I was not able to find much information with regards to either prayer, however, it seems as though St. Francis wrote a prayer before the Crucifix. Whether the contemporary version was adapted from this prototype or whether it is an entirely distinct prayer, I am uncertain. Here is the link for the prayer attributed to St. Francis: americancatholic.org/e-News/FriarJack/fj013008.asp
Eternal Rest is based on the apocryphal 2 Esdras 2:34-35 (named now 4 Esdras),
2 Esdras 2:34-35:
34 And therefore I say unto you, O ye heathen, that hear and understand, look for your Shepherd, he shall give you everlasting rest; for he is nigh at hand, that shall come in the end of the world.
35 Be ready to the reward of the kingdom, for the everlasting light shall shine upon you for evermore.
The phrase “Réquiem ætérnam dona eis, Dómine: et lux perpétua lúceat eis.” is not a direct quote from 4 Esdras. So who actually wrote that text or made it part of the Propers of the Missa defunctorum, I couldn’t tell you.
I can make an educated guess however. The Catholic Encyclopedia says
The date of the adoption of this Introit is not well known, but it is found in the so-called Antiphonary of St. Gregory Come of Albino
Since it doesn’t seem to be found in anything older than that (such as the Verona Sacramentary), it might have been codified by St. Gregory the Great, who is well known to have greatly reformed the liturgical texts during his Papacy.
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