Algebra/Al-Jaber الجبر/ الجابر

Discussion in 'العربية (Arabic)' started by almufadado, Feb 12, 2010.

  1. almufadado

    almufadado Senior Member

    Earth
    Português de Portugal
    Is Al-Jaber /Al-Jabr a name or a meaning ?

    I found this clearly as a name :

    وزارة الخارجية ـ المملكة العربية السعودية
    Ministério dos Negócios estrangeiros da Arábia Saudita
    http://www.google.pt/url?sa=t&sourc...ytGrCQ&usg=AFQjCNHTydGrib_tuSe7xgt3KD7scjfwkg

    I know this is also some sort of praise to the person.

    Yet, the word comes associated to "algebra" (portuguese: álgebra) ...
    wikipedia
    So, would some one please, tell me what would be the meaning and the right way to write it in roman alphabet ?
     
  2. clevermizo Moderator

    St. Louis, MO
    English (USA), Spanish
    What does that mean? Names almost always have meaning, despite how obscure they are.

    Indeed الجابر [al-jaaber] seems to be a name. I looked it up and it appears it means a "bonesetter" which is an old profession before there were chiropractors and orthopedists. So the name is related to a profession (like "Smith" in English).


    Indeed, "algebra" is taken from الجَبر (al-jabr) which means "compensation," I think. It refers to the fact that you're "compensating for" or using symbols (like "x,y,a,b,c") to represent data/numbers/quantities.

    There is no one right way to write Arabic in Latin characters. You can write it however it makes sense to you. Considering you speak Portuguese, I would transliterate the noun الجبر as [al-jabr] (this is where "algebra" comes from). The name or the profession الجابر I would transliterate as [al-jaabir] formally on the forum, but informally as Al-Jaber.

    The second [a] in al-jabr is short; the second [a] in al-Jaber ("jaabir") is long and more like 'a' in English [cat].

    You will find that when it comes to writing people's names in Latin characters, they end up getting romanized many different ways. I'm sure "Al-Jaber" is no different.
     
  3. almufadado

    almufadado Senior Member

    Earth
    Português de Portugal
    Shokran !
    ! شكرا
     
  4. origumi Senior Member

    Hebrew
    The term was coined by the mathematician Muhammad ibn Musa al-Khwarizmi, c. 825, along with some of his seminal works in this area. He meant "transposition" I think, not "compensation".
     
  5. Forero Senior Member

    Houston, Texas, USA
    USA English
    I have always heard that it referred both to reducing fractures and to reducing fractions.
     
  6. Faylasoof Senior Member

    Plato's Republic
    English (UK) & Urdu (Luckhnow), Hindi
    The term is indeed from al-Khwarizmi’s seminal work entitled:

    الكتاب المختصر في حساب الجبر والمقابلة

    The title is translated in a number of ways, e.g.

    The Concise Book about Calculation by Transposition and Reduction

    Where, “transposition” translates الجبر and المقابلة is “reduction”.

    Another is:

    The Compendious Book on Calculation by Completion and Balancing

    Where, “completion” translates الجبر and المقابلة is “balancing”.

    These are not literal meanings of course.

    The meanings of الجبر used in this context are: restoration, completion; but transposition is also used in some places.

    In this work everything is written out in words. You won’t see an equation as we know it!! But it was for the sophistication of the method that this work became famous as it provided general solutions by introducing the method of “transposition, reduction and balancing".

    Historians are still debating exactly what the terms الجبر and المقابلة really meant here. The usual interpretation is that the word الجبر most likely meant "restoration" or "completion", as it seems to refer to the act of transposing subtracted terms to the other side of an equation; while the word المقابلة appears to be "reduction" or "balancing" by cancellation of like terms on opposite sides of the equation.

    You can either read online or download the book (with an English translation) here.
     
  7. Mahaodeh Senior Member

    Arabic and English
    I have no idea why historians would be in adebate!! This is obviously the closest translation (literal, of course). I would understand, however, if mathamaticians would be in a debate :).

    The two words do not need to be opposites, I think that muqabala refers to the idea of equations (which were not yet exact) where you put one set of numbers or variables "facing" the other one and they are both equal.

    Al jabr, as I understand it, relates to filling the gaps created by the Xs and Ys and Zs of the equation. Naturally, he didn't think of them as variables. But when one considers the reason he started with the book (don't know if it was still the reason by the time he finished it though :), you know, inventing a new science and all) which was to find an accurate method for judges to calculate exactly how much each person would inherit when his next of kin dies (ex. the wife 1 quarter, the mother 1 third, the brother XXXX, depending on who is left behind to share) it seems to make perfect sense.
     
  8. Faylasoof Senior Member

    Plato's Republic
    English (UK) & Urdu (Luckhnow), Hindi
    The historians I refer to are mathematicians – historians of mathematics! They may be "historians" but are qualified in mathematics to a high level in order to appreciate what they are researching. Heavens help us if general historians or, say, those of hadith literature started to write about al-Khawrizmi’s highly specialized and technical work!!

    As to the general and specific meanings of the terms:
    جَبر = force, compulsion, violence; setting of bones, reduction of a fracture.

    جبر and جابر were used in poetry with reference to the idea of bone setting:

    لا يجبر الناس عظاما أنت كاسره
    ولا يهيضون عظاما أنت جابره

    But in mathematical terminology, usually, جَبر = Addition of something for the purpose of reparation / restoration.

    الجَبر و المُقابَلَۃ = addition for restoration and compensative subtraction - later shortened to restoration and compensation. But by some, الجبر is translated in this context as completion or transposition.

    These definitions of الجَبر (and المُقابَلَۃ) were arrived at by later mathematicians / scholars as these are the operations he performed repeatedly to arrive at solutions. Al-Khwarizmi himself never provided any explanation of using either terms.

    Unfortunately we can’t discuss these points here in any detail as they are beyond the scope of this forum. But just to clarify, I’ll merely say this. Neither did al-Khawarizmi use the Arabic equivalents of x, y and z notations (they were a much later introduction; in fact he used geometrical methods like completing the square to illustrate his methodology though the equation was there from the start despite the fact you don't see it - it is written out in prose) nor did he “invent” what we call algebra, nor were his reasons entirely utilitarian. The title of his work certainly gave the field the name it now carries because of its huge impact due to the rigorous methodology and copious examples it presented, but what we call algebra was known to the “ancients”. Babylonian mathematicians were familiar with algebraic calculations, as were those from ancient India and Greece, esp. Diophantus ofAlexandria who seems to have initiated the use of symbols to represent unknown quantities.
     

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