[Liber sextus Decretalium]

of the decadics another, and the only number that is perfect is 28. Its total parts are the half and less. In the Digest, "Of the signification of names," word "which," the half would not be found as aliquot parts, as above, Distinction 10, 13 is an aliquot part, which taken twice makes 26 The text contains a calculation error, 14*2=28; the author is illustrating the concept of aliquots. 12, 11, and 8, 5, 7 are not aliquot parts of 28, which taken several times do not result in this whole precisely, but more or less. For 8 taken twice makes 16, taken thrice makes 39, and so by more and less. And so, of the individual ones, 7 is an aliquot part, which taken four times results in this whole. 6 and 5 are not aliquot parts. 3 and 2 are not aliquot parts, which taken seven times results in this whole. 3 is not an aliquot part, but 2 and 1 are well and truly aliquot parts, because 14 times 2 makes 28, and 28 times 1 makes 28. It follows that all the aliquot parts of 28 are 14, 7, 4, 2, and 1. But from these aliquots added together results precisely the whole, for 14, 7, 4, 2, and 1 make 28. Therefore, such a number, no superior to 28, is a perfect number. And so also concerning other perfects. I have computed concerning this so that the statement concerning the number six may be better understood. And it is called imperfect when it finds itself diminished, of which an example is usually placed in the octonary. For three are the aliquot parts of eight: 4, 2, and 1. 2 and 4 make seven, and thus it is an imperfect diminished number. See the quaternary, of which two are the aliquot parts: 2 and 1, for twice two is 4, and four times one is 4. But 2 and 1 make 3, therefore the quaternary number is an imperfect diminished number. See the nine, of which also only two are the aliquot parts: 3 and 1, for 3 and 1 make 4, and thus it is an imperfect diminished number. In the imperfect abundant, an example is usually placed in the duodenary, of which the aliquots are 6, 4, 3, 2, and 1. But these aliquots, 10, 5, 9, 2, and 1, which added together return more than the whole, for 16, and thus the number is an imperfect abundant. These things, broadly and clearly, can be opportune so that it may be well understood, but that is not of the matter of justice. Therefore, it answers tacitly how and from whom

in the conducting of affairs it might attribute form and in morals discipline. Nor without cause did we omit to preserve in this part the custom of our predecessors, who, when they promulgated some constitutions, newly commanded them to be made according to the series of the ancient ones. We did the same so that it would not be necessary for infinite books to be destroyed and others to be made anew, not without the greatest loss of labor and expense.

To your University, therefore, we command by apostolic writings, that you receive with a ready affection this book, digested with great maturity, which we send to you under our bull. You may use it from now on in judgments and

a Nor could it be done without the antipore. Wherefore he did not command these decretals to be placed in the old compilation of Gregory under their titles.
b Predecessors. Innocent III and Gregory IX wrote in their prefaces to the doctors and scholars, that the decretals which they were sending under their titles, they commanded to be inserted in them. Whence some were causing them to be written at the end of the titles of the compilation of Gregory, and these were preserving the mandate which he was doing, but to the volumes. And this one was fulfilling the mandate of those, as in Book 3, S.P. III.
c Promulgated. Laws are instituted when they are promulgated.

d Into infinite, all, that is, edited before the compilation of this book.
e And labors. Not that there should be greater labors in writing books, and it is against scholars who are always for a long time in study, they make books to be written, they ought to labor for study. For such labors and expenses are to be spared.
f And to the University, conclusion, ought to be, regarding the apostolic.
g Maturity, that it be done, and above, of rescripts, to the audience, 1.

in schools, none others besides those which are inserted or specially reserved in it, or constitutions promulgated by any of our predecessors after the editing of the said volume, to be received further or to be held as decretals.

Of the Holy Trinity and the Catholic Faith.

By a faithful and devout profession we confess that the sempiternal proceeds eternally from the Father and the Son, not as from two principles but as from one principle, not by two spirations but by one spiration. This has been professed and preached until now

h Bull. Otherwise it is not believed to be the mandate of the prince.
i From now on, showing, therefore, it looks to the future. What shall I say about those pending? Above, of elections, in the canon, when they begin to bind the showings of this Sixth Book, I shall speak at the end of the book regarding the date.
k In schools. Explain this as noted in the preface of Gregory.
l Reserved. These determine what is to be followed, reserved, below, 8, etc. And all showings edited concerning the business of heretical depravity not contrary to the constitutions of this book are to be used, as below, of heretics, the last chapter, at the end. The same could be said concerning the inquisitors.
m Volume. That is, the compilation of Gregory.

The text notes: And thus you see today for this end that the Decretals on the Faith, "Pastoral," do not have a place in the Decretals edited after the compilation of Gregory IX and before this book; that is, it could have a place in the Decretals of Boniface edited after the compilation of this Seventh Book and in all those to be edited by him or his successors.

n Of the Holy Trinity of this Sixth Book. I say in my judgment that they are not, because according to what occurred, something had to be added, changed, subtracted, or corrected; thus, added, changed, subtracted, or corrected, they have been with regard to the ancient compilation and it itself has the order kept... The remainder of the marginal note is highly technical and discusses the editorial process of updating legal compilations.

Faithful. The error of the Greeks who used to say the Holy Spirit proceeds from the Father alone, having been extirpated by the canons, of the Faith, Distinction 5, chapter "the last." Further, certain others have fallen into error, denying that the Holy Spirit eternally proceeded from the Father and the Son, with others saying that He proceeds from both, not as from one principle but as from two principles and two inspirations. Gregory X in the general council of Lyons, first he placed his offense, which he also says is that of the sacred Roman Catholic Church, by the observation and doctrine of the teachers of the Greeks and Latins: that the Holy Spirit eternally [proceeds] from the Father and the Son, not as from one principle which...