Those then who fancy that they can divine by means of ciphers[73] and numbers, elements[74] and names, make the foundation of their attempted system to be this. They pretend that every number has a root:—in the thousands as many units as there are thousands. For example, the root of 6000 is 6 units, of 7000, 7 units, of 8000, 8 units, and with the rest in the same way. In the hundreds as many hundreds as there are, so the same number of units is the root of them. For example, in 700 there are 7 hundreds: 7 units is their root. In 600 there are 6 hundreds: 6 units is their root. In the same way in the decads: of 80 the root is 8 units, of 40, 4 units, of 10, 1 unit. In the units, the units themselves are the root; for instance, the unit of the 9 is 9, of the 8, 8, of the 7, 7. Thus then must we do with the component parts [of names]. For each element is arranged according to some number. For example, the Nu consists of 50 units; but of 50 units the root is 5, and of the letter p. 78. Nu the root is 5. Let it be granted that from the name we may take certain[75] of its roots. For example, from the name Agamemnon there comes from the Alpha one unit, from the Gamma 3 units, from the other Alpha 1 unit, from the Mu 4 units, from the Epsilon 5 units, from the Mu 4 units, from the Nu 5 units, from the Omega 8 units, from the Nu 5 units, which together in one row will be 1, 3, 1, 4, 5, 4, 5, 8, 5. These added together make 36 units. Again they take the roots of these and they become 3 for the 30, but 6 itself for the 6. Then the 3 and the 6 added together make 9, but the root of 9 is 9. Therefore the name Agamemnon ends in the root 9.
Let the same be done with another name, viz., Hector. The name Hector contains five elements, Epsilon, Kappa, Tau, Omega and Rho.[76] The roots of these are 5, 2, 3, 8, 1; these added together make 19 units. Again, the root of the 10 is 1, of the 9, 9, which added together make 10. The root of the 10 is one unit. Therefore the name of Hector when counted up[77] has made as its root one unit.
p. 79.
But it is easier to work this way. Divide by 9 the roots ascertained from the elements, as we have just found 19 units from the name Hector, and read the remaining root. For example, if I divide the 19 by 9, there remains a unit, for twice 9 is 18, and the remainder is a unit. For if I subtract 18 from the 19, the remainder is a unit. Again, of the name Patroclus[78] these numbers 8, 1, 3, 1, 7, 2, 3, 7, 2 are the roots; added together they make 34 units. The remainder of these units is 7, viz., 3 from the 30 and 4 from the 4. Therefore 7 units are the root of the name Patroclus. Those then who reckon by the rule of 9 take the 9th part of the number collected from the roots and describe the remainder as the sum of the roots; but those who reckon by the rule of 7 take the 7th part. For example, in the name Patroclus the aggregate of the roots is 34 units. This divided into sevens makes 4 sevens, which are 28; the p. 80. remainder is 6 units. He says that by the rule of 7, 6 is the root of the name Patroclus.[79] If, however, it be 43, the 7th part, he says, is 42, for 7 times 6 is 42, and the remainder is 1. Therefore the root from the 43 by the rule of 7 becomes a unit. But we must take notice of what happens if the given number when divided has no remainder,[80] as for example, if from one name, after adding together the roots, I find, e. g., 36 units. But 36 divided by 9 is exactly 4 enneads (for 9 times 4 is 36 and nothing over). Thus, he says the 9 itself is plainly the root. If again we divide the number 45 we find 9 and no remainder (for 9 times 5 is 45 and nothing over), in such cases we say the root is 9. And in the same way with the rule of 7: if, e. g., we divide 28 by 7 we shall have nothing over (for 7 times 4 is 28 and nothing left), [and] they say the root is 7. Yet when he reckons up the names and finds the same letter twice, he counts it only once. For example, the name p. 81. Patroclus has the Alpha twice and the Omicron twice,[81] therefore he counts the Alpha only once and the Omicron only once. According to this, then, the roots will be 8, 3, 1, 7, 2, 3, 2, and added together make 27,[82] and the root of the name by the rule of 9 will be the 9 itself and by that of 7, 6.
In the same way Sarpedon, when counted, makes by the rule of 9, 2 units; but Patroclus makes 9: Patroclus conquers. For when one number is odd and the other even, the odd conquers if it be the greater. But again if there were an 8, which is even, and a 5, which is odd, the 8 conquers, for it is greater. But if there are two numbers, for example, both even or both odd, the lesser conquers. But how does Sarpedon by the rule of 9 make 2 units? The element Omega is omitted; for when there are in a name the elements Omega and Eta, they omit the Omega p. 82. and use one element. For they say that they both have the same power, but are not to be counted twice, as has been said above. Again, Ajax (Αἴας)[83] makes 4 units, and Hector by the rule of 9 only one. But the 4 is even while the unit is odd. And since we have said that in such cases the greater conquers, Ajax is the victor. Take again Alexandros[84] and Menelaus. Alexandros has an individual[85] name [Paris]. The name Paris makes by the rule of 9, 4; Menelaus by the same rule 9, and the 9 conquers the 4. For it has been said that when one is odd and the other even, the greater conquers, but when both are even or both odd, the lesser. Take again Amycus and Polydeuces. Amycus makes by the rule of 9, 2 units, and Polydeuces 7: Polydeuces conquers. Ajax and Odysseus contended together in the funereal games. Ajax makes by the rule of 9, 4 units, and Odysseus by the same rule 8.[86] Is there not (here) then some epithet of Odysseus and not his individual name, for he conquered? According to the numbers Ajax conquers, but tradition says Odysseus. Or take again Achilles and Hector. Achilles by the rule of 9 makes 4; p. 83. Hector 1; Achilles conquers. Take again Achilles and Asteropæus. Achilles makes 4, Asteropæus 3;[87] Achilles conquers. Take again Euphorbus and Menelaus. Menelaus has 9 units, Euphorbus 8; Menelaus conquers.
But some say that by the rule of 7, they use only the vowels, and others that they put the vowels, semi-vowels and consonants by themselves, and interpret each column separately. But yet others do not use the usual numbers, but different ones. Thus, for example, they will not have Pi to have as a root 8 units, but 5 and the element Xi as a root 4 units; and turning about every way, they discover nothing sane. When, however, certain competitors contend a second time,[88] they take away the first element, and when a third, the two first elements of each, and counting up the rest, they interpret them.
p. 84.2. I should think that the design of the arithmeticians has been plainly set forth, who deem that by numbers and names they can judge life. And I notice that, as they have time to spare and have been trained in counting, they have wished by means of the art handed down to them by children to proclaim themselves well-approved diviners, and, measuring the letters topsy-turvy, have strayed into nonsense. For when they fail to hit the mark, they say in propounding the difficulty that the name in question is not a family name but an epithet; as also they plead as a subterfuge in the case of Ajax and Odysseus. Who that founds his tenets on this wonderful philosophy and wishes to be called heresiarch, will not be glorified?
3. Of Divination by Metoposcopy.[89]
1. But since there is another and more profound art among the all-wise investigators of the Greeks, whose disciples the heretics profess themselves because of the use they make of their opinions for their own designs, as we shall show before long, we shall not keep silence about this. This is the divination or rather madness by metoposcopy. p. 85. There are those who refer to the stars the forms of the types and patterns[90] and natures of men, summing them up by their births under certain stars. This is what they say: Those born under Aries will be like this, to wit, long-headed, red-haired, with eyebrows joined together, narrow forehead, sea-green eyes, hanging cheeks, long nose, expanded nostrils, thin lips, pointed chin, and wide mouth. They will partake, he says, of such a disposition as this: forethinking, versatile, cowardly, provident, easy-going, gentle, inquisitive, concealing their desires, equipped for everything, ruling more by judgment than by strength, laughing at the present, skilled writers, faithful, lovers of strife, provoking to controversy, given to desire, lovers of boys, understanding, turning from their own homes, displeased p. 86. with everything, litigious, madmen in their cups, contemptuous, casting away somewhat every year, useful in friendship by their goodness. Most often they die in a foreign land.[91]
2. Those born under Taurus will be of this type: round-headed, coarse-haired, with broad forehead, oblong eyes and great eyebrows if dark; if fair, thin veins, sanguine complexion, large and heavy eyelids, great ears, round mouth, thick nose, widely-open nostrils, thick lips. They are strong in their upper limbs, but are sluggish from the hips downwards from their birth. The same are of a disposition pleasing, understanding, naturally clever, religious, just, rustical, agreeable, laborious[92] after twelve years old, easily irritated, leisurely. Their appetite is small, they are quickly satisfied, wishing for many things, provident, thrifty towards themselves, liberal towards others; as a class they are sorrowful, useless in friendship, useful because of their minds, enduring ills.