One of the earliest references that has relevance to the notion of reception appears in the Thesaurus of Antiochus of Athens, written in the second half of the second century C.E. Although it appears to have been applied only to conjunctions (not aspects), we find mention of placement in the dignity of another planet being used to indicate transferal of power, and mutual reception of sign and house being used to indicate 'reciprocal mastership':
30. Concerning Participation
There is communion whenever two planets should be present upon one zoidion or should border upon it, while it should happen to be the house of one, the exaltation of the other.
32. Concerning Reciprocal Mastership
Stars are said to be masters of each other whenever the exaltation of the one and the house of the other should be the zoidia in which the stars happen to be.
33. Concerning the Ruler
A star is said to be the ruler whenever it should have more relationships of rulership in some one of the zoidia. I mean relationships of house, exaltation, trigon, boundary, phase or configuration.
The latter comment is in keeping with Ptolemy's instruction that the planet which holds the greatest influence over any specific place (such as the degree of an eclipse) is partly decided by the strongest rulership over the area by sign, exaltation, triplicity and term. 
The extent to which this kind of analysis influenced practical astrology in the classical period is difficult to assess at this point where research is ongoing. The determination of a governing 'ruler' obviously had tremendous significance and has remained an important consideration throughout the history of astrology, employed in a variety of techniques, such as establishing the lord of the geniture or hyleg. There are other scattered examples of the principle of reception being used in ancient texts such as that of Dorotheus, who tells us in book II of Carmen Astrologicum, (18v6) that a conjunction between the Sun and Saturn is damaging for the father, unless it occurs within the domicile of the Sun or Saturn. (Dorotheus also gives us a good sense of the use of dignity and disposition by describing how planets act in other planets' domiciles at 11.23).
As the later references show, at least by the Arabic period the ruling planet, as the one which was receiving the other into its dignity, was considered to 'take up' the influence of the planet which was aspecting it from its dignities. The word dispositor is applied to the dignity ruler, meaning 'the one who gives a final settlement', (to dispose of something means to settle it, to bring an end to it, or to arrange it into order). Through the use of this term we can see that, whilst the dispositing planet holds a position of control, it is also bound by a responsibility to accept the influence that is committed to it, to acknowledge it, and to do something with it. The state of acceptance is implicit in the word 'receiving'. We can also see very clearly from the Bonatus explanation, that where a planet is in aspect with a planet that is located in its own dignities, it "commits and gives its own disposition and nature and virtue to it", even, as Bonatus tells us, "if they were enemies".
It is worth including a mention to the astrological meaning of the related term 'disposition', which derives from the same root as the word dispose and dispositor but is used in a different sense. In general terms 'disposition' means something akin to character, temperament, or influence ('she had a sweet disposition', etc), and astrologically a planet 'committing its disposition to another' is used to demonstrate a planet impressing its influence upon another planet (the word itself, being drawn from an association with 'disposing', can be used to suggest the act of bestowing or transferring to another, just as the word 'influence' does). In aspects, the planet that is 'committing its disposition' is the swifter moving planet that is most readily forming the aspect, and the slower planet that is being applied to is the 'receiver of the disposition'.
So we see that there are two ways in which a planet can receive the influence of another. The first is by aspect, where the swifter planet (often referred to as the 'pushing planet' in classical works) brings its influence to the planet is it applying to. The second, by reception, introduces an element of attendance, a return of interest and virtue, and a bond against the planets harming each other in the process. In reception a dispositor accepts an application from a submissive planet in the same way that a king is obliged to be sympathetic to his own subjects and is expected to be representative of their will - and in granting the request can add all the benefits of his own position into the equation. Of course the submissive planet also offers its support to the needs of its ruler, as a subject must support the requests of his own king. Both benefit from the fact that they are involved in a connected hierarchy of power that binds them towards acknowledging and supporting each other. And after the contact, when the received planet makes a future aspect, it will be carrying or holding on to the power that was invested in it by its dispositor.
The four references below are chosen because each, in its own generation, has been highly influential. Though they show minor variances, they also demonstrate a continuance of theory that can be traced from our earliest detailed sources to the works of Lilly.
Abu Ma'shar (known in the west as Albumasar) 787-886 C.E.
From The Abbreviation of the Introduction to Astrology, Chapter Three, verses 52-53.
ARHAT Publications, 1994; edited and translated by Charles Burnett.
 'Reception' is when a planet (A) applies to a planet (B) from the house of the planet (B) to which it applies or from its (B's) exaltation, term, triplicity or decan: then it (B) receives it (A). Or the receiver of the application (B) is in the house of the pushing planet (A) or in its other shares which we have mentioned before, then it (A) receives it (B).
 The strongest of these is the Lord of the house or of the exaltation. The Lord of the term or triplicity or decan are weak unless two or more of them are joined.
 One of them may receive the other also by aspect without application, although the reception by application is stronger.
In other words:
Reception occurs when two planets are applying to aspect and one of them is in a position where the other has dignity by sign or exaltation. It can also occur with the lesser dignities but it is a weak reception unless two or more of the dignities are involved.
A milder form of reception exists where the two planets are in aspect according to their signs but the planets are not in the state of 'application'. 
Al Biruni 973-1048 AD
From The Book of Instruction in the Elements of the Art of Astrology, 1029. v.507, p.312 p.214
R. Ramsay Wright translation, London, 1934. Available from Ascella Reprints.
Reception. When an inferior planet arrives in one of the dignities proper to a superior one, and makes known to it the relation thus established, there is an exchange of compliments such as 'your servant' or 'your neighbour'. If further the superior planet happens to be in a situation proper to the inferior one, mutual reception takes place, and this is fortified, the richer the situation is in dignities, especially when the aspects indicate no enmity nor malevolence. When reception does not take place the result is negative.
In other words:
Reception occurs when a planet arrives in the dignities of another. The need for aspectual contact is implicit in the phrase "and makes known to it the relation thus established". Mutual reception occurs if the other planet is also in the first planet's dignities. The greater the dignities, the greater the strength of the reception, especially where the aspects are friendly. Lack of reception hinders perfection.
Abraham Ibn Ezra (also known as Avenezra) c. 1092 - 1167 AD
From The Beginning of Wisdom, Chapter VII, p.214.
The John Hopkins Studies in Romance Literatures and Languages, extra vol XIV; edited by Raphael Levy and Francisco Cantera. Oxford University Press, 1939. Available from Ascella Reprints.
Reception is noticed when a planet enters into conjunction or into aspect with a planet which is the master of its house, the master of the house of its honour, the master of the house of its triplicity, its limit, or its face, and it receives that planet. Likewise when one planet enters into conjunction with another planet, and the latter is in a house which communicates force or [is] in the house of honour, that again is reception; on the other hand, if it is in the house of its triplicity, or in its limit, or in its face, it will not receive a perfect reception. If two influences join together, the triplicity with the limit or the face, and the trine aspect with the sextile, that is also a reception. Again that is so if they should be in the degrees of signs which are equal in their ascent. The lucky planet receives the lucky one because their nature is straight. Mars and Saturn receive one another if they are in conjunction or in sextile or trine aspect, but not in the other aspects. The reception may be strong, moderate or weak. The strong reception always applies to the Moon with the Sun, because the former receives it from any sign and because its beams come from the Sun; from the opposition, however, it will be in pain and sorrow; if it should be in a sign lacking all power, then there are two receptions, as in the case of Mercury when it receives the planet in the sign of Virgo, because that is its house and the house of its honour; therefore that reception is perfect. The reception of the house is moderate. The reception of the triplicity, or of the limit, or of the face, is weak.
Liberality means that each of two planets is in the house of its companion, or in the house of its honour, or in any of its influences, and, even though they do not enter into conjunction or aspect with each other, still there will be reception between them.
In other words:
Reception occurs when a planet applies to an aspect with a planet that rules the sign or any of the essential dignities in which it is located, or when the applying planet is in its own house or exaltation, or in two of its minor dignities, or one of its minor dignities where a trine or sextile aspect is involved or an antiscia relationship. Planets in their correct phase
offer receptions to each other because of the directness of their motion. But Mars and Saturn can receive each other only by conjunction, sextile or trine, not the other aspects. The reception can be strong, moderate or weak. The Sun always offers a reception to the Moon because the Moon's light comes from the Sun, but where the Moon is in opposition to the Sun it is damaging unless it has dignity in the sign it is in.
Mercury offers a very strong reception to planets in Virgo because it receives the planet into its sign of rulership and exaltation. Reception by sign is moderate, but reception by triplicity, term or face is weak.
If planets are mutually placed in any of each other's dignities, they offer reception to each other even if there is no aspect between them. 
Bonatus c. 1210 - 1295 AD
From Liber Astronomiae (1550 Edition): Treatise 3 Part 2, Chapter XIII: On the Prohibition of Conjunction, and Why Sometimes Matters are Not Perfected. Col. 142-143.
Translated by Benjamin Dykes PhD. In preparation for publication.
And it is said that if some planet is joined with the Lord of the sign in which it is (or with the Lord of the exaltation of the same sign, or with the Lord of the term or triplicity, or decan [face]), whether by body or by aspect, that the planet who is the Lord of the sign (or some dignity of it), commits and gives its own disposition and nature and virtue to it.
It is for instance true, if it is joined with the Lord of the domicile or exaltation or with the Lord of two of the other minor dignities (namely with the Lord of the term and triplicity, or with the Lord of the term and the decan, or with the Lord of the decan and the triplicity). But if it is joined only with the Lord of the term, or with the Lord of the triplicity, or with the Lord of the decan, [then] the Lord of one of those dignities or terms - by only one - does not receive him, because they are not of so much virtue that one of them alone can make reception without the help of another. Whence a planet who receives another from these dignities, as I said, commits its own disposition to it, even if they were enemies, from whatever aspect or by conjunction.
For example, the Moon was in the third degree of Aries, and Mars (who is the Lord of Aries) was in the eighth degree of Gemini (or Cancer or Leo in front of her; or Aquarius, or Capricorn, or Sagittarius behind her): so the Moon was being received by Mars by aspect, and he was receiving her from his own domicile, and committed to her his own virtue and disposition.
Or the Moon was in the said third degree of Aries, and the Sun (who is the Lord of the exaltation of Aries) was in the eighth or ninth degree of Gemini (or Cancer or Leo in front of her), or in the eighth or ninth degree of Aquarius (or Capricorn or Sagittarius behind her): so the Moon was joined to the Sun by aspect, and he received her from his own exaltation, and committed his own fortitude to her.
Or the Moon was in the said third degree of Aries, and Jupiter (who is the Lord of the first term of Aries, and is even the Lord of the triplicity of Aries), was in the fifth degree of Gemini (or Cancer or Leo in front of her), or in the 5th degree of Aquarius (or Capricorn or Sagittarius behind her): so the Moon was joined to Jupiter by aspect, and he received her from his own term and triplicity, and committed his own virtue and disposition to her, just as if he received her by domicile or exaltation. This is the commission or giving of virtue and disposition of the planets.
But if the Moon was joining Saturn, who is a ruler of the Aries triplicity but does not have any other dignity there, he would not have received her: because he does not have more than one of the minor dignities in that place, by which it is not possible to perfect a reception.
In other words:
When a planet is in aspect with the ruler of the sign or exaltation, or of two of the minor dignities of term, triplicity, or face, the ruler of the dignity commits its own disposition and virtue to it, even if they are normally destructive to each other. If it aspects the ruler of only one of the minor dignities, it is not received, because these dignities are not strong enough to make reception without additional support.
I am grateful to Benjamin Dykes for providing the translation of the Bonatus passage. Ben has recently completed a translation of Abu Ma'shar's Flowers of Astrology and is currently engaged in the translation of works by Haly Abenragel, Albubater and Bonatus. He is also the author of Using Medieval Astrology Part I; Universal Astrology. Details of his works can be found on his website at http://www.bendykes.com
Notes & References:
The Thesaurus of Antiochus of Athens, Part I, verses 32-33. Project Hindsight Greek Track, Volume II-B, 1993; translated by Robert Schmidt, edited by Robert Hand.
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See for example, Tetrabiblos, II.7. F.E. Robbins translation, (Loeb Classical Library 1940).
It has often been claimed that Ptolemy described reception in his Tetrabiblos, where he mentions the increased reliability of friendly aspects when they come about by 'exchange'. His intended meaning has been disputed by various commentators however and cannot be relied upon as offering anything of great relevance to this discussion.
The passages that are usually referred to, and the disputes concerning them, are detailed below:
IV.5 (p.397) : Marriages for the most part are lasting when in both the genitures the luminaries happen to be in harmonious aspect, that is, in trine or in sextile to one another, and particularly when this comes about by exchange.
Robbins argues against the earlier assertion of Bouché-Leclerq that this implies mutual reception since the signs of the Sun and Moon are not in a traditional aspect. However, other authors have explained that mutual reception may occur between other dignities so this need not be a prohibiting factor. However, the Robert Schmidt Project Hindsight translation uses the word 'alternation' instead of exchange, and comments in a footnote that this is a common mathematical term for a manipulation of a proportion.
IV.7 (pp413-415) : (With regard to friendly dispositions and the opposite) … for if they chance to fall in the same signs of the zodiac, or if they exchange places.
The Schmidt translation suggests that this means where the Sun in one person's nativity occupies the degree of the Moon in the other person's (and vice versa). The same argument may of course be applied to the first quote.
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See Lilly's Use of Reception in Horary, by Deborah Houlding.
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Abu Ma'shar makes clear his distinction between 'aspect' and 'application' in chapter 2, v.10-13. Planets 'aspect' each other according to the relationship of the signs. If the two signs are able to 'behold' each other, all planets within those signs are capable of a platick (loose) relationship with each other.
"Application in longitude occurs only if a planet which is light in movement goes towards a planet which is slower than it, when it is in conjunction with or aspecting it. As long as the degrees of the light planet are less than the degrees of the heavy planet which it is in conjunction with or aspecting, then it is 'going into application with it'."
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5] || That is, separating from a union with the Sun but out of the sun beams - also called lucky, fortunate or rejoicing planets elsewhere. This is related to the benefits assigned to being oriental or occidental.
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The late 8th century Arabic astrologer, Omar of Tiberius, remarks upon this reception of the Moon by the Sun:
"Moreover, the Moon is received by the Sun because she receives light from the Sun from every house; but if she is received from opposition, she loses half of the reception. But if the Sun receives [the Moon] in his own domicile or exaltation, there will be two receptions."
Three Books on Nativities, translated by Robert Hand, PH :Latin Track XIV, section 6 p.33.
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Although Ezra's definition seems unnecessarily complicated, many of his points are reproduced elsewhere. Besides the comment found in Omar's work (previous footnote), consider this how closely it is mirrored by the content of a footnote that accompanies the ARHAT translation of Abu Ma'shar's Introduction to Astrology:
Note to sections 52-54: It is clear from this section that 'Reception' has various degrees of strength. A further statement on this is found in Adelard's Latin translation, corresponding to a section in the Great Introduction, [of Abu Ma'shar] as follows: "in generosity (ie reception) some are found stronger, some weaker, some of medium strength. The greatest generosity is between the Sun and the Moon. For the Moon takes from the Sun in any sign, except opposition, which is harming. Therefore, when the Moon comes into a sign in which the Sun enjoys some dignity, its benefit is doubled: for one gift is from the sign, the other from the nature. Mercury, when another planet is in Virgo, provides two benefits for it. But a medium benefit is what each star receives from another, either from its house or from its exaltation or its decan or its triplicity or its term. If two of these are given, it will be greater. Whatever is other than the aforesaid, will be weak".
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© Deborah Houlding. September 2005