works, which he had made. That, you see, is what is written: AndGodfinishedon
244 The Literal Meaning of Genesis exceed it, like twelve and eighteen, and many more such. So more numbers are to be found of any of these sorts, than of those which are called perfect in that they are completed by their parts of this kind being added up together. l mean, after six the next one we find is twenty-eight, which likewise consists of the total of its parts. Ofthese, you see, it has five; a twenty-eighth, a fourteenth, a seventh, a quarter, a half; that is, one and two and four and seven and fourteen, which added up together complete twenty-eight.7 And the further the series ofnumbers proceeds, the longer, proportionately, are the intervals at which these numbers are found, which equal the sum of their parts in this manner, and which are called perfect. Those numbers, you see, whose parts do not add up to the whole are called imperfect, while those whose parts exceed the whole are called pluper fect.8
6. So it was in a perfect number of days, that is, six, that God perfected his works, which he had made. That, you see, is what is written: AndGodfinishedon the sixth day9 his works which he had made (Gn 2:2). But I become even more addicted to this number when l also consider the order of the works themselves. Forjust as this number rises step by step in its parts into a triangle, l0 for one, you
7. 1 here omit a tautological phrase: "for they become twenty-eight." 1t is not quite so tautological in the Latin, because where he has been mostly using the ordinal numbers and talking, literally, of "the sixth number, the seventh, eighth, etc." until here we have just had "these added up complete the twenty-eighth," 1 have nearly always rendered with the cardinal, "number six, seven, etc." So here, after saying that these parts complete the twenty-eighth number he adds, indeed somewhat superfluously, "for they become twenty-eight." The whole exercise of these last few sections illustrates well enough what a fearfully cumbersome business arithmetic must have been in the ancient Roman world, before they were introduced to Arabic numerals. See note 5 above, where it is all put in a nutshell. 8. Latin appears not to have invented this useful grammatical term, which 1 here apply to mathematics to translate Augustine'spi/uj quam perfecti. Curiosity led me to look for a list of perfect numbers; the British Encyclopedia was totally uninformative; but the Oxford English Dictionary quoted V. Mandey's Syst. Math. Arith. 5 (1709-1728) as follows: "There are found but few Perfect Numbers: to wit from 1 to 40,000,000 only these: 6; 28; 496; 8128; 130,816; 2,096,128; 33,950,336." 1 note an interesting feature: that the final digit of all these numbers is alternately 6 and 8. 9. Augustine follows the Greek Septuagint in reading "the sixth day." Other ancient versions have the same, and are followed by some modern commentators, for example Bruce Vawter, A Path through Genesis (Sheed & Ward, London, 1957), p.46; the Catholic Biblical Association of America, The Book of Genesis (Confraternity of Christian Doctrine, Patterson NJ. 1 948), p.4. Claus Westermann, however, Genesis l-11; a Commentary (English translation, SPCK, London 1 984) 78, and note 2a.80, keeps to the Massoretic Hebrew text, which has "the seventh day," and says in his note, a little dogmatically one may think: "[Ancient versions] read 'the 6th day ' ; even though this reading makes more sense, the Massoretic Text should not be altered."
1n this learned obscurantism he is followed by all current English versions, including the Jerusalem Bible and its French original—all except the gallant American Confraternity Version. 10. A triangle standing on its apex. The easiest way for ancients to work with numbers was to imagine them as dots arranged in geometrical patterns; we inherit this manner when we talk about the square of numbers. For them, at least for Augustine, keen on the mystical symbolism of numbers, the triangle of numbers was quite as important as the square or the cube. The