12. Who will not wonder at so much activity of mind produced by so great labour? It seems that this Ptolemy[67] who busies himself with these matters is not without his use to me. This only grieves me that as one but lately born he was not serviceable to the sons of the giants,[68] who, being ignorant of these measurements, thought they were near high heaven and began to make a useless tower. Had he been at hand to explain these measurements to them they would not have ventured on the foolishness. But if any one thinks he can disbelieve this let him take the measurements and be convinced; for one cannot have for the unbelieving a more manifold proof than this. O puffing-up of vainly-toiling soul and unbelieving belief, when Ptolemy is considered wise in everything by those trained in the like wisdom![69]
13. Certain men in part intent on these things as judging [Sidenote: p. 76.] them mighty and worthy of argument have constructed measureless[70] and boundless heresies. Among whom is one Colarbasus,[71] who undertakes to set forth religion by measures and numbers. And there are others whom we shall likewise point out when we begin to speak of those who give heed to Pythagorean reckoning as if it were powerful and neglect the true philosophy for numbers and elements, thus making vain divinations. Collecting whose words, certain men have led astray the uneducated, pretending to know the future and when they chance to divine one thing aright are not ashamed of their many failures, but make a boast of their one success. Nor shall I pass over their unwise wisdom, but when I have set forth their attempts to establish a religion from these sources, I shall refute them as being disciples of a school inconsistent and full of trickery.
[Sidenote: p. 77.] 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 [Sidenote: 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.