explain:-

<...the book> gives step-by-step instructions about how to solve algebraic problems through the two steps mentioned in the title: reunion (or completion) and opposition (or balancing), today known as transposition and cancellation.

To trace the etymology of al-jabr further is interesting, but goes beyond the scope English language usage: The name of the method of finding unknowns by the manipulation of equations came from the name of al-Kwarizmi's book.

On the other hand, the actual algebraic method goes back much earlier. To find the area of a field in the Nile delta with a view to taxing it required carrying out something like the instruction

multiply the length by the breadth to find the size/area.

To all intents and purposes, this was algebra Egypt-style. They even found a complicated way of calculating a field in a semicircular bend in the Nile. So at least a shadow of π was already there, leading by the time of Eratosthenes a pretty respectable stab at calculating the circumference of Earth.

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    Your paragraph about semitic and European languages is both irrelevant to the question, and factually wrong. Semitic language are not largely without vowels. The word for 'book' is not "ktb": that is a transliteration of the way it is conventionally written, but the word is kitab.
    – Colin Fine
    Mar 24, 2021 at 14:42
  • Yes, you are right that there are some what we would call vowel sounds in arabic, not least the alif in kitab. I shall correct this. There is no written vowel sound between the 'Ta' and the 'baa' at the beginning. And I do agree that I went off at a tangent. So I shall remove it. Thank you.
    – Tuffy
    Mar 24, 2021 at 16:52
  • you miss my point. Like many people, you are confusing the language with the script that is used to write it. Alif is not a vowel sound: alif is a letter. A letter is not a sound. Arabic has plenty of vowel sounds, like almost every other language. The fact that many of them are not explicitly written in the standard Arabic script, is not a property of the Arabic language, but of the way it is cusomarily written.
    – Colin Fine
    Mar 24, 2021 at 17:15
  • Obviously I expressed myself badly. i did briefly learn enough Arabic to read at least printed text, but obviously "a little learning ... ".
    – Tuffy
    Mar 24, 2021 at 17:25
  • I'm sorry if I was a bit heavy with you, @Tuffy: it's very common nowadays for people to think they are talking about a language when they're actually only talking about how the language is written.
    – Colin Fine
    Mar 24, 2021 at 18:07
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It comes from (part of) the name of the fellow, Al-jebra, who first wrote out the method of balancing mathematical terms. The use of balancing then went to medical usage for bone setting. Others may have done it first but getting into print in 1550s is tough to beat.

Here is one source but I have seen plenty more all about the same. "formal mathematics; the analysis of equations; the art of reasoning about quantitative relations by the aid of a compact and highly systematized notation," 1550s, from Medieval Latin algebra, from Arabic "al-mukhtasar fi hisab al-jabr wa al-muqabala" ("the compendium on calculation by restoring and balancing"), the title of the famous 9c. treatise on equations by Baghdad mathematician Abu Ja'far Muhammad ibn Musa al-Khwarizmi

etymonline.com/search?q=algebra

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    No, you are probably thinking of the term "algorithm" which is derived from the name al-Khwarizmi
    – Colin
    Mar 24, 2021 at 0:44
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    Indeed. This answer is quite simply wrong.
    – Colin Fine
    Mar 24, 2021 at 14:37
  • @CFine; Thanks for providing the source of your research.
    – Elliot
    Mar 25, 2021 at 0:27

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