The question has arisen, mainly because of the lack of the Typikon of the Great Church (Violakis, TME 1888, p. 58 and p. 54) to include it, should Δόξα σοι Κύριε be chanted before the Gospel reading?
See J. Goar, Euchologion, 1730 (second edition
Euchologion - Goar - 1730), p. 56. Here it clearly states that it is chanted before the Gospel however, curious enough, no mention is made of it being chanted after the Gospel reading - most likely because it is assumed common knowledge.
I would defer to the common practice that exists almost universally in the Orthodox Church of chanting it before and after the Gospel reading. One only need look at the modern practice of the Ecumenical Patriarchate today at the Patriarchal Cathedral which includes the chanting of it both before and after the Gospel testifying to an older accepted tradition of the Great Church.
Curiously enough one hears in the modern practice of the Church of Greece, at least at it's Metropolitan Cathedral and at other Athens parishes, the chanting of Δόξα σοι Κύριε before the priest or deacons' exclamation of Πρόσχωμεν before the Gospel reading.
It is most likely the case that the omission of this rubric in the TME is a case of assumed knowledge of the divine services and their common elements by the authors of the 1888 edition. There are many areas in the Typikon both in the 1888 edition and in previous editions where common elements are left out, partially described and assumed to be known by the reader. For instance to speak of the previous editions of Konstantinos' Typika, they remain silent on the subject not including detailed rubrics for the Gospel reading.
