take the seventh [part of the aggregate number of roots]; for example, in the case of the name Patroclus, the aggregate in the matter of roots is 34 monads. This divided into seven parts makes four, which [multiplied into each other] are 28. There are six remaining monads; [so that a person using this method] says, according to the rule of the number seven, that six monads are the root of the name Patroclus. If, however, it be 43, [six] taken seven times,[1] he says, are 42; for seven times six are 42, and one is the remainder. A monad, therefore, is the root of the number 43, according to the rule of the number seven. But one ought to observe if the assumed number, when divided, has no remainder; for example, if from any name, after having added together the roots, I find, to give an instance, 36 monads. But the number 36 divided into nine makes exactly 4 enneads; for nine times 4 are 36, and nothing is over. It is evident, then, that the actual root is 9. And again, dividing the number forty-five, we find nine[2] and nothing over (for nine times five are forty-five, and nothing remains); [wherefore] in the case of such they assert the root itself to be nine. And as regards the number seven, the case is similar: if, for example we divide 28 into 7, we have nothing over; for seven times four are 28, and nothing remains; [wherefore] they say that seven is the root. But when one computes names, and finds the same letter occurring twice, he calculates it once; for instance, the name Patroclus has the pa twice,[3] and the o twice: they therefore calculate the a once and the o once. According to this, then, the roots will be 8, 1, 3, 1, 7, 2, 3, 2, and added together they make 27 monads; and the root of the name will be, according to the rule of the number nine, nine itself, but according to the rule of the number seven, six.
In like manner, [the name] Sarpedon, when made the sub-
- ↑ That is, calculated according to the rule of a division by seven.
- ↑ We should expect rather five instead of 9, if the division be by nine.
- ↑ There is some confusion in the text. Miller conjectures that the reading should be: "As, for instance, the name Patroclus has the letter o occurring twice in it, they therefore take it into calculation once." Schneidewin suggests that the form of the name may be Papatroclus.
