January 1 - The Circumcision of Christ and Mary, Mother of God (the Octave of Christmas)

The propers of the feast (without the readings), from the Vatican Gelasian Sacramentary, aka Old Gelasian (Vatican, Bibliotheca Apostolica, Reg. lat. 316/Paris, B.N., 7193, 41-56):

ITEM IN OCTABAS DOMINI. KALENDAS IANUARIAS
(Liber I.VIIII)

Deus qui bonis nati saluatoris diem celebrare concedis octauum, fac, quaesumus, nos esse perpetua diuinitate munere, cuius sumus carnali conmercio reparati: per.

Omnipotens sempiterne deus, qui unigenito tuo nouam creaturam nos tibi esse fecisti, custodi opera misericordiae tuae et ab omnibus nos maculis uetustatis emunda, ut per auxilium gratiae tuae in illius inueniamur forma, in quo tecum est nostra substantia: per.

(secreta) Praesta, quaesumus, domine, ut per hanc munera, qui domini Iesu Christi arcanae natiuitatis mysterio gerimus, purificate mentes intellegentiam consequamur: per dominum.

Uere dignum: per Christum dominum nostrum. Cuius hodie octauas nati celebrantes tua, domine, mirabilia ueneramur, quia qui peperit, et mater et uirgo est; qui natus est, et infans et deus est. Merito caeli locuti Sunt, angeli gratulati, pastores laetati, magi mutati, regis turbati, paruoli gloriosa passione coronati. Lacta, mater, cybum nostrum, lacta panem de caelo uenientem, in praesepio positum uelut piorum cybaria iumentorum. Illic namque agnouit bos possessorem suum et asinus praesepium domini sui, circumcisio scilicet et praeputium. Quod etiam saluator et dominus noster a Symione susceptus in templo plenissimae dignatus est adimplere. Et ideo cum angelis et archangelis.

(post communionem) Praesta, quaesumus, domine, ut guod saluatoris nostri iterata solempnitate percipimus, perpetuae nobis redemptionis conferat medicinam: per.

(ad populum) Omnipotens sempiterne deus, qui tuae mensae participes a diabolico iubes abstinere conuiuio, da, quaesumus, plebi tuae, ut gustum mortiferae profanitatis abiecto puris mentibus ad aepulas aeternae salutis accedat: per.

From the Angoulême Sacramentary (B.N. Lat. 816):

XII. KALENDAS IANVARII. OCTABAS DOMINI AD SANCTAM MARIAM
(Liber I. VIIII)

Deus qui bonis nati saluatoris diem celebrare concedis octauum, fac, quaesumus, nos esse perpetua diuinitate munere, cuius sumus carnali conmercio reparati: per.

Omnipotens sempiterne deus, qui unigenito tuo nouam creaturam nos tibi esse fecisti, custodi opera misericordiae tuae et ab omnibus nos maculis uetustatis emunda, ut per auxilium gratiae tuae in illius inueniamur forma, in quo tecum est nostra substantia: per.

(secreta) Praesta, quaesumus, domine, ut per hanc munera, qui domini Iesu Christi arcanae natiuitatis mysterio gerimus, purificate mentes intellegentiam consequamur: per dominum.

Uere dignum: per Christum dominum nostrum. Cuius hodie octauas nati celebrantes tua, domine, mirabilia ueneramur, quia qui peperit, et mater et uirgo est; qui natus est, et infans et deus est. Merito caeli locuti Sunt, angeli gratulati, pastores laetati, magi mutati, regis turbati, paruoli gloriosa passione coronati. Lacta, mater, cybum nostrum, lacta panem de caelo uenientem, in praesepio positum uelut piorum cybaria iumentorum. Illic namque agnouit bos possessorem suum et asinus praesepium domini sui, circumcisio scilicet et praeputium. Quod etiam saluator et dominus noster a Symione susceptus in templo plenissimae dignatus est adimplere. Et ideo cum angelis et archangelis.

(post communionem) Praesta, quaesumus, domine, ut guod saluatoris nostri iterata solempnitate percipimus, perpetuae nobis redemptionis conferat medicinam: per.

(ad populum) Omnipotens sempiterne deus, qui tuae mensae participes a diabolico iubes abstinere conuiuio, da, quaesumus, plebi tuae, ut gustum mortiferae profanitatis abiecto puris mentibus ad aepulas aeternae salutis accedat: per.

From the Cambrai Hadrianum (Bibl. Municipale MS 164):

MENSE IANUARIO IN OCTABAS DOMINI AD SANCTAM MARIAM AD MARTYRES

Deus, qui salutis aeternae beatae mariae virginitate fecunda humano generi praemia praestitisti, tribue quaesumus, ut ipsam pro nobis intercedere sentiamus, per quam meruimus auctorem vitae suscipere. Per dominum.

Super oblata. Muneribus nostris quaesumus, domine, precibusque susceptis, et caelestibus nos munda mysteriis et clementer exaudi. Per dominum.

Ad completa. Haec nos communio domine purget a crimine, et caelestibus remediis faciat esse consortes. Per.

From the 1962 Missale Romanum:

IN OCTAVA NATIVITATIS DOMINI
I classis
Statio ad S. Mariam trans Tiberim

Oratio: Deus, qui salutis aeternae, beatae Mariae virginitate fecunda, humano generi praemia praestitisti: tribue, quaesumus; ut ipsam pro nobis intercedere sentiamus, per quam meruimus auctorem vitae suscipere, Dominum nostrum Iesum Christum, Filium tuum: Qui tecum vivit et regnat in unitate.

Secreta: Muneribus nostris, qusesumus, Domine, precibusque susceptis: et caelestibus nos munda mysteriis, et clementer exaudi. Per Dominum nostrum Iesum Christum.

(Praefatio et Communicantes de Nativitate)

Postcommunio: Haec nos communio, Domine, purget a crimine: et, intercedente beata Virgine Dei Genetrice Maria, caelestis remedii faciat esse consortes. Per eundem Dominum nostrum Iesum Christum, Filium tuum: Qui tecum vivitet regnat in unitate.

From the 2002 Missale Romanum:

SOLLEMNITAS SANCTAE DEI GENITRICIS MARIAE IN OCTAVA NATIVITATIS DOMINI
Deus, qui salutis aeternae, beatae Mariae virginitate fecunda, humano generi praemia praestitisti, tribue, quaesumus, ut ipsam pro nobis intercedere sentiamus, per quam meruimus Filium tuum auctorem vitae suscipere...

Super Oblata: Deus, qui bona cuncta inchoas benignus et perficis, da nobis, de sollemnitate sanctae Dei Genetricis laetantibus, sicut de initiis tuae gratiae gloriamur, ita de perfectione gaudere.

Postcommunio: Sumpsimus, Domine, laeti sacramenta caelestia: praesta, quaesumus, ut ad vitam nobis proficient sempiternam, qui beatam semper Virginem Mariam Filii tui Genetricem et Ecclesiae Matrem profiteri gloriamur...

January 1 - Solemnity of the Blessed Virgin Mary, the Mother of God (aka Octave of the Nativity, Feast of the Circumcision of Christ)

1.) OLD ROMAN LECTIONARY

(Luke 2:21)

At that time, when eight days were completed for His circumcision, His name was called Jesus, which was called by the angel before He was conceived in the womb.

2.) NEW ROMAN LECTIONARY

(Luke 2:16-21)

The shepherds went in haste and found Mary and Joseph, and the Child lying in the manger. And when they saw, they made known the word which had been spoken to them about this Child, and all who heard it marveled at what the shepherds said. But Mary treasured up all these things and pondered them in her heart. And the shepherds returned, glorifying and praising God for all they had heard and seen, just as had been told them.

And when eight days were completed for His circumcision, His name was called Jesus, which was called by the angel before He was conceived in the womb.

3.) MOZARABIC LECTIONARY

(Luke 2:21-40)

At that time, when eight days were completed for His circumcision, His name was called Jesus, which was called by the angel before He was conceived in the womb.
And when the days of their purification according to the law of Moses were fulfilled, they brought Him to Jerusalem to present Him to the Lord (as it is written in the Law of the Lord: 'Every male who opens the womb shall be called holy to the Lord'), and to offer a sacrifice according to that which is said in the Law of the Lord: a pair of turtledoves, or two young pigeons.

And behold there was a man in Jerusalem whose name was Simeon, and this man was righteous and devout, waiting for the consolation of Israel; and the Holy Spirit was upon him. And he had received an answer from the Holy Spirit that that he would not see death before he had seen the Lord's Christ. And he came by the Spirit into the temple, and when His parents brought in the child Jesus to do for Him according to the custom of the Law, and he took Him into his arms and blessed God and said, "Now you are dismissing your servant, O Lord, in peace, according to your word; for my eyes have seen your salvation, which you have prepared before the face of all peoples; a light for revelation to the Nations, and the glory of your people Israel." And His father and mother were marveling at the things which were spoken concerning Him.

And Simeon blessed them, and said to Mary His mother, "Behold, this child is set for the falling and the rising of many in Israel and for a sign of contradiction (and a sword will pierce your own soul also), that the thoughts of many hearts may be revealed."

And here was also a prophetess, Anna the daughter of Phanuel, of the tribe of Asher. She was very old in her many days and had lived with her husband for seven years from her virginity; and she was a widow for eighty four years, who did not depart from the temple, worshipping night and day with fastings and prayers. And coming up to them at that very hour she began to give thanks to God and to speak about Him to all who were waiting for the redemption of Israel.

And when they had performed all things according to the law of the Lord, they returned to Galilee, to their own town, Nazareth. And the child grew and became strong in spirit, filled with wisdom; and the grace of God was upon Him.

4.) BYZANTINE LECTIONARY

(Luke 2:20-21, 40-52)

The shepherds returned, glorifying and praising God for all they had heard and seen, just as had been told them. And when eight days were completed for the circumcision of the child, He was named Jesus, which was called by the angel before He was conceived in the womb. And the child grew and became strong in spirit, filled with wisdom; and the grace of God was upon Him.

And His parents went every year to Jerusalem at the feast of the Passover. And when He was twelve years old, they went up to Jerusalem according to the custom of the feast. And when they had fulfilled the days, as they were returning, the boy Jesus stayed behind in Jerusalem, and Joseph and His mother did not know, but supposing Him to be in the company, they went a day's journey, and were searching for Him among their relatives and among their acquaintances; and when they did not find Him they turned back again to Jerusalem, seeking Him.

And it happened that after three days they found Him in the temple sitting in the midst of the teachers, both listening to them and questioning them, and all who heard Him were amazed at His understanding and His answers.

And when they saw Him, they were astonished, and his mother said to Him, "Son, why have you done this to us? Behold, your father and I were looking for you in sorrow." And He said to them, "Why were you looking for me? Did you not know that I must be in my Father's house?" And they did not understand the saying which He spoke to them.

And He went down with them, and came to Nazareth, and was subject to them, and His mother kept all these sayings in her heart. And Jesus increased in wisdom and stature, and in favor with God and men.