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The term ajr is in this context synonymous with faridah in its specific sense of "dower" (mahr): see surah {2}, note [224].
As pointed out in several places (see, in particular, note [32] on 4:25 ), Islam does not countenance any form of concubinage, and categorically prohibits sexual relations between a man and a woman unless they are lawfully married to one another. In this respect, the only difference between a "free" woman and a slave is that whereas the former must receive a dower from her husband, no such obligation is imposed on a man who marries his rightfully owned slave (lit., "one whom his right hand possesses") - that is, a woman taken captive in a "holy war" (jihad ) waged in defence of the Faith or of liberty (note [167] on 2:190 and note [72] on 8:67 ) - : for, in such a case, the freedom conferred upon the bride by the very act of marriage is considered to be equivalent to a dower.
The relevant clause reads, literally, "if she offered herself as a gift (in wahabat nafsaha) to the Prophet". Most of the classical commentators take this to mean "without demanding or expecting a dower (mahr)", which, as far as ordinary Muslims are concerned, is an essential item in a marriage agreement (cf. 4:4 and {24}, and the corresponding notes; also surah {2}, note [224]).
This was - in addition to his not being allowed to divorce any of his wives (see verse {52} below) - a further restriction imposed on the Prophet in the matter of marriage: whereas all other Muslims are free to marry any of their paternal or maternal cousins, the Prophet was allowed to marry only such from among them as had proved their strong, early attachment to Islam by having accompanied him on his exodus (the hijrah) from Mecca to Medina. In the opinion of Baghawi - an opinion obviously based on the corresponding, ancient Arabian usage - the term "daughters of thy paternal uncles and aunts" comprises in this context not only the actual paternal cousins but, in general, all women of the tribe of Quraysh, to which Muhammad's father belonged, while the term "daughters of thy maternal uncles and aunts" comprises all women of his mother's tribe, the Banu Zuhrah.
The above parenthetic sentence refers to the previously revealed, general laws relating to marriage (see 2:221 , {4:3-4} and {19-25}, as well as the corresponding notes; also surah {2}, note {224}).
See footnote for 4:3.
This ruling was exclusively for the Prophet (which he never took advantage of), but Muslims have to pay a dowry to their wives. Some women did offer themselves to the Prophet (ﷺ) in marriage, but he declined.
This introduces no new exemption or privilege. Verses 50-52 merely declare the points in which, on account of the special circumstances (see n. 3706 above), the Prophet's marriages differed from those of ordinary Muslims. This is considered under four heads, which we shall examine in the four notes following.
Head 1. Marriage with dower (iv. 4): this is the universal Muslim marriage. The difference in the Prophet's case was that there was no limitation to the number of four (iv. 3), and women of the People of the Book (v. 6) were not among his wives, but only Believers. These points are not expressly mentioned here, but are inferred by his actual practice. Obviously women who are expected to instruct other women in Islam must be Muslims.
Head 2. Women Prisoners of War: the same remark as in the last note.
Head 3. These are first cousins, and not within the Prohibited Degrees of Marriage (see iv. 23-24). These are specially mentioned here by way of limitation. None of them could marry the Prophet unless she had performed the Hijrat with him.
Head 4. A believing woman who gives herself to the Prophet: obviously this case, like the last, is only applicable to the Prophet, and it is hedged round with the limitation that the Prophet considers it suitable.
The ordinary law of Muslim marriage will be found chiefly in ii. 221-235, iv. 19-25, iv. 34-35, and v. 6.
The words "this only for thee ... right hands possess" are parenthetical, and the words "in order that..." connect on with the previous clauses beginning with "O Prophet, We have made lawful .... wishes to wed her".
Marriage is an important relationship not only in our physical life, but in our moral and spiritual life, and its effects extend not only to the parties themselves but to children and future generations, A number of special problems arise according to special circumstances. Every man and woman must seriously consider all sides of the question and must do the best in his or her power to temper instincts and inclinations with wisdom and guidance from Allah. Allah wishes to make every one's path easy, for He is indeed "Oft-Forgiving, Most Merciful".