Page:The Algebra of Mohammed Ben Musa (1831).djvu/195

 The verb جبر is not likewise used, when in an equation an integer is substituted for a fractional power of the unknown quantity: the proper expression for this is either the second or fourth conjugation of, or the second كمل, of تمّ.

The word مقابلة mokābalah is a noun of action of the verb قبل to be in front of a thing, which in the third conjugation is used in a reciprocal sense of two objects being opposite one another or standing face to face; and in the transitive sense of putting two things face to face, of confronting or comparing two things with one another.

In mathematical language it is employed to express the comparison between positive and negative terms in a compound quantity, and the reduction subsequent to such comparison. Thus $$100+10x-10x+x^2$$ is reduced to $$100+x^2$$ بعد ان قابلنا به “after we have made a comparison.”

When applied to equations, it signifies, to take away such quantities as are the same and equal on both sides. Thus the direction for reducing $$x^2+x=x^2+4$$ to $$x=4$$ will be expressed by قابل.

In either application the verb requires the preposition ب before a pronoun implying the entire equation or compound quantity, within which the comparison and subsequent reduction is to take place.

The verb قابل is not likewise used, when the reduction of an equation is to be performed by means of a division: the proper term for this operation being ردّ.