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 for Normal equations
From The Collaborative International Dictionary of English v.0.48 :

  Normal \Nor"mal\ (n[^o]r"mal), a. [L. normalis, fr. norma rule,
     pattern, carpenter's square; prob. akin to noscere to know;
     cf. Gr. gnw`rimos well known, gnw`mwn gnomon, also,
     carpenter's square: cf. F. normal. See Known, and cf.
     Abnormal, Enormous.]
     [1913 Webster]
     1. According to an established norm, rule, or principle;
        conformed to a type, standard, or regular form; performing
        the proper functions; not abnormal; regular; natural;
        [1913 Webster]
              Deviations from the normal type.      --Hallam.
        [1913 Webster]
     2. (Geom.) According to a square or rule; perpendicular;
        forming a right angle; as, a line normal to the base.
        Specifically: Of or pertaining to a normal.
        [1913 Webster]
     3. (Chem.) Standard; original; exact; typical. Specifically:
        (a) (Quantitative Analysis) Denoting a solution of such
            strength that every cubic centimeter contains the same
            number of milligrams of the element in question as the
            number of its molecular weight.
        (b) (Chem.) Denoting certain hypothetical compounds, as
            acids from which the real acids are obtained by
            dehydration; thus, normal sulphuric acid and normal
            nitric acid are respectively S(OH)6, and N(OH)5.
        (c) (Organ. Chem.) Denoting that series of hydrocarbons in
            which no carbon atom is bound to more than two other
            carbon atoms; as, normal pentane, hexane, etc. Cf.
            [1913 Webster]
     Normal equations (Method of Least Squares), a set of
        equations of the first degree equal in number to the
        number of unknown quantities, and derived from the
        observations by a specified process. The solution of the
        normal equations gives the most probable values of the
        unknown quantities.
     Normal group (Geol.), a group of rocks taken as a standard.
     Normal place (of a planet or comet) (Astron.), the apparent
        place in the heavens of a planet or comet at a specified
        time, the place having been determined by a considerable
        number of observations, extending perhaps over many days,
        and so combined that the accidental errors of observation
        have largely balanced each other.
     Normal school, a school whose methods of instruction are to
        serve as a model for imitation; an institution for the
        training of teachers.
        [1913 Webster]
     Syn: Normal, Regular, Ordinary.
     Usage: Regular and ordinary are popular terms of well-known
            signification; normal has now a more specific sense,
            arising out of its use in science. A thing is normal,
            or in its normal state, when strictly conformed to
            those principles of its constitution which mark its
            species or to the standard of a healthy and natural
            condition. It is abnormal when it departs from those
            [1913 Webster]

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