What is the mathematical intuition behind àl-jàbrà? The term algebra comes from the arabic term àl-jàbrà that means "to force", "to restore". Over centuries mathematicians, in east and west, celebrate by this term mathematical disciplines.

What is the mathematical intuition behind this term ("to force", "to restore") and modern
derivatives such as in abstract algebra and algebraic geometry?


Append found the following information:
In Arabic, al- is the definite article "the." The first noun in the
title is jebr "reunion of broken parts," from the verb jabara "to
reunite, to consolidate." The second noun is from the verb qabala,
with meanings that include "to place in front of, to balance, to
oppose, to set equal." Together the two nouns describe some of the
manipulations so common in algebra: combining like terms, transposing
a term to the opposite side of an equation, setting two quantities
equal, etc. Because the original Arabic title was so long, and because
it was in Arabic, Europeans soon shortened it. The result was algeber
or something phonetically similar, which then took on the meanings of
both nouns and eventually acquired its modern sense...
 A: From Wikipedia (or rather, its citation of "The Arabic Hegemony" by Carl Boyer): 

The word al-jabr presumably meant something like "restoration" or "completion" and seems to refer to the transposition of subtracted terms to the other side of an equation.

Other uses of the word algebra or its root simply stem from this original use (just like things involving the word geometry no longer actually have to be about measuring the earth).
A: 
"The word “algebra”—al jebr in Arabic—was first used by Mohammed of
  Kharizm, who taught mathematics in Baghdad during the ninth century.
  The word may be roughly translated as “reunion,” and describes his
  method for collecting the terms of an equation in order to solve it.
  It is an amusing fact that the word “algebra” was first used in Europe
  in quite another context. In Spain barbers were called algebristas, or
  bonesetters (they reunited broken bones), because medieval barbers did
  bonesetting and bloodletting as a sideline to their usual business.
  The origin of the word clearly reflects the actual context of algebra
  at that time, for it was mainly concerned with ways of solving
  equations. In fact, Omar Khayyam, who is best remembered for his
  brilliant verses on wine, song, love, and friendship which are
  collected in the Rubaiyat—but who was also a great
  mathematician—explicitly defined algebra as the science of solving
  equations."

(it's from the book - "A Book of Abstact Algebra" by Charles C. Pinter).
