The Collaborative International Dictionary of English v.0.48:

Petition \Pe*ti"tion\, n. [F. p['e]tition, L. petitio, fr.
   petere, petitum, to beg, ask, seek; perh. akin to E. feather,
   or find.]
   1. A prayer; a supplication; an imploration; an entreaty;
      especially, a request of a solemn or formal kind; a prayer
      to the Supreme Being, or to a person of superior power,
      rank, or authority; also, a single clause in such a
      prayer.
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            A house of prayer and petition for thy people. --1
                                                  Macc. vii. 37.
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            This last petition heard of all her prayer.
                                                  --Dryden.
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   2. A formal written request addressed to an official person,
      or to an organized body, having power to grant it.
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   3. Specifically: (Law), A request to government, in either of
      its branches, for the granting of a particular grace or
      right, or for the legislature to take a specific action;
      -- in distinction from a memorial, which calls certain
      facts to mind. The petition may be signed by one or any
      number of persons.
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   4. The written document containing a petition (senses 1 or
      2).
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   Petition of right (Law), a petition to obtain possession or
      restitution of property, either real or personal, from the
      Crown, which suggests such a title as controverts the
      title of the Crown, grounded on facts disclosed in the
      petition itself. --Mozley & W.

   The Petition of Right (Eng. Hist.), the parliamentary
      declaration of the rights of the people, assented to by
      Charles I.
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Bouvier's Law Dictionary, Revised 6th Ed (1856):

PETITION OF RIGHT, Eng. law. When the crown is in possession, or any title
is vested in it which is claimed by a subject, as no suit can be brought
against the king, the subject is allowed to file in chancery a petition of
right to the king.
     2. This is in the, nature of an action against a subject, in which the
petitioner sets out his right to that which is demanded by him, and prays
the king to do him right and justice; and, upon a due and lawful trial of
the right, to make him restitution. It is called a petition of right,
because the king is bound of right to answer it, and let the matter therein
contained be determined in a legal way, in like manner as causes between
subject and subject. The petition is presented to the king, who subscribes
it, with these words, soit droit fait al partie, and thereupon it is
delivered to the chancellor to be executed according to law. Coke's Entr.
419, 422 b; Mitf. Eq. Pl. 30, 31; Coop. Eq. Pl. 22, 23.