Source : Webster's Revised Unabridged Dictionary (1913)

Convince \Con*vince"\, v. t. [imp. & p. p. {Convinced}; p. pr. &
   vb. n. {Convincing}.] [L. convincere, -victum, to refute,
   prove; con- + vincere to conquer. See {Victor}, and cf.
   {Convict}.]
   1. To overpower; to overcome; to subdue or master. [Obs.]

            His two chamberlains Will I with wine and wassail so
            convince That memory, the warder of the brain, Shall
            be a fume.                            --Shak.

   2. To overcome by argument; to force to yield assent to
      truth; to satisfy by proof.

            Such convincing proofs and assurances of it as might
            enable them to convince others.       --Atterbury.

   3. To confute; to prove the fallacy of. [Obs.]

            God never wrought miracle to convince atheism,
            because his ordinary works convince it. --Bacon.

   4. To prove guilty; to convict. [Obs.]

            Which of you convinceth me of sin?    --John viii.
                                                  46.

            Seek not to convince me of a crime Which I can ne'er
            repent, nor you can pardon.           --Dryden.

   Syn: To persuade; satisfy; convict.

   Usage: To {Convince}, {persuade}. To convince is an act of
          the understanding; to persuade, of the will or
          feelings. The one is effected by argument, the other
          by motives. There are cases, however, in which
          persuade may seem to be used in reference only to the
          assent of the understanding; as when we say, I am
          persuaded it is so; I can not persuade myself of the
          fact. But in such instances there is usually or always
          a degree of awakened feeling which has had its share
          in producing the assent of the understanding.

Source : WordNet®

convincing
     adj 1: causing one to believe the truth of something; "a convincing
            story"; "a convincing manner" [ant: {unconvincing}]
     2: capable of convincing or persuading; "a convincing argument"