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The mathematical application of the substantives جبر and مقابلة will appear from the following extracts.
1. A marginal note on one of the first leaves of the Oxford manuscript lays down the following distinction:
من اما الجبر وهو اتمام كل شيء ناقص بما يتم من غير جنسه والمقابلة من المفاعلة وهو المواجهة ولهذا يقال للمصلي القبلة اذا واجهها فلما صار لهذا الحساب جزيل عمله جبر الناقص [بما] نقص منه وزيادة مثل ما جبر به الناقص علي الجنس المقابل لتقابل الزيادة مثلما جبر به الناقص وكثر الاستعمال في ذلك فسمي جبرا ومقابلة لانه يجبر كل شيء بما نقص منه و تقابل الاجناس بعضها الي بعض ...... وقد صارت المقابلة ايضا تعرف [عند] اهل الحساب حذف المقادير المتشابهة
“Jebr is the restoration of anything defective by means of what is complete of another kind. Mokābalah, a noun of action of the third conjugation, is the facing a thing: whence it is applied to one praying, who turns his face towards the kiblah. In this branch of calculation, the method commonly employed is the restoring of something defective in its deficiency, and the adding of an amount equal to this restoration to the other side, so as to make the completion (on the one side) and this addition (on the other side) to face (or to balance) one another. As this method is frequently resorted to, it has been named jebr and mokābalah (or Restoring and Balancing), since here every thing is made complete if it is deficient, and the opposite sides are made to balance one another. . . . . . . Mathematicians also take
