Like which saint wrote them??
It's good to add this, otherwise you might get many glib answers saying: The Holy Spirit wrote these prayers. It's true, and worth remembering; however there is nothing wrong in knowing through which Saint these hymns were penned, if such information is known (a number of hymns are anonymous).
I think all Orthodox Christians would recognize these prayers, as they are part of the Daily Office, and are included in most Church services. In fact, I have just sung both these prayers at Vespers and will do again tomorrow at Divine Liturgy, God-willing.
Well, when I say "these prayers" I refer to the main part of them, not the entire quote.
O Most Holy Trinity, have mercy on us! Lord, cleanse us from our sins! Master, pardon our transgressions! Holy One, visit and heal our infirmities for Thy name's sake.
...is one prayer.
Lord, have mercy! (3 times)
....is another, and....
O Christ God, bless the food and drink of Thy servants, for Thou art holy, always, now and ever and unto ages of ages. Amen.
....is a third. Obviously this last one relates to the prayer before breakfast, and is not used part of the Daily Office etc.
The prayer "O Most-Holy Trinity" is ascribed to Mark the Monk, from the 5th century. I think.
More honorable than the Cherubim, and more glorious beyond compare than the Seraphim: without defilement you gave birth to God the Word: true Theotokos, we magnify you.
Is ascribed to St Cosmas the Hymnographer (8th century). Later, two lines were added to the beginning of the prayer:
"It is truly right to bless thee, O Theotokos,
ever blessed, and most pure, and the Mother of our God.."
These were revealed to a monk on Mt Athos by the Angel Gabriel. Because of this, the prayer is sometimes known as the Axion Estin in Greek or Dostóino yesť in Slavonic (both meaning "It is truly meet*...")
I am welcome to correction on the above.
here being an old way of saying "fitting" or "right."